Class Polynomial

Returns

Copy of the polynomial

Divide by a set of polynomials fs = [f_1, ..., f_n] using lex

Returns

quotients for each polynomial in fs, remainder and steps if verbose

Checks if polynomials are equivalent

Exponent of this polynomial

Greatest common divider of this polynomial and g

Checks if this polynomial is greater or equal to q using lex

List of monomials making the array ordered by lex

List of variables of the ring of this polynomial

Checks if all variables in v are variables of the ring of this polynomial

Inserts new variables before the existing ones to the ring and updates the exponent for every monomial

Checks if polynomial is equivalent to zero

Leader coefficient

Lowest common multiple of this polynomial and g

Checks if this polynomial is less or equal to q using lex

Leader monomial

Leader term

Substraction of this polynomial with q

Product of this polynomial with q

Sum of this polynomial with q

Concatenates new variables to the ring and updates the exponent for every monomial

Checks if polynomial reduces to 0 in G

Remove variables of the ring and updates the exponent for every monomial

Checks if this polynomial and p are in the same ring

Second leader coefficient

Second leader monomial

Second leader term

Support of the polynomial

String representation of the polynomial using lex

Checks if all variables in v are used in this polynomial

Checks if any variables in v are used in this polynomial

List of the variables from the ring used by the polynomial

Computes a Groebner base of I using Buchberger's Algorithm

Computes a reduced Groebner base of I using Buchberger's Algorithm and Criteria

Array of exponents of each polynomial in F

Chacks if a>b using lex.

Checks if G is a Groebner basis of <F>

Checks if G is a reduced Groebner basis of <F>

Reduces a Groebner base

Returns

S-Polynomial of f and g. Asummes that f and g use the same variables