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:
  • DetStrategy => ..., default value Cofactor, DetStrateg is a strategy for allowing the user to choose how determinants (or rank), is computed
  • PeriodicCheckFunction => ..., default value null
  • PointOptions => ..., default value new HashTable from {Strategy => Default, ProjectionAttempts => 0, NumThreadsToUse => 1, Codimension => null, MaxCoordinatesToTrivialize => infinity, PointCheckAttempts => 100, IntersectionAttempts => 20, Homogeneous => false, ExtendField => true, Verbose => false, MaxCoordinatesToReplace => 1, Replacement => Binomial}, options to pass to functions in the package RandomRationalPoints
  • Strategy => ..., default value new HashTable 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 |

o2 : Sequence

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

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

o3 : Ideal of R