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BUILT-IN MATHEMATICA SYMBOL
GroebnerBasis
GroebnerBasis[{poly1, poly2, ...}, {x1, x2, ...}]
gives a list of polynomials that form a Gröbner basis for the set of polynomials 
.
GroebnerBasis[{poly1, poly2, ...}, {x1, x2, ...}, {y1, y2, ...}]
finds a Gröbner basis in which the 
have been eliminated.
Details and Options
- The set of polynomials in a Gröbner basis have the same collection of roots as the original polynomials.
- For polynomials in one variable, GroebnerBasis reduces to PolynomialGCD.
- For linear functions in any number of variables, GroebnerBasis is equivalent to Gaussian elimination.
- The Gröbner basis in general depends on the ordering assigned to monomials. This ordering is affected by the ordering of the
. - The following options can be given:
-
MonomialOrder Lexicographic the criterion used for ordering monomials CoefficientDomain Automatic the type of objects assumed to be coefficients Method Automatic the method to use Modulus 0 the modulus for numerical coefficients - Possible settings for
are 
, 
, 
, or an explicit weight matrix. Monomials are specified for the purpose of 
by lists of the exponents with which the 
appear in them. - The ordering of the
and the setting for 
can substantially affect the efficiency of GroebnerBasis. - Possible settings for
are 
, Rationals, 
, and 
. - Possible settings for the Method option include
and 
.
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