IntegrationResult(F)
intaux.spad line 1
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If a function f has an elementary integral g, then g can be written in the form g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un) where h, which is in the same field as f, is called the rational part of the integral, and c1 log(u1) + ... cn log(un) is called the logarithmic part of the integral. This domain manipulates integrals represented in that form, by keeping both parts separately. The logs are not explicitly computed.
- * : (%, Fraction(Integer)) -> %
- from RightModule(Fraction(Integer))
- * : (Fraction(Integer), %) -> %
- from LeftModule(Fraction(Integer))
- * : (Integer, %) -> %
- from AbelianGroup
- * : (NonNegativeInteger, %) -> %
- from AbelianMonoid
- * : (PositiveInteger, %) -> %
- from AbelianSemiGroup
- + : (%, %) -> %
- from AbelianSemiGroup
- - : % -> %
- from AbelianGroup
- - : (%, %) -> %
- from AbelianGroup
- 0 : () -> %
- from AbelianMonoid
- = : (%, %) -> Boolean
- from BasicType
- coerce : F -> %
- from CoercibleFrom(F)
- coerce : % -> OutputForm
- from CoercibleTo(OutputForm)
- differentiate : (%, Mapping(F, F)) -> F
differentiate(ir, D) differentiates ir with respect to the derivation D.
- differentiate : (%, Symbol) -> F if F has PartialDifferentialRing(Symbol)
differentiate(ir, x) differentiates ir with respect to x
- elem? : % -> Boolean
elem?(ir) tests if an integration result is elementary over F?
- integral : (F, F) -> %
integral(f, x) returns the formal integral of f with respect to x
- integral : (F, Symbol) -> % if F has RetractableTo(Symbol)
integral(f, x) returns the formal integral of f with respect to x
- latex : % -> String
- from SetCategory
- logpart : % -> List(Record(scalar : Fraction(Integer), coeff : SparseUnivariatePolynomial(F), logand : SparseUnivariatePolynomial(F)))
logpart(ir) returns the logarithmic part of an integration result
- mkAnswer : (F, List(Record(scalar : Fraction(Integer), coeff : SparseUnivariatePolynomial(F), logand : SparseUnivariatePolynomial(F))), List(Record(integrand : F, intvar : F))) -> %
mkAnswer(r, l, ne) creates an integration result from a rational part r, a logarithmic part l, and a non-elementary part ne.
- notelem : % -> List(Record(integrand : F, intvar : F))
notelem(ir) returns the non-elementary part of an integration result
- opposite? : (%, %) -> Boolean
- from AbelianMonoid
- ratpart : % -> F
ratpart(ir) returns the rational part of an integration result
- retract : % -> F
- from RetractableTo(F)
- retractIfCan : % -> Union(F, "failed")
- from RetractableTo(F)
- sample : () -> %
- from AbelianMonoid
- subtractIfCan : (%, %) -> Union(%, "failed")
- from CancellationAbelianMonoid
- zero? : % -> Boolean
- from AbelianMonoid
- ~= : (%, %) -> Boolean
- from BasicType
CancellationAbelianMonoid
CoercibleTo(OutputForm)
AbelianMonoid
AbelianSemiGroup
RetractableTo(F)
BasicType
Module(Fraction(Integer))
CoercibleFrom(F)
SetCategory
AbelianGroup
BiModule(Fraction(Integer), Fraction(Integer))
LeftModule(Fraction(Integer))
RightModule(Fraction(Integer))