changes, 1.9
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major improvements and additions:
- Fast minimal betti number and non-minimal resolution code, for homogeneous ideals and modules over polynomial rings over finite prime fields. Also is functional for ideals and modules over exterior algebras. See FastNonminimal and betti(...,Minimize=>...). For computing minimal betti numbers, on larger examples, this code is often hundreds to thousands of times faster than standard use of resolution and is also, in many cases, much faster than the similar code in Singular version 4.0.2 described in Erocal, Motsak, Schreyer, Steenpass, Refined Algorithms to compute syzygies, arxiv 1502.01654. A paper describing our algorithm and implementation is forthcoming.
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packages that have been published and certified:
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HighestWeights, a package by Federico Galetto for decomposing free resolutions and graded modules with a semisimple Lie group action, has been published. -
Posets, a package by David Cook II, Sonja Mapes, and Gwyn Whieldon, for processing partially ordered sets, has been published.
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MultiplierIdeals, a package by Zach Teitler for computing multiplier ideals of monomial ideals, has been published.
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CharacteristicClasses, a package by Christine Jost and Martin Helmer for computing characteristic classes on toric varieties, has been published.
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new packages:
- MCMApproximations, a package by David Eisenbud for maximal Cohen-Macaulay approximations and complete intersections, has been added.
- MultiplierIdealsDim2, a package by Ferran Dachs-Cadefau for computing multiplier ideals in 2-dimensional rings, has been added.
- RunExternalM2, a package by Brian Pike for running Macaulay2 functions outside the current Macaulay2 process, has been added.
- SLPexpressions, a package by Anton Leykin for straight line programs and algebraic circuits, has been added.
- NumericalSchubertCalculus, a package by Anton Leykin, Abraham Martin del Campo, and Jan Verschelde, for numerical methods in Schubert Calculus, has been added.
- ToricTopology, a package by Alvise Trevisan and Alexander I. Suciu for toric topology, has been added.
- Cremona, a package by Giovanni Staglianò for rational maps between projective varieties, has been added.
- Resultants, a package by Giovanni Staglianò for resultants and discriminants for multivariate polynomials, has been added (originally called MultipolynomialResultants).
- VectorFields, a package by Brian Pike for vector fields, has been added.
- RandomIdeals, a package by David Eisenbud for creating random ideals of various sorts, has been added.
- Miura, a package by Joe Suzuki for divisor class groups on curves, has been added.
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functionality added or improved:
- The new function installedPackages returns a list of names of packages installed by the user with installPackage.
- The new function uninstallAllPackages uninstalls all the packages installed by the user with installPackage.
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useful functions involving prime numbers, submitted by Frank Schreyer:
- nextPrime, a simple function to find the first prime number at least as large as a given number
- getPrimeWithRootOfUnity, used to find a prime number p s.t. ZZ/p contains a n-th root of unity
- randomKRationalPoint, a function to find a random rational point on a variety over a finite field