isRankAtLeast -- determines if the matrix has rank at least a number

Synopsis

• Usage:

  isRankAtLeast(n1, M1)

• Inputs:
  • n1, an integer,
  • M1, a matrix,
• Optional inputs:
  • DetStrategy => ..., default value Rank, DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
  • MaxMinors => ..., default value null, an option to control depth of search
  • PointOptions => ..., default value {Strategy => Default, Homogeneous => false, Replacement => Binomial, ExtendField => true, PointCheckAttempts => 0, DecompositionStrategy => Decompose, NumThreadsToUse => 1, DimensionFunction => dim, Verbose => false}, options to pass to functions in the package RandomPoints
  • Strategy => ..., default value new OptionTable from {Points => 0, Random => 0, GRevLexLargest => 0, LexSmallestTerm => 25, LexLargest => 0, LexSmallest => 25, GRevLexSmallestTerm => 25, RandomNonzero => 0, GRevLexSmallest => 25}, strategies for choosing submatrices
  • Threads => ..., default value 1
  • Verbose => ..., default value false
• Outputs:
  • a Boolean value,

Description

i1 : R = QQ[x,y];

i2 : M = matrix{{x,y,2,0,2*x+y}, {0,0,1,0,x}, {x,y,0,0,y}};

             3       5
o2 : Matrix R  <--- R

i3 : rank M

o3 = 2

i4 : isRankAtLeast(2, M)

o4 = true

i5 : isRankAtLeast(3, M)

o5 = false

See also

• getSubmatrixOfRank -- tries to find a submatrix of the given rank
• isRankAtLeast(...,Strategy=>...) -- strategies for choosing submatrices