Subsections

• Arithmetic
• Equality and Membership
• Numerator and Denominator
• Predicates on Ring Elements
• Evaluation

+ a : FldFunElt -> FldFunElt

- a : FldFunElt -> FldFunElt

a + b : FldFunElt, FldFunElt -> FldFunElt

a - b : FldFunElt, FldFunElt -> FldFunElt

a * b : FldFunElt, FldFunElt -> FldFunElt

a / b : FldFunElt, FldFunElt -> FldFunElt

a ^ k : FldFunElt, RngIntElt -> FldFunElt

a +:= b : RngPolElt, RngPolElt -> RngPolElt

a -:= b : RngPolElt, RngPolElt -> RngPolElt

a *:= b : RngPolElt, RngPolElt -> RngPolElt

a eq b : FldFunElt, FldFunElt -> BoolElt

a ne b : FldFunElt, FldFunElt -> BoolElt

a in F : FldFunElt, FldFun -> BoolElt

a notin F : FldFunElt, FldFun -> BoolElt

Given a rational function f in K, the field of fractions of R, this function returns the numerator P of f=P/Q as an element of the polynomial ring R.

Given a rational function f in K, the field of fractions of R, this function returns the denominator Q of f=P/Q as an element of the polynomial ring R.

IsZero(a) : FldFunElt -> BoolElt

IsOne(a) : FldFunElt -> BoolElt

IsMinusOne(a) : FldFunElt -> BoolElt

IsNilpotent(a) : FldFunElt -> BoolElt

IsIdempotent(a) : FldFunElt -> BoolElt

IsUnit(a) : FldFunElt -> BoolElt

IsZeroDivisor(a) : FldFunElt -> BoolElt

IsRegular(a) : FldFunElt -> BoolElt

Given a univariate rational function f in F, return the rational function in F obtained by evaluating the indeterminate in r, which must be from (or coercible into) the coefficient ring of the integers of F.

Evaluate(f, v, r) : FldFunElt, RngIntElt, RngElt -> FldFunElt

Given a rational function f in F, return the rational function in F obtained by evaluating the v-th principal indeterminate in r, which must be from (or coercible into) the coefficient ring of the integers of F.