improvement to StrongTableaux to_transposition algorithm

[zabrocki]

In discussions after #17252, Jennifer Morse pointed out that the algorithm to convert a strong marked column strict tableau to a sequence of transpositions could be made more efficient by always choosing the largest rightmost marking as the end point. The previous version of this algorithm scanned the potential marked column strict tableaux from right to left and pulled off markings if applying a transposition lowered the length of the core by one. This version will test fewer potential marked ribbons.

[zabrocki]

I will continue to run a few tests to make sure, but I think that this version shaves a few seconds off of the tests of k_tableau.py

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New commits:

​a17a36a

fix to marked_CST_to_transposition_sequence in StrongTableaux

[zabrocki]

This version seems to be slightly faster in practice. On my laptop I see around 24-25 seconds with the patch, 24-26 without.

[tscrim]

So I've made some changes and massaged out some more speed. My timings are below. I've also marked two tests as long because the file takes some 110s to run on mine (each were about 9s). However I'll let someone else (Anne) do the final review on the math portion.

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Original timings:

sage: CST_to_trans = StrongTableaux.marked_CST_to_transposition_sequence
sage: %timeit CST_to_trans([[-1, -1, -1], [1]], 2)
100 loops, best of 3: 8.32 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -2, -2, -2], [-2, 2], [2]], 3)
10 loops, best of 3: 21.1 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -5, 5, -5, 5, -5], [-3, -4, 5, 5], [5]],3)
10 loops, best of 3: 104 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -3, 4, -7], [-4, -6], [-5, 6]],3)
10 loops, best of 3: 29.7 ms per loop
sage: %timeit CST_to_trans([], 2)
100000 loops, best of 3: 2.46 µs per loop

Without my changes:

sage: CST_to_trans = StrongTableaux.marked_CST_to_transposition_sequence
sage: %timeit CST_to_trans([[-1, -1, -1], [1]], 2)
100 loops, best of 3: 8.29 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -2, -2, -2], [-2, 2], [2]], 3)
10 loops, best of 3: 21 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -5, 5, -5, 5, -5], [-3, -4, 5, 5], [5]],3)
10 loops, best of 3: 48 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -3, 4, -7], [-4, -6], [-5, 6]],3)
10 loops, best of 3: 29.3 ms per loop
sage: %timeit CST_to_trans([], 2)
100000 loops, best of 3: 2.4 µs per loop

With my changes:

sage: CST_to_trans = StrongTableaux.marked_CST_to_transposition_sequence
sage: %timeit CST_to_trans([[-1, -1, -1], [1]], 2)
100 loops, best of 3: 7.7 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -2, -2, -2], [-2, 2], [2]], 3)
10 loops, best of 3: 18.3 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -5, 5, -5, 5, -5], [-3, -4, 5, 5], [5]],3)
10 loops, best of 3: 43.3 ms per loop
sage: %timeit CST_to_trans([[-1, -2, -3, 4, -7], [-4, -6], [-5, 6]],3)
10 loops, best of 3: 26.1 ms per loop
sage: %timeit CST_to_trans([], 2)
100000 loops, best of 3: 2 µs per loop

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New commits:

​b87a736

Changed some things around to make it faster and marked tests as long.

[aschilling]

Hi Mike, thanks for implementing this! Looks good to me. Anne

[zabrocki]

I've been calculating larger examples to make sure going from and to transposition sequences are consistent and have found no faults.

Thanks Travis and Anne.