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Next: Modules over Affine Algebras
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Ideal Theory and Gröbner Bases
New Features:
- The F4 algorithm is now used for computing with ideals having fixed
bases. Thus the coordinate matrix for a GB is now found much more
quickly.
- A new function NormalForm(L, G), based on Faugere F4
techniques, is now provided to reduce a sequence of polynomials L modulo
another sequence of polynomials G (or an ideal). This is important for
the efficient computation of the secondary invariants of a finite group.
- The memory management in the F4 algorithm has been improved so that
less memory is used when there are extremely large ultrasparse matrices;
the time is significantly reduced in such cases.
- The main strategy to compute the GB of an ideal has been improved
through the introduction of various preprocessing techniques.
- Computation of GBs over algebraic number fields (including cyclotomic
and quadratic fields) has been greatly improved.
- Computation of GBs over rational function fields with a small number
of indeterminates has been improved.
- The primary decomposition and radical algorithms have been improved
by heuristics to quickly determine whether or not the ideal is prime
or radical (thus catching common cases quickly).
- The computation of the Hilbert series of an ideal has been improved by
more efficient selection of a suitable GB.
Next: Modules over Affine Algebras
Up: Commutative Algebra
Previous: Commutative Algebra
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