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2.9.5 Term Orderings
Polynomials are always sorted with respect to the ordering of their base ring; this ordering is specified when the ring is created. All operations involving polynomials utilize and preserve this ordering. There are mnemonic keywords for some predefined term-orderings; otherwise a custom ordering defined by an "ordering matrix" can be specified when using the function NewPolyRing .

The predefined term-orderings are:

* standard-degree reverse lexicographic: DegRevLex (default)

* standard-degree lexicographic: DegLex

* pure lexicographic: Lex (no grading)

* pure xel: Xel (NOT YET IMPLEMENTED)

If the indeterminates are given in the order x_1, ...,x_n , then x_1 > ... > x_n with respect to Lex, and x_1 < ... < x_n with respect to Xel.

Example
-- Specify the ordering when you create the ring:
/**/  P ::= QQ[x,y,z];             --> default is DegRevLex
/**/  P ::= QQ[x,y,z], DegRevLex;  --> same as above
/**/  P ::= QQ[x,y,z], lex;
/**/  P ::= QQ[x,y,z], DegLex;