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

Description

For skeptical users. Generates a few non-standard tableaux of shape lambda in the chosen basis convention, then for each:

(a) computes
applyLR(shapes, Q, T, n, Convention => conv)
directly (which uses the convention's straightening internally),
(b) independently straightens T into a sum of standard tableaux,
(c) computes the same sum applied to the standards,
(d) asserts (a) and (c) agree.

If the matrix were silently using the wrong straightening relations (e.g. PieriMaps row-Garnir on a SchurFunctors column-form Filling input), the check fails and prints the offending case.

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

Ways to use verifyWellDefined:

verifyWellDefined(List,List,PolynomialRing)
verifyWellDefined(Sequence,List,ZZ)

For the programmer

The object verifyWellDefined is a method function with options.

The source of this document is in PieriMaps/doc.m2:931:0.

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

Description

See also

Ways to use verifyWellDefined:

For the programmer