chooseGoodMinors -- returns an ideal generated by interesting minors in a matrix

Synopsis

• Usage:

  chooseGoodMinors(count, minorSize, M)

  chooseGoodMinors(count, minorSize, M, I)

• Inputs:
  • count, an integer,
  • minorSize, an integer,
  • M, a matrix,
  • I, an ideal,
• Optional inputs:
  • PeriodicCheckFunction => a function, default value null, a function whose argument is the ideal of minors computed so far and which outputs whether the chooseGoodMinors should continue
  • PointOptions => a list, default value {Strategy => Default, Homogeneous => false, Replacement => Binomial, ExtendField => true, PointCheckAttempts => 0, DecompositionStrategy => Decompose, NumThreadsToUse => 1, DimensionFunction => dim, Verbose => false}, options to be passed to the RandomPoints package
  • DetStrategy => ..., default value Cofactor, DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
  • Strategy => ..., default value new OptionTable from {Points => 0, Random => 16, GRevLexLargest => 0, LexSmallestTerm => 16, LexLargest => 0, LexSmallest => 16, GRevLexSmallestTerm => 16, RandomNonzero => 16, GRevLexSmallest => 16}, strategies for choosing submatrices
  • Verbose => ..., default value false
• Outputs:
  • an ideal,

Description

i1 : R = QQ[x, y, z];

i2 : M = matrix{{x,y,0}, {y,z,0}, {0,0,0}}

o2 = | x y 0 |
     | y z 0 |
     | 0 0 0 |

             3      3
o2 : Matrix R  <-- R

i3 : chooseGoodMinors(1, 2, M, Strategy=>StrategyDefaultNonRandom)

              2
o3 = ideal(- y  + x*z)

o3 : Ideal of R