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axiom
-- not allowed: )spool pfaffian.output
axiom
)sys
Your argument list is not valid.
axiom
)set message test on
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)set message auto off
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)clear all
All user variables and function definitions have been cleared.
--S 1 of 9 B0 n == matrix [[(if i=j+1 and odd? j then -1 else _ if i=j-1 and odd? i then 1 else 0) _ for j in 1..n] for i in 1..n]
Type: Void
axiom
--R
--R
Type: Void
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--E 1
--S 2 of 9 PfChar(lambda, A) == n := nrows A (n = 2) => lambda^2 + A.(1,2) M := subMatrix(A, 3, n, 3, n) r := subMatrix(A, 1, 1, 3, n) s := subMatrix(A, 3, n, 2, 2)
p := PfChar(lambda, M) d := degree(p, lambda)
B := B0(n-2) C := r*B g := [(C*s).(1,1), A.(1,2), 1] if d >= 4 then B := M*B for i in 4..d by 2 repeat C := C*B g := cons((C*s).(1,1), g) g := reverse! g
res := 0 for i in 0..d by 2 for j in 2..d+2 repeat c := coefficient(p, lambda, i) for e in first(g, j) for k in 2..-d by -2 repeat res := res + c * e * lambda^(k+i)
res
Type: Void
axiom
--R
--R
Type: Void
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--E 2
--S 3 of 9 pfaffian A == eval(PfChar(l, A), l=0)
Type: Void
axiom
--R
--R
Type: Void
axiom
--E 3
--S 4 of 9 m:Matrix(Integer):=[[0,15],[-15,0]]

\label{eq1}\left[ 
\begin{array}{cc}
0 &{15}
\
-{15}& 0 
(1)
Type: Matrix(Integer)
axiom
--R
--R        + 0    15+
--R   (4)  |        |
--R        +- 15  0 +
--R
Type: Matrix Integer
axiom
--E 4
--S 5 of 9 pfaffian m
axiom
Compiling function B0 with type Integer -> Matrix(Integer) 
   The type of the local variable res has changed in the computation.
   We will attempt to interpret the code.
   Cannot compile map: PfChar 
   We will attempt to interpret the code.

\label{eq2}15(2)
Type: Polynomial(Integer)
axiom
--R
--R   (5)  15
--R
Type: Polynomial Integer
axiom
--E 5
--S 6 of 9 (a,b,c,d,e,f):=(3,5,7,11,13,17)

\label{eq3}17(3)
Type: PositiveInteger
axiom
--R
--R   (6)  17
--R
Type: PositiveInteger
axiom
--E
--S 7 of 9 m1:Matrix(Integer):=[[0,a,b,c],[-a,0,d,e],[-b,-d,0,f],[-c,-e,-f,0]]

\label{eq4}\left[ 
\begin{array}{cccc}
0 & 3 & 5 & 7 
\
- 3 & 0 &{11}&{13}
\
- 5 & -{11}& 0 &{17}
\
- 7 & -{13}& -{17}& 0 
(4)
Type: Matrix(Integer)
axiom
--R
--R        + 0    3     5    7 +
--R        |                   |
--R        |- 3   0     11   13|
--R   (7)  |                   |
--R        |- 5  - 11   0    17|
--R        |                   |
--R        +- 7  - 13  - 17  0 +
--R
Type: Matrix Integer
axiom
--E 7
--S 8 of 9 m1ans:=a*f-b*e+d*c

\label{eq5}63(5)
Type: PositiveInteger
axiom
--R
--R
--R   (8)  63
--R
Type: PositiveInteger
axiom
--E 8
--S 9 of 9 pfaffian m1
axiom
Compiling function B0 with type PositiveInteger -> Matrix(Integer)

\label{eq6}63(6)
Type: Polynomial(Integer)




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