BinomialEdgeIdeals, a package by Tobias Windisch for computations with binomial edge ideals, has been added.
TateOnProducts, a package by Daniel Erman, David Eisenbud, and Frank-Olaf Schreyer for Tate resolutions on products of projective spaces, has been added.
LatticePolytopes, a package by Anders Lundman and Gustav Sædén Ståhl for computations with lattice polytopes, has been added.
FiniteFittingIdeals, a package by Gustav Sædén Ståhl for computing Fitting ideals of finite modules, has been added.
HigherCIOperators, a package by David Eisenbud for computing higher complete intersection operators, has been added. It implements some work of Burke, Eisenbud and Schreyer on a structure that exists on resolutions over a complete intersection. This structure allows one to lift a resolution over a complete intersection to a resolution over the ambient ring -— a construction dual, in a sense, to the well known Eisenbud-Shamash construction, which is also implemented.
LieTypes, a package by Dave Swinarski for defining types used by the package ConformalBlocks, has been added.
ConformalBlocks, a package by Dave Swinarski for computing ranks and first Chern classes of conformal block bundles on the moduli space of n-pointed curves of genus 0, has been added.
M0nbar, a package by Han-Bom Moon and David Swinarski for calculations for divisors and F-curves on the moduli space of stable n-pointed genus zero curves, has been added.
AnalyzeSheafOnP1, a package by David Eisenbud for decomposing a coherent sheaf on the projective line into a direct sum of line bundles and cyclic skyscraper sheaves, has been added.
improved packages:
The package Binomials has been upgraded from version 1.0 to 1.2.
The package BoijSoederberg has been upgraded from version 1.2 to 1.5.
The package ChainComplexExtras has been upgraded from version 0.5 to version 1.
The package MultiplierIdeals has been upgraded from version 1.0 to version 1.1.
The package CompleteIntersectionResolutions has been upgraded from version 0.8 to version 0.9. It implements a number of old and new ideas about minimal resolutions over a complete intersection developed by Eisenbud-Peeva, Avramov-Jorgensen, Eisenbud-Peeva-Schreyer, and Burke-Eisenbud-Schreyer. Let S = k[x_1..x_n] be a polynomial ring, ff a codimension c regular sequence of homogeneous forms of the same degree, and R = S/(ff). It contains:
routines to compute the structure of higher matrix factorization on a high R-syzygy M — one for which the modules Ext_R^even(M,k) and Ext_R^odd(M,k) have negative regularity over the ring of CI operators. There are also routines to extract various information from the higher matrix factorization.
routines that implement the reconstruction algorithm of Avramov and Jorgensen that constructs modules M having (certain kinds of) specified Ext-modules.
routines to test of a conjecture of Eisenbud about the vanishing of certain local cohomology of Ext-modules, implementing the map from a module to its saturation.
routines to compute the higher homotopies for ff on an S-free resolution of an S-module M annihilated by ff, and understanding the structure of module over an exterior algebra, determined by the ff-homotopies on a resolution of M, on Tor^S(M,N) and Ext_S(M,N), when M and N are S-modules annihilated by ff. These routines led to conjectures that were later proven, and will appear in a work-in-progress of Eisenbud, Peeva and Schreyer.
routines to compute Hom in the stable category of Cohen-Macaulay R-modules, and test for stable triviality. This is used in understanding possible obstructions to commutativity of CI-operators.
functionality added or improved:
The function pairs will now accept (basic) list (or sequence) x and return the list of pairs (i,x#i), thanks to Zach Teitler.
The function minimalPresentation has been modified so that it applies its degree-preserving method also for homogeneous modules over affine algebras over affine algebras.
The function applyKeys will now accept an additional function to be called when collisions occur between new keys, for combining the corresponding values, thanks to Paul Zinn-Justin.
The function partition now takes a third argument: a list of additional values in the range of the function, allowing members of the resulting partition to be empty.
The function loadPackage can now be used to reload a package by giving the package itself as the argument. This is easier than setting the loadPackage(...,Reload=>...) option.
The function adjoint has been improved to work not just for free modules, and the function adjoint1 has been replaced by adjoint'. This pair of function now implements both direction in the adjointness between Hom and tensor product.
The new function homomorphism' complements homomorphism. From a map between modules it produces the element of Hom.
The new function compose expresses composition of maps between modules as a bilinear map between Hom-modules.
Bracket powers of ideals (Ideal ^ Array) have been added, thanks to Frank Moore.
Several bugs related to computing Groebner bases in polynomial rings over ZZ have been fixed. trim I in this case now returns an ideal or module with a Groebner basis as generating set, as a minimal generating set isn't well-defined. In a future release, we hope to provide a function to determine a smaller set of generators. mingens I also returns the Groebner basis matrix. In a future release this function might be changed to give an error in cases where there is not a well-defined notion of minimal generators.
functionality changed:
The function export now accepts strings and options only, not symbols.