Groebner bases
Symbolics.groebner_basis
— Functiongroebner_basis(polynomials; ordering=:deglex)
Computes a Groebner basis of the ideal generated by the given polynomials
. The basis is reduced, thus guaranteed to be unique.
Example
julia> using Symbolics
julia> @variables x y;
julia> groebner_basis([x*y^2 + x, x^2*y + y])
The coefficients in the resulting basis are in the same domain as for input polynomials. Hence, if the coefficient becomes too large to be represented exactly, DomainError
is throwed.
By default, degree lexicographic monomial ordering is used. All possible orderings are:
lex
for lexicographic;deglex
for degree lexicographic;degrevlex
for degree reversed lexicographic.
The basis will be correct with respect to the specified ordering, however, the terms in the output will always be ordered with deglex
.