IntegrationResult FΒΆ

intaux.spad line 1

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.

0: %
from AbelianMonoid
*: (%, 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
=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: F -> %
from RetractableTo F
differentiate: (%, 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?
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(Fraction Integer, Fraction Integer)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule Fraction Integer

Module Fraction Integer

RetractableTo F

RightModule Fraction Integer

SetCategory