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FastLinAlg :: FastLinAlg

FastLinAlg -- faster linear algebra in certain cases

Description

FastLinAlg is a for computing (applications of) function field linear algebra more quickly in certain settings.

This package is still experimental. It provides functionality for doing certain linear algebra operations in function fields quickly. There is some multithreaded capability which is disabled by default.

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
  • Rn checks whether a ring is regular in codimension n only in the affirmative.
  • 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.
Many of these functions have extensive options for fine tuning their behavior, for instance by controlling how submatrices are chosen. See the documentation for StrategyDefault

Acknowledgements:

The authors would like to thank David Eisenbud 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 while developing this package.
Yuhui (Wei) Yao received funding from the University of Utah Mathematics Department REU program, while developing this package

Authors

Version

This documentation describes version 0.1 of FastLinAlg.

Source code

The source code from which this documentation is derived is in the file FastLinAlg.m2.

Exports

  • Functions and commands
  • Symbols
    • DetStrategy -- DetStrateg is a strategy for allowing the user to choose how determinants (or rank), is computed
    • Rank, see DetStrategy -- DetStrateg is a strategy for allowing the user to choose how determinants (or rank), is computed
    • Recursive, see DetStrategy -- DetStrateg is a strategy for allowing the user to choose how determinants (or rank), is computed
    • GRevLexLargest -- strategies for choosing submatrices
    • GRevLexSmallest, see GRevLexLargest -- strategies for choosing submatrices
    • GRevLexSmallestTerm, see GRevLexLargest -- strategies for choosing submatrices
    • LexLargest, see GRevLexLargest -- strategies for choosing submatrices
    • LexSmallest, see GRevLexLargest -- strategies for choosing submatrices
    • LexSmallestTerm, see GRevLexLargest -- strategies for choosing submatrices
    • Random, see GRevLexLargest -- strategies for choosing submatrices
    • RandomNonzero, see GRevLexLargest -- strategies for choosing submatrices
    • StrategyDefault, see GRevLexLargest -- strategies for choosing submatrices
    • MaxMinors -- an option to control depth of search
    • MinDimension -- an option for projDim
    • ModP -- an option for Rn
    • MinorsCache, see recursiveMinors -- uses a recursive cofactor algorithm to compute the ideal of minors of a matrix
    • Threads -- an option for various functions
  • Other things