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.
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;