# GroebnerLexDeg Command

## CAS Syntax

GroebnerLexDeg( <List of Polynomials> )
Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the variables (also known as grlex, tdeg, lexdeg, total degree lexicographic ordering or elimination ordering).
Example: GroebnerLexDeg({x^3 - y - 2, x^2 + y + 1}) yields {\mathrm{\mathsf{ -y^{2} + x - 3 y - 3, -x y - x - y - 2, x^{2} + y + 1 }}}.
GroebnerLexDeg( <List of Polynomials>, <List of Variables> )
Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the given variables (also known as grlex, tdeg, lexdeg, total degree lexicographic ordering or elimination ordering).
Example: GroebnerLexDeg({x^3 - y -2, x^2 + y + 1},{y, x}) yields {\mathrm{\mathsf{ x^{2} + y + 1, -y x - y - x - 2, y^{2} + 3 y - x + 3 }}}.