verifyWellDefined -- verify an LR map respects the chosen convention's straightening relations

• Usage:

  verifyWellDefined((lambda, mu, nu), Q, n, Convention => ...)

• Inputs:
  • (lambda, mu, nu), a sequence, three partitions for the LR data
  • Q, a list, an LR tableau as returned by lrTableaux
  • n, an integer, the dimension of $V$
• Optional inputs:
  • Convention => a string, default value "Row", , basis convention to check
  • Verbose => a Boolean value, default value true, , whether to print per-test progress (default true)
  • Direction => ..., default value "Inclusion"
• Outputs:
  • a Boolean value, true if all generated tests pass, false otherwise

i1 : needsPackage "SchurFunctors";

i2 : Qs = lrTableaux({3,2,1}, {2,1}, {2,1});

i3 : verifyWellDefined(({3,2,1},{2,1},{2,1}), Qs#0, 3, Convention => "Filling")
  Test #1 (T = Filling{{1, 0, 2}, {0, 1}, {0}}): OK
  Test #2 (T = Filling{{0, 1, 2}, {1, 0}, {0}}): OK
  Test #3 (T = Filling{{1, 0, 2}, {0, 1}, {1}}): OK
verifyWellDefined: 3 test(s) all PASSED for convention Filling.

o3 = true

i4 : verifyWellDefined(({3,2,1},{2,1},{2,1}), Qs#0, 3, Convention => "Row")
  Test #1 (T = {{0, 0, 0}, {2, 1}, {2}}): OK
  Test #2 (T = {{0, 0, 1}, {2, 1}, {2}}): OK
  Test #3 (T = {{0, 0, 2}, {2, 1}, {2}}): OK
verifyWellDefined: 3 test(s) all PASSED for convention Row.

o4 = true