`ordering_t`

Synopsis#include <flint/mpoly.h>

ordering_t

An enumeration of the supported monomial orderings: ORD_LEX, ORD_DEGLEX and ORD_DEGREVLEX.

With variables $x_0 > x_1 > \cdots > x_{n-1}$ and exponent vectors $a$ , $b$ :

ORD_LEX: $x^a > x^b$ if the first nonzero entry of $a - b$ is positive.
ORD_DEGLEX: $x^a > x^b$ if $|a| > |b|$ , or $|a| = |b|$ and $x^a > x^b$ in lex order, where $|a| = a_0 + \cdots + a_{n-1}$ .
ORD_DEGREVLEX: $x^a > x^b$ if $|a| > |b|$ , or $|a| = |b|$ and the last nonzero entry of $a - b$ is negative.

All three are monomial orderings: total orders compatible with multiplication in which $1$ is the smallest monomial.

Guides#

Getting started with fmpz_mpoly (fmpz_mpoly)

Cite this page

The FLINT team, “ordering_t (mpoly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/mpoly/ordering_t.html (generated 2026-11-02).

@misc{flint-doc-mpoly-ordering-t,
  author       = {{The FLINT team}},
  title        = {{ordering\_t (mpoly.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/mpoly/ordering_t.html},
  note         = {Generated 2026-11-02}
}

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