The following operations are used internally to perform the arithmetic for polynomials in their ``external'' representation (see The Defining Attributes of Rational Functions) as lists.
ZippedSum( z1, z2, czero, funcs ) O
computes the sum of two external representations of polynomials z1 and
z2. czero is the appropriate coefficient zero and funcs a list
[ monomial less, coefficient sum ] containing a monomial comparison
and a coefficient addition function. This list can be found in the
component fam!.zippedSum of the rational functions family.
ZippedProduct( z1, z2, czero, funcs ) O
computes the product of two external representations of polynomials z1
and z2. czero is the appropriate coefficient zero and funcs a list
[monomial prod,monomial less,coefficient sum,coefficient prod ]
containing functions to multiply and compare monomials, to add and to
multiply coefficients. This list can be found in the component
fam!.zippedProduct of the rational functions family.
QuotientPolynomialsExtRep( fam, a, b ) F
Let a and b the external representations of two polynomials in the
rational functions family fam. This function computes the external
representation of the quotient of both polynomials, it returns fail if
b does not divide a.
Functions to perform arithmetic with the coefficient lists of Laurent polynomials are described in section Coefficient List Arithmetic.
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GAP 4 manual