Adjusted SchurIndexByCharacter to use character descent (2nd attempt)

[drallenherman]

This is a better attempt of PR #66.

• Revise SchurIndexByCharacter to use character descent
• fixed bug in DefiningCharacterOfCyclotomicAlgebra
• revised documentation

Closes issue #65

[olexandr-konovalov]

This had master as a base branch - changed it to divalg, but it's still incorrect. First, please:

• Edit the title of the PR to be more informative
• explain that this is new attempt of #66
• close #66

We will then try to edit this PR using interactive rebase in git command line to get rid of all unwanted commits.

[codecov[bot]]

Codecov Report

Merging #67 into divalg will increase coverage by 0.03%. The diff coverage is 91.30%.

@@            Coverage Diff             @@
##           divalg      #67      +/-   ##
==========================================
+ Coverage   79.35%   79.38%   +0.03%     
==========================================
  Files          11       11              
  Lines        5313     5321       +8     
==========================================
+ Hits         4216     4224       +8     
  Misses       1097     1097              

Impacted Files	Coverage Δ
lib/div-alg.gi	80.05% <91.30%> (+0.03%)	:arrow_up:
lib/main.gi	81.51% <0.00%> (+0.07%)	:arrow_up:

[olexandr-konovalov]

The new example triggered another diff in tests:

testing: /Users/alexk/.gap/pkg/wedderga/tst/wedderga07.tst
########> Diff in /Users/alexk/.gap/pkg/wedderga/tst/wedderga07.tst:389
# Input is:
b:=Basis(last);
# Expected output:
CanonicalBasis( <algebra-with-one of dimension 4 over NF(24,[ 1, 11 ])> )
# But found:
Basis( <algebra-with-one of dimension 4 over NF(24,[ 1, 11 ])>, ... )
########

I have a fixup commit - shall I push it?

[drallenherman]

I discovered why J2 was performing well on my computer. I had done J1 already. After J1 the Schur indices of J2 characters up to Irr(G)[20] run almost immediately. J1 has order 175560 and Irr(G)[11] runs in just over 2 minutes. So these are a bit slow.

For G:=AtlasGroup("2.A8"); wedderga computes SchurIndexByCharacter(Rationals,G,15)=2 in under 4 seconds from a cold start. The group order is 40320 and this is its unique character of degree 48. So it is safer to use this example instead of the J2 one.

[drallenherman]

The new example triggered another diff in tests:

testing: /Users/alexk/.gap/pkg/wedderga/tst/wedderga07.tst
########> Diff in /Users/alexk/.gap/pkg/wedderga/tst/wedderga07.tst:389
# Input is:
b:=Basis(last);
# Expected output:
CanonicalBasis( <algebra-with-one of dimension 4 over NF(24,[ 1, 11 ])> )
# But found:
Basis( <algebra-with-one of dimension 4 over NF(24,[ 1, 11 ])>, ... )
########

I have a fixup commit - shall I push it?

Yes. I don't think this will make much difference, except perhaps it won't be in agreement with tests running on other versions of GAP?

[olexandr-konovalov]

@drallenherman

Yes. I don't think this will make much difference, except perhaps it won't be in agreement with tests running on other versions of GAP?

No, it happened in all 5 combinations. Some effect of loading methods perhaps, triggered by using AtlasRep package. I've pushed a fixup commit.

[olexandr-konovalov]

We can keep J2 example in the manual, and have J1 and anything else in tst/div-alg.tst where you should be easily able to add them yourself. 2 minutes is OK.

[drallenherman]

We can keep J2 example in the manual, and have J1 and anything else in tst/div-alg.tst where you should be easily able to add them yourself. 2 minutes is OK.

Ok. the 2.A8 example is one of the only accessible ones that gives a nontrivial Schur index in a reasonable amount of time that's why I like it. J2 and J1 return Schur index 1 for all characters. I will take care of this when I review documentation. Important now to get Angel's version merged and stable with the rebased divalg.

[olexandr-konovalov]

@drallenherman @angeldelriomateos rebased this PR, now reduced to 5 commits, will merge after the round of tests.

[olexandr-konovalov]

Merged. @drallenherman now do this:

git checkout divalg
git pull origin divalg

to update your divalg branch, and then

git branch -D pr/65

to delete pr/65 branch which you don't need any more.

[drallenherman]

Merged. @drallenherman now do this:

git checkout divalg
git pull origin divalg

to update your divalg branch, and then

git branch -D pr/65

to delete pr/65 branch which you don't need any more.

ok. done. I think successfully. Thank you!