RationalFunction R

rf.spad line 153 [edit on github]

Utilities that provide the same top-level manipulations on fractions than on polynomials.

coerce: R -> Fraction Polynomial R

coerce(r) returns r viewed as a rational function over R.

eval: (Fraction Polynomial R, Equation Fraction Polynomial R) -> Fraction Polynomial R

eval(f, v = g) returns f with v replaced by g. Error: if v is not a symbol.

eval: (Fraction Polynomial R, List Equation Fraction Polynomial R) -> Fraction Polynomial R

eval(f, [v1 = g1, ..., vn = gn]) returns f with each vi replaced by gi in parallel, i.e. vi's appearing inside the gi's are not replaced. Error: if any vi is not a symbol.

eval: (Fraction Polynomial R, List Symbol, List Fraction Polynomial R) -> Fraction Polynomial R

eval(f, [v1, ..., vn], [g1, ..., gn]) returns f with each vi replaced by gi in parallel, i.e. vi's appearing inside the gi's are not replaced.

eval: (Fraction Polynomial R, Symbol, Fraction Polynomial R) -> Fraction Polynomial R

eval(f, v, g) returns f with v replaced by g.

mainVariable: Fraction Polynomial R -> Union(Symbol, failed)

mainVariable(f) returns the highest variable appearing in the numerator or the denominator of f, “failed” if f has no variables.

multivariate: (Fraction SparseUnivariatePolynomial Fraction Polynomial R, Symbol) -> Fraction Polynomial R

multivariate(f, v) applies both the numerator and denominator of f to v.

univariate: (Fraction Polynomial R, Symbol) -> Fraction SparseUnivariatePolynomial Fraction Polynomial R

univariate(f, v) returns f viewed as a univariate rational function in v.

variables: Fraction Polynomial R -> List Symbol

variables(f) returns the list of variables appearing in the numerator or the denominator of f.