# FullPartialFractionExpansion(F, UP)ΒΆ

Full partial fraction expansion of rational functions Author: Manuel Bronstein Date Created: 9 December 1992 References: M.Bronstein & B.Salvy, Full Partial Fraction Decomposition of Rational Functions, in Proceedings of ISSAC'93, Kiev, ACM Press.

+: (UP, %) -> %

p + x returns the sum of p and x

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
construct: List Record(exponent: NonNegativeInteger, center: UP, num: UP) -> %

construct(l) is the inverse of fracPart.

convert: % -> Fraction UP

from ConvertibleTo Fraction UP

D: % -> %

D(f) returns the derivative of f.

D: (%, NonNegativeInteger) -> %

D(f, n) returns the n-th derivative of f.

differentiate: % -> %

differentiate(f) returns the derivative of f.

differentiate: (%, NonNegativeInteger) -> %

differentiate(f, n) returns the n-th derivative of f.

fracPart: % -> List Record(exponent: NonNegativeInteger, center: UP, num: UP)

fracPart(f) returns the list of summands of the fractional part of f.

fullPartialFraction: Fraction UP -> %

fullPartialFraction(f) returns [p, [[j, Dj, Hj]...]] such that f = p(x) + \sum_{[j, Dj, Hj] in l} \sum_{Dj(a)=0} Hj(a)/(x - a)\^j.

latex: % -> String

from SetCategory

polyPart: % -> UP

polyPart(f) returns the polynomial part of f.

BasicType

SetCategory