FullPartialFractionExpansion(F, UP)

fparfrac.spad line 1 [edit on github]

• F : Join(Field, CharacteristicZero)
• UP : UnivariatePolynomialCategory(F)

Full partial fraction expansion of rational functions.

+ : (UP, %) -> %

p + x returns the sum of p and x

= : (%, %) -> Boolean

from BasicType

D : % -> %

D(f) returns the derivative of f.

D : (%, NonNegativeInteger) -> %

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

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

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

construct(l) is the inverse of fracPart.

convert : % -> Fraction(UP)

from ConvertibleTo(Fraction(UP))

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.

~= : (%, %) -> Boolean

from BasicType

CoercibleTo(OutputForm)

SetCategory

BasicType

ConvertibleTo(Fraction(UP))