FunctionSpace(R)

fspace.spad line 1158 [edit on github]

undocumented

* : (%, %) -> % if R has SemiGroup
from Magma
* : (%, R) -> % if R has Ring
from RightModule(R)
* : (%, Fraction(Integer)) -> % if R has IntegralDomain
from RightModule(Fraction(Integer))
* : (%, Integer) -> % if R has LinearlyExplicitOver(Integer) and R has Ring
from RightModule(Integer)
* : (R, %) -> % if R has CommutativeRing
from LeftModule(R)
* : (Fraction(Integer), %) -> % if R has IntegralDomain
from LeftModule(Fraction(Integer))
* : (Integer, %) -> % if R has AbelianGroup
from AbelianGroup
* : (NonNegativeInteger, %) -> % if R has AbelianSemiGroup
from AbelianMonoid
* : (PositiveInteger, %) -> % if R has AbelianSemiGroup
from AbelianSemiGroup
+ : (%, %) -> % if R has AbelianSemiGroup
from AbelianSemiGroup
- : % -> % if R has AbelianGroup
from AbelianGroup
- : (%, %) -> % if R has AbelianGroup
from AbelianGroup
/ : (%, %) -> % if R has Group or R has IntegralDomain
from Group
/ : (SparseMultivariatePolynomial(R, Kernel(%)), SparseMultivariatePolynomial(R, Kernel(%))) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
0 : () -> % if R has AbelianSemiGroup
from AbelianMonoid
1 : () -> % if R has SemiGroup
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
D : (%, List(Symbol)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
D : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
D : (%, Symbol) -> % if R has Ring
from PartialDifferentialRing(Symbol)
D : (%, Symbol, NonNegativeInteger) -> % if R has Ring
from PartialDifferentialRing(Symbol)
^ : (%, Integer) -> % if R has Group or R has IntegralDomain
from Group
^ : (%, NonNegativeInteger) -> % if R has SemiGroup
from MagmaWithUnit
^ : (%, PositiveInteger) -> % if R has SemiGroup
from Magma
algtower : % -> List(Kernel(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
algtower : List(%) -> List(Kernel(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
annihilate? : (%, %) -> Boolean if R has Ring
from Rng
antiCommutator : (%, %) -> % if R has Ring
from NonAssociativeSemiRng
applyQuote : (Symbol, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, %, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, %, %, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, %, %, %, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, List(%)) -> %
from FunctionSpace2(R, Kernel(%))
associates? : (%, %) -> Boolean if R has IntegralDomain
from EntireRing
associator : (%, %, %) -> % if R has Ring
from NonAssociativeRng
belong? : BasicOperator -> Boolean
from ExpressionSpace2(Kernel(%))
box : % -> %
from ExpressionSpace2(Kernel(%))
characteristic : () -> NonNegativeInteger if R has Ring
from NonAssociativeRing
charthRoot : % -> Union(%, "failed") if R has CharacteristicNonZero
from CharacteristicNonZero
coerce : % -> % if R has IntegralDomain
from Algebra(%)
coerce : R -> %
from CoercibleFrom(R)
coerce : Fraction(R) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
coerce : Fraction(Integer) -> % if R has RetractableTo(Fraction(Integer)) or R has IntegralDomain
from CoercibleFrom(Fraction(Integer))
coerce : Fraction(Polynomial(R)) -> % if R has IntegralDomain
from CoercibleFrom(Fraction(Polynomial(R)))
coerce : Fraction(Polynomial(Fraction(R))) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
coerce : Integer -> % if R has RetractableTo(Integer) or R has Ring
from CoercibleFrom(Integer)
coerce : Kernel(%) -> %
from CoercibleFrom(Kernel(%))
coerce : Polynomial(R) -> % if R has Ring
from CoercibleFrom(Polynomial(R))
coerce : Polynomial(Fraction(R)) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
coerce : SparseMultivariatePolynomial(R, Kernel(%)) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
coerce : Symbol -> %
from CoercibleFrom(Symbol)
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
commutator : (%, %) -> % if R has Group or R has Ring
from NonAssociativeRng
conjugate : (%, %) -> % if R has Group
from Group
convert : Factored(%) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
convert : % -> InputForm if R has ConvertibleTo(InputForm)
from ConvertibleTo(InputForm)
convert : % -> Pattern(Float) if R has ConvertibleTo(Pattern(Float))
from ConvertibleTo(Pattern(Float))
convert : % -> Pattern(Integer) if R has ConvertibleTo(Pattern(Integer))
from ConvertibleTo(Pattern(Integer))
definingPolynomial : % -> % if % has Ring
from ExpressionSpace2(Kernel(%))
denom : % -> SparseMultivariatePolynomial(R, Kernel(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
denominator : % -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
differentiate : (%, List(Symbol)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
differentiate : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
differentiate : (%, Symbol) -> % if R has Ring
from PartialDifferentialRing(Symbol)
differentiate : (%, Symbol, NonNegativeInteger) -> % if R has Ring
from PartialDifferentialRing(Symbol)
distribute : % -> %
from ExpressionSpace2(Kernel(%))
distribute : (%, %) -> %
from ExpressionSpace2(Kernel(%))
divide : (%, %) -> Record(quotient : %, remainder : %) if R has IntegralDomain
from EuclideanDomain
elt : (BasicOperator, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, List(%)) -> %
from ExpressionSpace2(Kernel(%))
euclideanSize : % -> NonNegativeInteger if R has IntegralDomain
from EuclideanDomain
eval : (%, %, %) -> %
from InnerEvalable(%, %)
eval : (%, BasicOperator, %, Symbol) -> % if R has ConvertibleTo(InputForm)
from FunctionSpace2(R, Kernel(%))
eval : (%, BasicOperator, Mapping(%, %)) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, BasicOperator, Mapping(%, List(%))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, Equation(%)) -> %
from Evalable(%)
eval : (%, Kernel(%), %) -> %
from InnerEvalable(Kernel(%), %)
eval : (%, List(%), List(%)) -> %
from InnerEvalable(%, %)
eval : (%, List(BasicOperator), List(%), Symbol) -> % if R has ConvertibleTo(InputForm)
from FunctionSpace2(R, Kernel(%))
eval : (%, List(BasicOperator), List(Mapping(%, %))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(BasicOperator), List(Mapping(%, List(%)))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(Equation(%))) -> %
from Evalable(%)
eval : (%, List(Kernel(%)), List(%)) -> %
from InnerEvalable(Kernel(%), %)
eval : (%, List(Symbol), List(Mapping(%, %))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(Symbol), List(Mapping(%, List(%)))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(Symbol), List(NonNegativeInteger), List(Mapping(%, %))) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
eval : (%, List(Symbol), List(NonNegativeInteger), List(Mapping(%, List(%)))) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
eval : (%, Symbol, Mapping(%, %)) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, Symbol, Mapping(%, List(%))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, Symbol, NonNegativeInteger, Mapping(%, %)) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
eval : (%, Symbol, NonNegativeInteger, Mapping(%, List(%))) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
even? : % -> Boolean if % has RetractableTo(Integer)
from ExpressionSpace2(Kernel(%))
expressIdealMember : (List(%), %) -> Union(List(%), "failed") if R has IntegralDomain
from PrincipalIdealDomain
exquo : (%, %) -> Union(%, "failed") if R has IntegralDomain
from EntireRing
extendedEuclidean : (%, %) -> Record(coef1 : %, coef2 : %, generator : %) if R has IntegralDomain
from EuclideanDomain
extendedEuclidean : (%, %, %) -> Union(Record(coef1 : %, coef2 : %), "failed") if R has IntegralDomain
from EuclideanDomain
factor : % -> Factored(%) if R has IntegralDomain
from UniqueFactorizationDomain
freeOf? : (%, %) -> Boolean
from ExpressionSpace2(Kernel(%))
freeOf? : (%, Symbol) -> Boolean
from ExpressionSpace2(Kernel(%))
gcd : (%, %) -> % if R has IntegralDomain
from GcdDomain
gcd : List(%) -> % if R has IntegralDomain
from GcdDomain
gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has IntegralDomain
from GcdDomain
ground : % -> R
from FunctionSpace2(R, Kernel(%))
ground? : % -> Boolean
from FunctionSpace2(R, Kernel(%))
height : % -> NonNegativeInteger
from ExpressionSpace2(Kernel(%))
inv : % -> % if R has Group or R has IntegralDomain
from Group
is? : (%, BasicOperator) -> Boolean
from ExpressionSpace2(Kernel(%))
is? : (%, Symbol) -> Boolean
from ExpressionSpace2(Kernel(%))
isExpt : % -> Union(Record(var : Kernel(%), exponent : Integer), "failed") if R has SemiGroup
from FunctionSpace2(R, Kernel(%))
isExpt : (%, BasicOperator) -> Union(Record(var : Kernel(%), exponent : Integer), "failed") if R has Ring
from FunctionSpace2(R, Kernel(%))
isExpt : (%, Symbol) -> Union(Record(var : Kernel(%), exponent : Integer), "failed") if R has Ring
from FunctionSpace2(R, Kernel(%))
isMult : % -> Union(Record(coef : Integer, var : Kernel(%)), "failed") if R has AbelianSemiGroup
from FunctionSpace2(R, Kernel(%))
isPlus : % -> Union(List(%), "failed") if R has AbelianSemiGroup
from FunctionSpace2(R, Kernel(%))
isPower : % -> Union(Record(val : %, exponent : Integer), "failed") if R has Ring
from FunctionSpace2(R, Kernel(%))
isTimes : % -> Union(List(%), "failed") if R has SemiGroup
from FunctionSpace2(R, Kernel(%))
kernel : (BasicOperator, %) -> %
from ExpressionSpace2(Kernel(%))
kernel : (BasicOperator, List(%)) -> %
from ExpressionSpace2(Kernel(%))
kernels : % -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
kernels : List(%) -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
latex : % -> String
from SetCategory
lcm : (%, %) -> % if R has IntegralDomain
from GcdDomain
lcm : List(%) -> % if R has IntegralDomain
from GcdDomain
lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %) if R has IntegralDomain
from LeftOreRing
leftPower : (%, NonNegativeInteger) -> % if R has SemiGroup
from MagmaWithUnit
leftPower : (%, PositiveInteger) -> % if R has SemiGroup
from Magma
leftRecip : % -> Union(%, "failed") if R has SemiGroup
from MagmaWithUnit
mainKernel : % -> Union(Kernel(%), "failed")
from ExpressionSpace2(Kernel(%))
map : (Mapping(%, %), Kernel(%)) -> %
from ExpressionSpace2(Kernel(%))
minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if % has Ring
from ExpressionSpace2(Kernel(%))
multiEuclidean : (List(%), %) -> Union(List(%), "failed") if R has IntegralDomain
from EuclideanDomain
numer : % -> SparseMultivariatePolynomial(R, Kernel(%)) if R has Ring
from FunctionSpace2(R, Kernel(%))
numerator : % -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
odd? : % -> Boolean if % has RetractableTo(Integer)
from ExpressionSpace2(Kernel(%))
one? : % -> Boolean if R has SemiGroup
from MagmaWithUnit
operator : BasicOperator -> BasicOperator
from ExpressionSpace2(Kernel(%))
operators : % -> List(BasicOperator)
from ExpressionSpace2(Kernel(%))
opposite? : (%, %) -> Boolean if R has AbelianSemiGroup
from AbelianMonoid
paren : % -> %
from ExpressionSpace2(Kernel(%))
patternMatch : (%, Pattern(Float), PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if R has PatternMatchable(Float)
from PatternMatchable(Float)
patternMatch : (%, Pattern(Integer), PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if R has PatternMatchable(Integer)
from PatternMatchable(Integer)
plenaryPower : (%, PositiveInteger) -> % if R has CommutativeRing
from NonAssociativeAlgebra(R)
prime? : % -> Boolean if R has IntegralDomain
from UniqueFactorizationDomain
principalIdeal : List(%) -> Record(coef : List(%), generator : %) if R has IntegralDomain
from PrincipalIdealDomain
quo : (%, %) -> % if R has IntegralDomain
from EuclideanDomain
recip : % -> Union(%, "failed") if R has SemiGroup
from MagmaWithUnit
reducedSystem : Matrix(%) -> Matrix(R) if R has Ring
from LinearlyExplicitOver(R)
reducedSystem : Matrix(%) -> Matrix(Integer) if R has LinearlyExplicitOver(Integer) and R has Ring
from LinearlyExplicitOver(Integer)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(R), vec : Vector(R)) if R has Ring
from LinearlyExplicitOver(R)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(Integer), vec : Vector(Integer)) if R has LinearlyExplicitOver(Integer) and R has Ring
from LinearlyExplicitOver(Integer)
rem : (%, %) -> % if R has IntegralDomain
from EuclideanDomain
retract : % -> R
from RetractableTo(R)
retract : % -> Fraction(Integer) if R has RetractableTo(Fraction(Integer)) or R has RetractableTo(Integer) and R has IntegralDomain
from RetractableTo(Fraction(Integer))
retract : % -> Fraction(Polynomial(R)) if R has IntegralDomain
from RetractableTo(Fraction(Polynomial(R)))
retract : % -> Integer if R has RetractableTo(Integer)
from RetractableTo(Integer)
retract : % -> Kernel(%)
from RetractableTo(Kernel(%))
retract : % -> Polynomial(R) if R has Ring
from RetractableTo(Polynomial(R))
retract : % -> Symbol
from RetractableTo(Symbol)
retractIfCan : % -> Union(R, "failed")
from RetractableTo(R)
retractIfCan : % -> Union(Fraction(Integer), "failed") if R has RetractableTo(Fraction(Integer)) or R has RetractableTo(Integer) and R has IntegralDomain
from RetractableTo(Fraction(Integer))
retractIfCan : % -> Union(Fraction(Polynomial(R)), "failed") if R has IntegralDomain
from RetractableTo(Fraction(Polynomial(R)))
retractIfCan : % -> Union(Integer, "failed") if R has RetractableTo(Integer)
from RetractableTo(Integer)
retractIfCan : % -> Union(Kernel(%), "failed")
from RetractableTo(Kernel(%))
retractIfCan : % -> Union(Polynomial(R), "failed") if R has Ring
from RetractableTo(Polynomial(R))
retractIfCan : % -> Union(Symbol, "failed")
from RetractableTo(Symbol)
rightPower : (%, NonNegativeInteger) -> % if R has SemiGroup
from MagmaWithUnit
rightPower : (%, PositiveInteger) -> % if R has SemiGroup
from Magma
rightRecip : % -> Union(%, "failed") if R has SemiGroup
from MagmaWithUnit
sample : () -> % if R has AbelianSemiGroup or R has SemiGroup
from AbelianMonoid
sizeLess? : (%, %) -> Boolean if R has IntegralDomain
from EuclideanDomain
smaller? : (%, %) -> Boolean
from Comparable
squareFree : % -> Factored(%) if R has IntegralDomain
from UniqueFactorizationDomain
squareFreePart : % -> % if R has IntegralDomain
from UniqueFactorizationDomain
subst : (%, Equation(%)) -> %
from ExpressionSpace2(Kernel(%))
subst : (%, List(Equation(%))) -> %
from ExpressionSpace2(Kernel(%))
subst : (%, List(Kernel(%)), List(%)) -> %
from ExpressionSpace2(Kernel(%))
subtractIfCan : (%, %) -> Union(%, "failed") if R has AbelianGroup
from CancellationAbelianMonoid
tower : % -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
tower : List(%) -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
unit? : % -> Boolean if R has IntegralDomain
from EntireRing
unitCanonical : % -> % if R has IntegralDomain
from EntireRing
unitNormal : % -> Record(unit : %, canonical : %, associate : %) if R has IntegralDomain
from EntireRing
univariate : (%, Kernel(%)) -> Fraction(SparseUnivariatePolynomial(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
variables : % -> List(Symbol)
from FunctionSpace2(R, Kernel(%))
variables : List(%) -> List(Symbol)
from FunctionSpace2(R, Kernel(%))
zero? : % -> Boolean if R has AbelianSemiGroup
from AbelianMonoid
~= : (%, %) -> Boolean
from BasicType

PatternMatchable(Integer)

Module(Fraction(Integer))

PrincipalIdealDomain

NonAssociativeSemiRing

LeftModule(R)

BiModule(%, %)

ConvertibleTo(InputForm)

Field

canonicalUnitNormal

Rng

CoercibleFrom(Integer)

FullyRetractableTo(R)

SemiRing

EntireRing

NonAssociativeAlgebra(Fraction(Integer))

RetractableTo(R)

unitsKnown

AbelianGroup

FullyLinearlyExplicitOver(R)

PatternMatchable(Float)

CharacteristicNonZero

SetCategory

ConvertibleTo(Pattern(Float))

RetractableTo(Fraction(Polynomial(R)))

InnerEvalable(%, %)

SemiGroup

RightModule(Fraction(Integer))

Magma

RightModule(R)

RetractableTo(Symbol)

IntegralDomain

LeftModule(%)

LinearlyExplicitOver(Integer)

NonAssociativeRing

UniqueFactorizationDomain

ExpressionSpace2(Kernel(%))

GcdDomain

PartialDifferentialRing(Symbol)

CharacteristicZero

RetractableTo(Kernel(%))

Group

Algebra(%)

Module(R)

CoercibleFrom(Fraction(Polynomial(R)))

BiModule(R, R)

DivisionRing

Algebra(R)

CommutativeRing

LinearlyExplicitOver(R)

Evalable(%)

NonAssociativeSemiRng

NonAssociativeAlgebra(R)

CancellationAbelianMonoid

EuclideanDomain

canonicalsClosed

TwoSidedRecip

RetractableTo(Integer)

RightModule(Integer)

CommutativeStar

AbelianMonoid

MagmaWithUnit

Comparable

CoercibleFrom(Symbol)

RightModule(%)

CoercibleFrom(Polynomial(R))

CoercibleFrom(Kernel(%))

Module(%)

FunctionSpace2(R, Kernel(%))

CoercibleTo(OutputForm)

ConvertibleTo(Pattern(Integer))

SemiRng

Patternable(R)

Monoid

RetractableTo(Polynomial(R))

LeftOreRing

NonAssociativeAlgebra(%)

Algebra(Fraction(Integer))

BasicType

Ring

InnerEvalable(Kernel(%), %)

LeftModule(Fraction(Integer))

ExpressionSpace

AbelianSemiGroup

noZeroDivisors

CoercibleFrom(Fraction(Integer))

NonAssociativeRng

CoercibleFrom(R)

BiModule(Fraction(Integer), Fraction(Integer))

FullyPatternMatchable(R)

RetractableTo(Fraction(Integer))