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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
; this is useful
for specifying an
elimination order via a matrix created by
ElimMat
.
The predefined term-orderings are:
* standard-degree reverse lexicographic:
DegRevLex (default)
* standard-degree lexicographic:
DegLex
* pure lexicographic:
Lex (no grading)
* pure xel:
Xel (no grading)
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.
-- 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;
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