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Obs(3) is a 9 dimensional Frobenius Algrebra

fricas
)set output abbreviate on
V := OrderedVariableList [p,q,r]
 (1)
Type: TYPE
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M := FreeMonoid V
 (2)
Type: TYPE
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gens:List M := enumerate()$V  (3) Type: LIST(FMONOID(OVAR([p,q,r]))) fricas divisible := Record(lm: M,rm: M)  (4) Type: TYPE fricas leftDiv(k:Union(divisible,"failed")):M == (k::divisible).lm Function declaration leftDiv : Union(Record(lm: FMONOID(OVAR([p,q,r] )),rm: FMONOID(OVAR([p,q,r]))),"failed") -> FMONOID(OVAR([p,q,r]) ) has been added to workspace. Type: VOID fricas rightDiv(k:Union(divisible,"failed")):M == (k::divisible).rm Function declaration rightDiv : Union(Record(lm: FMONOID(OVAR([p,q,r ])),rm: FMONOID(OVAR([p,q,r]))),"failed") -> FMONOID(OVAR([p,q,r] )) has been added to workspace. Type: VOID fricas K := FRAC POLY INT  (5) Type: TYPE fricas MK := FreeModule(K,M)  (6) Type: TYPE fricas coeff(x:MK):K == leadingCoefficient(x) Function declaration coeff : FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r] ))) -> FRAC(POLY(INT)) has been added to workspace. Type: VOID fricas monomial(x:MK):M == leadingSupport(x) Function declaration monomial : FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q ,r]))) -> FMONOID(OVAR([p,q,r])) has been added to workspace. Type: VOID fricas m(x:M):K == subscript('m,[retract(x)::Symbol]) Function declaration m : FMONOID(OVAR([p,q,r])) -> FRAC(POLY(INT)) has been added to workspace. Type: VOID fricas γ(x:M,y:M):K == subscript('γ,[concat(string retract x, string retract y)::Symbol]) Function declaration γ : (FMONOID(OVAR([p,q,r])),FMONOID(OVAR([p,q,r ]))) -> FRAC(POLY(INT)) has been added to workspace. Type: VOID Basis fricas basis := concat(gens,concat [[j*i for i in gens | i~=j] for j in gens])  (7) Type: LIST(FMONOID(OVAR([p,q,r]))) Idempotent fricas rule1(ij:MK):MK == for k in gens repeat kk := divide(monomial(ij),k*k) if kk case divisible then ij:=(coeff(ij) * m(k)*γ(k,k)) * (leftDiv(kk) * k * rightDiv(kk)) return(ij) Function declaration rule1 : FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r] ))) -> FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r]))) has been added to workspace. Type: VOID Reduction fricas rule2(ij:MK):MK == for i in gens repeat for j in gens | j ~= i repeat for k in gens | k ~= j repeat ijk:=divide(monomial(ij),i*j*k) if ijk case divisible then if i=k then ij := (coeff(ij)*m(i)*m(j)*γ(i,j)*γ(j,i) ) * _ (leftDiv(ijk)*i*rightDiv(ijk)) else ij := (coeff(ij)*m(j)*γ(i,j)*γ(j,k) / γ(i,k) ) * _ (leftDiv(ijk)*i*k*rightDiv(ijk)) return(ij) Function declaration rule2 : FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r] ))) -> FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r]))) has been added to workspace. Type: VOID Modulo fixed point of applied rules fricas mod(ij:MK):MK == ijFix:MK := 1 while ijFix~=ij repeat ijFix := ij ij := rule1(ij) ij := rule2(ij) return(ij) Function declaration mod : FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r])) ) -> FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r]))) has been added to workspace. Type: VOID Matrix Multiplication is monoidal concatenation modulo the fixed point fricas --MT := [[mod(i*j) for j in basis] for i in basis] -- idempotent MT := [[monomial(eval(coeff(mod(i*j)),[γ(gens(1),gens(1))=1,γ(gens(2),gens(2))=1,γ(gens(3),gens(3))=1,γ(gens(2),gens(1))=γ(gens(1),gens(2)),γ(gens(3),gens(2))=γ(gens(2),gens(3)),γ(gens(3),gens(1))=γ(gens(1),gens(3))]),monomial(mod(i*j)))$MK for j in basis] for i in basis]
fricas
Compiling function monomial with type FM(FRAC(POLY(INT)),FMONOID(
OVAR([p,q,r]))) -> FMONOID(OVAR([p,q,r]))
fricas
Compiling function coeff with type FM(FRAC(POLY(INT)),FMONOID(OVAR([
p,q,r]))) -> FRAC(POLY(INT))
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Compiling function m with type FMONOID(OVAR([p,q,r])) -> FRAC(POLY(
INT))
fricas
Compiling function γ with type (FMONOID(OVAR([p,q,r])),FMONOID(OVAR(
[p,q,r]))) -> FRAC(POLY(INT))
fricas
Compiling function leftDiv with type Union(Record(lm: FMONOID(OVAR([
p,q,r])),rm: FMONOID(OVAR([p,q,r]))),"failed") -> FMONOID(OVAR([p
,q,r]))
fricas
Compiling function rightDiv with type Union(Record(lm: FMONOID(OVAR(
[p,q,r])),rm: FMONOID(OVAR([p,q,r]))),"failed") -> FMONOID(OVAR([
p,q,r]))
fricas
Compiling function rule1 with type FM(FRAC(POLY(INT)),FMONOID(OVAR([
p,q,r]))) -> FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r])))
fricas
Compiling function rule2 with type FM(FRAC(POLY(INT)),FMONOID(OVAR([
p,q,r]))) -> FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r])))
fricas
Compiling function mod with type FM(FRAC(POLY(INT)),FMONOID(OVAR([p,
q,r]))) -> FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r])))
 (8)
Type: LIST(LIST(FM(FRAC(POLY(INT)),FMONOID(OVAR([p,q,r])))))

Structure Constants

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R:=FRAC DMP(concat [[m(i) for i in gens],concat [[γ(j,i) for i in gens] for j in gens]], INT)
 (9)
Type: TYPE
fricas
mat3(y:M):List List R == map(z+->map(x+->coefficient(x,y)::FRAC POLY INT,z),MT)
Function declaration mat3 : FMONOID(OVAR([p,q,r])) -> LIST(LIST(FRAC
(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[
rq],γ[rr]],INT)))) has been added to workspace.
Type: VOID
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ss:=map(mat3, basis)
fricas
Compiling function mat3 with type FMONOID(OVAR([p,q,r])) -> LIST(
LIST(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr]
,γ[rp],γ[rq],γ[rr]],INT))))
 (10)
Type: LIST(LIST(LIST(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)))))

Algebra

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cats(m:M):Symbol==concat(map(x+->string(x.gen::Symbol),factors m))::Symbol
Function declaration cats : FMONOID(OVAR([p,q,r])) -> SYMBOL has
been added to workspace.
Type: VOID
fricas
A:=AlgebraGivenByStructuralConstants(R,#(basis)::PI,map(cats,basis),ss::Vector(Matrix R))
fricas
Compiling function cats with type FMONOID(OVAR([p,q,r])) -> SYMBOL
 (11)
Type: TYPE
fricas
alternative?()$A algebra satisfies 2*associator(a,b,b) = 0 = 2*associator(a,a,b) = 0  (12) Type: BOOLEAN fricas antiAssociative?()$A
algebra is not anti-associative
 (13)
Type: BOOLEAN
fricas
antiCommutative?()$A algebra is not anti-commutative  (14) Type: BOOLEAN fricas associative?()$A
algebra is associative
 (15)
Type: BOOLEAN
fricas
commutative?()$A algebra is not commutative  (16) Type: BOOLEAN fricas flexible?()$A
algebra is flexible
 (17)
Type: BOOLEAN
fricas
jacobiIdentity?()$A Jacobi identity does not hold  (18) Type: BOOLEAN fricas jordanAdmissible?()$A
algebra is not Jordan admissible
 (19)
Type: BOOLEAN
fricas
jordanAlgebra?()$A algebra is not commutative this is not a Jordan algebra  (20) Type: BOOLEAN fricas leftAlternative?()$A
algebra is left alternative
 (21)
Type: BOOLEAN
fricas
rightAlternative?()$A algebra is right alternative  (22) Type: BOOLEAN fricas lieAdmissible?()$A
algebra is Lie admissible
 (23)
Type: BOOLEAN
fricas
lieAlgebra?()$A algebra is not anti-commutative this is not a Lie algebra  (24) Type: BOOLEAN fricas powerAssociative?()$A
Internal Error
The function powerAssociative? with signature hashcode is missing
from domain AlgebraGivenByStructuralConstants
(Fraction (DistributedMultivariatePolynomial ((*01000m p) (*01000m q) (*01000m r) (*01000γ pp) (*01000γ pq) (*01000γ pr) (*01000γ qp) (*01000γ qq) (*01000γ qr) (*01000γ rp) (*01000γ rq) (*01000γ rr)) (Integer)))
9(p q r pq pr qp qr rp rq)UNPRINTABLE

Check Multiplication

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AB := entries basis()$A  (25) Type: LIST(ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])) fricas p:=AB(1); q:=AB(2); r:=AB(3); Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas A2MK(z:A):MK==reduce(+,map((x:R,y:M):MK+->(x::K)*y,coordinates(z),basis)) Function declaration A2MK : ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[ pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq, pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[ pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq] ^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr] ,0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0 ,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[ 0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m [q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0 ,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^ 2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]] ,[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0, m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0 ,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr] ^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0, 0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2 ,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0 ,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2* m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]] ,[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq ]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p] *m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0, 0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]] ,[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0, 0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]* γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ [pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0, 0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0 ,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0, 0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m [q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0, 0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0, 0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p] *γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0, 0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^ 2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[ r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0, 0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,( m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0, 0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[ p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr], 0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0, 0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr ],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0, 0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p ]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]* m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) -> FM(FRAC(POLY(INT)), FMONOID(OVAR([p,q,r]))) has been added to workspace. Type: VOID fricas test(MT=map(x+->map(A2MK,x),[[i*j for j in AB] for i in AB])) fricas Compiling function A2MK with type ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[ pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q ,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[ r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]* γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]* γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[ qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0 ,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0] ,[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0, 0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ [pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ [qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0 ,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0] ],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]* γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[ pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0, 0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[ q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ [pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q] *γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0 ,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0, 0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]* m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m [r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0, 0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m [p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq] ,0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0 ,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0, (m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,( m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[ p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0, 0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0 ,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0 ,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ [pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[ [0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr]) /γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0 ,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0, m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) -> FM(FRAC(POLY( INT)),FMONOID(OVAR([p,q,r])))  (26) Type: BOOLEAN fricas p*p  (27) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas p*q*p  (28) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas p*q*r  (29) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) Trace fricas [rightTrace(i)$A for i in AB]
 (30)
Type: LIST(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)))
fricas
[leftTrace(i)$A for i in AB]  (31) Type: LIST(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas trace(i)==rightTrace(i) / #gens Type: VOID fricas trace(p) fricas Compiling function trace with type ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[ pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q ,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[ r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]* γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]* γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[ qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0 ,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0] ,[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0, 0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ [pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ [qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0 ,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0] ],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]* γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[ pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0, 0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[ q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ [pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q] *γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0 ,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0, 0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]* m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m [r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0, 0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m [p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq] ,0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0 ,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0, (m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,( m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[ p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0, 0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0 ,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0 ,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ [pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[ [0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr]) /γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0 ,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0, m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) -> FRAC(DMP([m[p] ,m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]] ,INT))  (32) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas [trace(i) for i in AB]  (33) Type: LIST(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) Lie Bracket fricas pq:=p*q-q*p  (34) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(pq)  (35) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) Lie derivations fricas D(p:A):(A->A) == (q:A):A +-> (p*q - q*p) Function declaration D : ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq], γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr, qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^ 2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0 ,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0], [m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p ]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0, 0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q], 0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0 ],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0, m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0, m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q] *m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0 ,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0 ,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[ 0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m [p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m [q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r] *γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0, 0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2, 0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r ]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0] ,[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0 ,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[ 0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq ]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr] ^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0, 0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0], [1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0] ,[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]* γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0, m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0, 0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[ pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0 ,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ [pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]* γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0 ,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q ]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0 ,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]* m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0 ,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0 ,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2 *γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q ]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) -> (ALGSC(FRAC(DMP([m[p], m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]], INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq] ^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0] ,[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]* γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[ pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0, 0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^ 2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0 ,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ [pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[ pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0 ,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r] ,0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0] ,[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ [pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[ pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]* γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[ q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]* γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[ pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0, 0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr] )/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0, 0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0, 0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0 ]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq ],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0], [m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[ pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr]) /γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0, 0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]* γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0 ],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0, 0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0, 0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q ]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[ r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m [p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq ]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[ pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) -> ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq], γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p ],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0 ,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2* γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2, 0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0] ,[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2 ,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0, 0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2 ,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0 ,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0 ,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0, 0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2, 0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2, 0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0, m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0, 1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0 ,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ [qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,( m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0 ],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q] *γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0], [0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq] *γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr ]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0 ,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,( m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0 ],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r] *γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0 ,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0 ,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m [q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0 ,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0, m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]* γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr] ,0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0 ,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]* m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ [qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0, 0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0 ,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr], 0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[ q]*m[r]*γ[qr]^2]]])) has been added to workspace. Type: VOID fricas (D p) p fricas Compiling function D with type ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp], γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r, pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]* γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[ pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[ qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr ],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0 ],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[ 0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0, 0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[ pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[ qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0, 0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]] ,[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ [pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0, 0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[ pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0, 0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[ q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ [pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q] *γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0 ,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0, 0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]* m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m [r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0, 0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0 ,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m [p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq] ,0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0 ,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0, (m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,( m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[ p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0, 0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0 ,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0 ,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ [pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[ [0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr]) /γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0 ,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0, m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) -> (ALGSC(FRAC( DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[ rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p] *m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0 ,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p] *m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m [q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0, 0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0 ]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]* m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0, 0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]* m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r ]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0 ,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0] ,[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0, 0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0 ,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[ r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r] *γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0 ,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0 ,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[ r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ [qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0 ,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/ γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[ pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr] ,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0 ,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0, 0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[ qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0, 0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[ (m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr ]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0, 0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0 ,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p ]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[ pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0] ,[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0 ,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[ 0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0 ,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2 ,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr], 0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0], [0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0] ,[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,( m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p] *m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr ]^2]]]) -> ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp] ,γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq] ,[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0, 0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]* m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ [pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[ pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0 ,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q] *γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0, 0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q] *γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ [qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[ qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0 ,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r] *γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0, 0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r] *γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ [qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0 ,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0, 0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[ q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2, 0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0, 0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p ],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0, 0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q ]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]* m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0, 0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0 ,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0, 0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0, m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]* γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0, 0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/ γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0, 0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr]) /γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m [q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[ 0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[ qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0 ,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq] ^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q] ^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0 ],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r ]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0 ,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[ pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2 ,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]))  (36) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas test( (D p)(q*r) = (D p)(q)*r + q*(D p)(r) )  (37) Type: BOOLEAN fricas -- Define ((D p) (D q)) r = (D p) ((D q) r) - (D q) ((D p) r)  (38) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas -- (D p) q  (39) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas (D p) ((D p) q)  (40) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas (D p) ((D p) ((D p) q))  (41) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas test( (D p) ((D p) ((D p) q)) = trace(p)^2*(D p) q )  (42) Type: BOOLEAN fricas test( (D p) ((D p) ((D p) ((D q) r))) = trace(p)^2*(D p) ((D q) r) )  (43) Type: BOOLEAN fricas -- (D p) ((D q) ((D p) r))  (44) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas (D q) ((D p) ((D q) r))  (45) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas (D p) ((D p) ((D q) r))  (46) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas (D p) ((D q) ((D q) r))  (47) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) Scalar Product fricas matrix [[trace(i*j) for j in [AB.1,AB.2,AB.3]] for i in [AB.1,AB.2,AB.3]]  (48) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.1,AB.2,AB.3]] for i in [AB.4,AB.5,AB.6]]  (49) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.1,AB.2,AB.3]] for i in [AB.7,AB.8,AB.9]]  (50) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.4,AB.5,AB.6]] for i in [AB.1,AB.2,AB.3]]  (51) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.4,AB.5,AB.6]] for i in [AB.4,AB.5,AB.6]]  (52) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.4,AB.5,AB.6]] for i in [AB.7,AB.8,AB.9]]  (53) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.7,AB.8,AB.9]] for i in [AB.1,AB.2,AB.3]]  (54) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.7,AB.8,AB.9]] for i in [AB.4,AB.5,AB.6]]  (55) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) fricas matrix [[trace(i*j) for j in [AB.7,AB.8,AB.9]] for i in [AB.7,AB.8,AB.9]]  (56) Type: MATRIX(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))) Center fricas C:=basisOfCenter()$AlgebraPackage(R,A); # C
 (57)
Type: PI
fricas
c:=C(1)
 (58)
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])
fricas
[c*i-i*c for i in AB]
 (59)
Type: LIST(ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]))
fricas
test(c*c=c)
 (60)
Type: BOOLEAN

Unit

fricas
rightTrace(c)
 (61)
Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))
fricas
n := #basis / rightTrace(c) * c
 (62)
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])
fricas
trace(n)
 (63)
Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))
fricas
test(n*n=n)
 (64)
Type: BOOLEAN
fricas
[n*i-i for i in AB]
 (65)
Type: LIST(ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]))
fricas
[i*n-i for i in AB]
 (66)
Type: LIST(ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]))

fricas
test(n=unit()$A)  (67) Type: BOOLEAN fricas f:=gcd map(x+->denom x,coordinates(n))  (68) Type: DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT) fricas --ff:= matrix [[γ(i,j)::R for j in gens] for i in gens] ff:= matrix [[eval(γ(i,j)::R,[γ(gens(1),gens(1))=1,γ(gens(2),gens(2))=1,γ(gens(3),gens(3))=1,γ(gens(2),gens(1))=γ(gens(1),gens(2)),γ(gens(3),gens(2))=γ(gens(2),gens(3)),γ(gens(3),gens(1))=γ(gens(1),gens(3))]) for j in gens] for i in gens]  (69) Type: MATRIX(FRAC(POLY(INT))) fricas --ff:= matrix [[eval(γ(i,j)::R,[γ(gens(1),gens(1))=0,γ(gens(2),gens(2))=0,γ(gens(3),gens(3))=0,γ(gens(2),gens(1))=γ(gens(1),gens(2)),γ(gens(3),gens(2))=γ(gens(2),gens(3)),γ(gens(3),gens(1))=γ(gens(1),gens(3))]) for j in gens] for i in gens] -determinant(ff)  (70) Type: FRAC(POLY(INT)) fricas test(f = %)  (71) Type: BOOLEAN fricas (f*n)::OutputForm / f::OutputForm  (72) Type: OUTFORM Orthogonal Observers fricas p' := n - (1/trace(p))*p  (73) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(p')  (74) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas p*p'  (75) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas test(p'*p=p*p')  (76) Type: BOOLEAN fricas p'*p' - p'  (77) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas f*p'  (78) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas q' := n - (1/trace(q))*q  (79) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(q')  (80) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas q*q'  (81) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas test(q'*q=q*q')  (82) Type: BOOLEAN fricas q'*q' - q'  (83) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas f*q'  (84) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) Orthogonal Observers are not Derivations fricas p'*(q*r) = (p'*q)*r + q*(p'*r)  (85) Type: EQ(ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])) fricas test %  (86) Type: BOOLEAN Lie Bracket fricas pq:=p*q-q*p  (87) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(pq)  (88) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas pqr:=pq*r  (89) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(pqr)  (90) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas pqr*pqr  (91) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas q' := n - (1/trace(q))*q  (92) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas p'q' := p'*q' - q'*p'  (93) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(p'q')  (94) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas p'q'r:=p'q'*r  (95) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(p'q'r)  (96) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas p'q'r * p'q'r  (97) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas p'q'r * pqr  (98) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas pq' := p*q' - q'*p  (99) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(pq')  (100) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas pq'r:=pq'*r  (101) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas pq'r * pq'r  (102) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas p'q := p'*q - q*p'  (103) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas trace(p'q)  (104) Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)) fricas p'qr:=p'q*r  (105) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) fricas p'qr*p'qr  (106) Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]]) Momentum fricas P:=reduce(+,concat [[(1/ ( i<j=>γ(basis(i),basis(j)); i>j=>γ(basis(j),basis(i));1) )::R*AB(i)*AB(j) for j in 1..size()$V] for i in 1..size()\$V])
 (107)
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])
fricas
M2:=trace(P)
 (108)
Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))
fricas
P*P-trace(P)*P
 (109)
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])

fricas
P' := n - (1/trace(P))*P;
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])
fricas
trace(P')
 (110)
Type: FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))
fricas
P'*P' - P'
 (111)
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])
fricas
P*P'
 (112)
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])
fricas
fP':=gcd map(x+->denom x,coordinates(P'))
 (113)
Type: DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)
fricas
factor(fP')
 (114)
Type: FR(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT))
fricas
test(fP'=f*M2)
 (115)
Type: BOOLEAN
fricas
fP' * P'
 (116)
Type: ALGSC(FRAC(DMP([m[p],m[q],m[r],γ[pp],γ[pq],γ[pr],γ[qp],γ[qq],γ[qr],γ[rp],γ[rq],γ[rr]],INT)),9,[p,q,r,pq,pr,qp,qr,rp,rq],[[[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p]*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]^2*γ[pq]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0],[m[p]*m[r]*γ[pr]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[p]*m[r]^2*γ[pr]^2,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[p]*m[q]*γ[pq]^2,0,m[p]^2*m[q]*γ[pq]^2,0,0,0,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr]],[0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0,0,0,m[q]*m[r]^2*γ[qr]^2],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,m[p]*m[r]*γ[pr]^2,0,m[p]^2*m[r]*γ[pr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,0],[0,0,m[q]*m[r]*γ[qr]^2,0,m[p]*m[q]*m[r]*γ[pq]*γ[pr]*γ[qr],0,m[q]^2*m[r]*γ[qr]^2,0,0]],[[0,1,0,m[p],0,0,0,0,(m[r]*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2],[0,(m[r]*γ[pr]*γ[qr])/γ[pq],0,m[p]*m[r]*γ[pr]^2,0,0,0,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,1,0,m[p],0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[p]*m[q]*γ[pq]^2,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,m[q],0,(m[r]*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[r]*γ[pr]*γ[qr])/γ[pq],0,0,0,0,m[q]*m[r]*γ[qr]^2,0,(m[r]^2*γ[pr]*γ[qr])/γ[pq],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,m[q],0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,m[p]*m[q]*γ[pq]^2,0,0],[0,0,m[r],0,m[p]*m[r]*γ[pr]^2,0,m[q]*m[r]*γ[qr]^2,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,0,0,0,0,(m[q]*γ[pq]*γ[qr])/γ[pr],0,m[r],0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[m[p],0,0,0,0,m[p]*m[q]*γ[pq]^2,0,m[p]*m[r]*γ[pr]^2,0],[(m[q]*γ[pq]*γ[qr])/γ[pr],0,0,0,0,(m[q]^2*γ[pq]*γ[qr])/γ[pr],0,m[q]*m[r]*γ[qr]^2,0]],[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[r]],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,(m[p]*γ[pq]*γ[pr])/γ[qr],0,(m[p]^2*γ[pq]*γ[pr])/γ[qr],0,0,0,0,m[p]*m[r]*γ[pr]^2],[0,m[q],0,m[p]*m[q]*γ[pq]^2,0,0,0,0,m[q]*m[r]*γ[qr]^2]]])

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