AngouriMath
Fglm
Description
Summary
Converts a degree-reverse-lexicographic Gröbner basis of a zero-dimensional ideal
into the lexicographic one.
into the lexicographic one.
Remarks
computed; lexicographic is what can be back-substituted, because its basis is
triangular and leaves the last variable a univariate polynomial with rational
coefficients. So the system is solved in one order and answered in the other.
ideal the quotient ring is a finite-dimensional vector space spanned by the monomials
no leading term divides, so every monomial reduces to a point in it. Walking
monomials in lexicographic order and asking which is the first to be a combination of
those already seen produces the basis directly: each dependency *is* an element, and
the coefficients of the combination are its terms.
counted with multiplicity — a different quantity from anything that bounds Buchberger.
A system can have a basis that computes in milliseconds and a conversion that does
not finish, so MaxQuotientDimension is checked before any
of the work below is done rather than discovered partway through it.
Members
Angouri © 2019-2023 · Project's repo · Site's repo · Octicons · Transparency · 1953 pages online