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Ideal Theory and Gröbner Bases
New Features:
- The pair handling in the F4 algorithm has been improved, leading
to speedups in computing Groebner bases for some inputs.
- The new parameter ReversePairs has been introduced for Groebner
and related functions. It is relevant when setting PairsLimit to a
particular value, so as to choose the subset of pairs in opposite order
rather than by default.
- The intrinsic ColonIdeal is now much faster for certain inputs.
- New function MinimalDecomposition to minimize a decomposition
of an ideal.
- The function AbsoluteAlgebra now accepts affine algebras over
finite fields.
- New function RegularSequence computes a maximal regular sequence
in an ideal of a polynomial ring over a field. The algorithm used is
that of Eisenbud and Sturmfels. It is designed to produce a sequence
of reasonably sparse polynomials.
- New function ReesIdeal. For an ideal I of an affine algebra R,
given by an ideal in the polynomial ring of which R is a quotient, this
function returns a polynomial ideal J whose quotient algebra is isomorphic
to the Rees algebra R(I) of I over R. There is also a ``flattening"
option that quotients out by a-torsion for a a given non-zero
divisor of R.
Next: Differential Rings
Up: Commutative Algebra
Previous: Multivariate Polynomial Rings
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