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- Returns
- a domain of categories ExpressionSpade?, AlgebraicallyClosedField?, RetractableTo?(Integer), RetractableTo?(Fraction(Integer)), LinearlyExplicitRingOver?(Fraction(Integer)), CharacteristicZero?,
ConvertibleTo?(Complex(Float)), DifferentialRing? and with explicit exports
- Description
- Algebraic closure of the rational numbers, with mathematical =
axiom )show AlgebraicNumber
AlgebraicNumber is a domain constructor
Abbreviation for AlgebraicNumber is AN
This constructor is exposed in this frame.
Issue )edit /usr/local/lib/axiom/target/x86_64-unknown-linux/../../src/algebra/AN.spad to
see algebra source code for AN
------------------------------- Operations --------------------------------
?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> %
?*? : (%,%) -> % ?*? : (%,Fraction Integer) -> %
?*? : (Fraction Integer,%) -> % ?**? : (%,PositiveInteger) ->
%
?**? : (%,Integer) -> % ?**? : (%,Fraction Integer)
-> %
?+? : (%,%) -> % -? : % -> %
?-? : (%,%) -> % ?/? : (%,%) -> %
?<? : (%,%) -> Boolean ?<=? : (%,%) -> Boolean
?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean
?>=? : (%,%) -> Boolean D : % -> %
D : (%,NonNegativeInteger) -> % 1 : () -> %
0 : () -> % ?^? : (%,PositiveInteger) -> %
?^? : (%,Integer) -> % associates? : (%,%) -> Boolean
belong? : BasicOperator -> Boolean box : List % -> %
box : % -> % coerce : Integer -> %
coerce : % -> % coerce : Fraction Integer -> %
coerce : Kernel % -> % coerce : % -> OutputForm
convert : % -> Complex Float convert : % -> DoubleFloat
convert : % -> Float differentiate : % -> %
distribute : (%,%) -> % distribute : % -> %
elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> %
eval : (%,List %,List %) -> % eval : (%,%,%) -> %
eval : (%,Equation %) -> % eval : (%,List Equation %) -> %
eval : (%,Kernel %,%) -> % factor : % -> Factored %
freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean
gcd : (%,%) -> % gcd : List % -> %
hash : % -> SingleInteger height : % -> NonNegativeInteger
inv : % -> % is? : (%,Symbol) -> Boolean
kernel : (BasicOperator,%) -> % kernels : % -> List Kernel %
latex : % -> String lcm : (%,%) -> %
lcm : List % -> % map : ((% -> %),Kernel %) -> %
max : (%,%) -> % min : (%,%) -> %
norm : (%,List Kernel %) -> % norm : (%,Kernel %) -> %
nthRoot : (%,Integer) -> % one? : % -> Boolean
paren : List % -> % paren : % -> %
prime? : % -> Boolean ?quo? : (%,%) -> %
recip : % -> Union(%,"failed") reduce : % -> %
?rem? : (%,%) -> % retract : % -> Fraction Integer
retract : % -> Integer retract : % -> Kernel %
rootOf : Polynomial % -> % rootsOf : Polynomial % -> List %
sample : () -> % sizeLess? : (%,%) -> Boolean
sqrt : % -> % squareFree : % -> Factored %
squareFreePart : % -> % subst : (%,Equation %) -> %
tower : % -> List Kernel % unit? : % -> Boolean
unitCanonical : % -> % zero? : % -> Boolean
zeroOf : Polynomial % -> % zerosOf : Polynomial % -> List %
?~=? : (%,%) -> Boolean
?*? : (NonNegativeInteger,%) -> %
?**? : (%,NonNegativeInteger) -> %
?^? : (%,NonNegativeInteger) -> %
characteristic : () -> NonNegativeInteger
coerce : SparseMultivariatePolynomial(Integer,Kernel %) -> %
definingPolynomial : % -> % if $ has RING
denom : % -> SparseMultivariatePolynomial(Integer,Kernel %)
differentiate : (%,NonNegativeInteger) -> %
divide : (%,%) -> Record(quotient: %,remainder: %)
elt : (BasicOperator,List %) -> %
elt : (BasicOperator,%,%,%,%) -> %
elt : (BasicOperator,%,%,%) -> %
euclideanSize : % -> NonNegativeInteger
eval : (%,BasicOperator,(% -> %)) -> %
eval : (%,BasicOperator,(List % -> %)) -> %
eval : (%,List BasicOperator,List (List % -> %)) -> %
eval : (%,List BasicOperator,List (% -> %)) -> %
eval : (%,Symbol,(% -> %)) -> %
eval : (%,Symbol,(List % -> %)) -> %
eval : (%,List Symbol,List (List % -> %)) -> %
eval : (%,List Symbol,List (% -> %)) -> %
eval : (%,List Kernel %,List %) -> %
even? : % -> Boolean if $ has RETRACT INT
expressIdealMember : (List %,%) -> Union(List %,"failed")
exquo : (%,%) -> Union(%,"failed")
extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2:
%),"failed")
gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) ->
SparseUnivariatePolynomial %
is? : (%,BasicOperator) -> Boolean
kernel : (BasicOperator,List %) -> %
mainKernel : % -> Union(Kernel %,"failed")
minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING
multiEuclidean : (List %,%) -> Union(List %,"failed")
norm : (SparseUnivariatePolynomial %,List Kernel %) -> SparseUnivariatePolynomial %
norm : (SparseUnivariatePolynomial %,Kernel %) -> SparseUnivariatePolynomial %
numer : % -> SparseMultivariatePolynomial(Integer,Kernel %)
odd? : % -> Boolean if $ has RETRACT INT
operator : BasicOperator -> BasicOperator
operators : % -> List BasicOperator
principalIdeal : List % -> Record(coef: List %,generator: %)
reducedSystem : Matrix % -> Matrix Fraction Integer
reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction Integer,vec:
Vector Fraction Integer)
reducedSystem : Matrix % -> Matrix Integer
reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector
Integer)
retractIfCan : % -> Union(Fraction Integer,"failed")
retractIfCan : % -> Union(Integer,"failed")
retractIfCan : % -> Union(Kernel %,"failed")
rootOf : SparseUnivariatePolynomial % -> %
rootOf : (SparseUnivariatePolynomial %,Symbol) -> %
rootsOf : SparseUnivariatePolynomial % -> List %
rootsOf : (SparseUnivariatePolynomial %,Symbol) -> List %
subst : (%,List Kernel %,List %) -> %
subst : (%,List Equation %) -> %
subtractIfCan : (%,%) -> Union(%,"failed")
unitNormal : % -> Record(unit: %,canonical: %,associate: %)
zeroOf : SparseUnivariatePolynomial % -> %
zeroOf : (SparseUnivariatePolynomial %,Symbol) -> %
zerosOf : SparseUnivariatePolynomial % -> List %
zerosOf : (SparseUnivariatePolynomial %,Symbol) -> List %
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