is a package for computing relevant minors (determinants of submatrices) of matrices of polynomial functions quickly
This package provides functionality for doing certain linear algebra operations over rings quickly. There is also some multithreaded capability which is disabled by default. Note this package was previously called FastLinAlg.Tutorials:
There are tutorials on how to use various strategies and options in FastMinorsStrategyTutorial
which we recommend the user explore if they are interested in the more advanced features of the package.Useful functions:
chooseGoodMinors Tries to find interesting minors of a matrix.
isRankAtLeast Tries to show that a matrix has rank at least a given number by looking at submatrices
regularInCodimension checks whether a ring is regular in codimension n, but doesn't return false.
projDim checks the projective dimension of a module and may give better answers than pdim in the case that R is not homogeneous
recursiveMinors provides a different strategy for computing minors of a matrix. It is a cofactor strategy where the determinants of smaller minors are stored.
isCodimAtLeast provides a way for finding lower bounds for the codimension of an ideal, without actually computing the codimension.
Many of these functions have extensive options for finetuning their behavior, for instance by controlling how submatrices are chosen. See the documentation for StrategyDefaultAcknowledgements:
The authors would like to thank the anonymous referee, David Eisenbud, Eloisa Grifo, and Srikanth Iyengar for useful conversations and comments on the development of this package.
Boyana Martinova received funding from the University of Utah Mathematics Department REU program and from the ACCESS program at the University of Utah, while developing this package.
Marcus Robinson received funding from the NSF RTG grant 1246989 while developing this package.
Karl Schwede received funding from NSF grant 1801849 and a fellowship from the Simons Foundation while developing this package.
Yuhui (Wei) Yao received funding from the University of Utah Mathematics Department REU program, while developing this package