Improvements to reesmat code and new tests #1676

wilfwilson · 2017-09-06T13:37:31Z

This PR resolves issues #1659 and #1661, as well as a couple of other small bugs I detected and fixed whilst working on this PR.

My purpose with this PR was to increase my confidence in the library's Rees (0-)matrix semigroup code, since I'd never really looked at it before. I was concerned with making sure that the code correct rather than more efficient, and I was writing test coverage as a way of achieving this confidence.

@james-d-mitchell already had good coverage of lib/reesmat.gi with his test file tst/teststandard/reesmat.tst, which contains more complicated tests than the ones I have added in this PR. I have put my new tests into tst/testinstall/reesmat.tst, which on its own gives 98% coverage of lib/reesmat.gi. I started my new file so that I could approach the problem fresh.

In doing so, I found several instances where methods either returned wrong answers, or unnecessarily led to break loops. I have fixed these problems, and re-written some very small parts of the code for either improved readability or consistency. More detail on the specific changes is given in the relevant commit messages. In summary, there were problems with

IsFinite
IsOne
Enumerator
IsReesMatrixSemigroup
IsReesZeroMatrixSemigroup

This PR increases the code coverage of lib/reesmat.gi almost as far as I can without running into technical difficulties (having test coverage of some errors, for instance, will mean that the tests will fail when the Semigroups package is loaded, since Semigroups replaces some of the relevant methods, and uses different error messages). I make no claim that lib/reesmat.gi is perfect now, but I think this PR is a good start.

I apologise for this being a large number of changes in one PR; however most of the lines are simply new tests. The changes to lib/reesmat.gi themselves are quite small and I think it makes sense to bundle them together.

Previously, IsFinite used the logic that for a subsemigroup <S> of a Rees (0-)matrix semigroup <R>, <S> is finite if and only if <R> is finite. You can use the information that <R> is finite to deduce that <S> is finite, but if <R> is infinite you cannot immediately deduce the (in)finiteness of <S>. Resolves gap-system#1659

IsOne: IsOne for a Rees (0-)matrix semigroup element doesn't make sense, since a Rees (0-)matrix semigroup is never IsMagmaWithOne. Furthermore, even interpreting `IsOne` as menaing `IsMultiplicativeNeutralElement`, the methods were invalid. Therefore, I've removed them. Resolves gap-system#1661

fingolfin

Looks very clean and orderly to me, only have some very small and optional remarks.
However, I don't know anything about the mathematical side of this, so it'd be great if somebody who does could glance at it as well.

fingolfin · 2017-09-06T15:29:24Z

lib/reesmat.gi

@@ -77,15 +77,21 @@ end);
 InstallMethod(IsIdempotent, "for a Rees 0-matrix semigroup element",
 [IsReesZeroMatrixSemigroupElement], 
 function(x)
-  local R;
+  local matrix_entry, g;


commit message: "no affect on performance" should be "no effect on performance"

fingolfin · 2017-09-06T15:32:52Z

lib/reesmat.gi

+  fi;
+
+  g := UnderlyingElementOfReesZeroMatrixSemigroupElement(x);
+  return g * matrix_entry * g = g;


Since I don't know how these things are stored internally, I cannot at all determine whether this change is valid. (E.g. an inversion happened in the old code which didn't happen before).
So I'll just trust that you know what you are doing :-).

In case you are interested @fingolfin - if not, no need to read further!:

A Rees matrix semigroup element is a triple (i, g, j), where i and j are indices (referring to a column and row of a matrix, respectively), g is an element of a semigroup, and the multiplication is

(i, g, j)(k, h, l) = (i, g * mat[j][k] * h, l)

where mat is the matrix associated to the Rees matrix semigroup. So an element is an idempotent whenever g * mat[j][i] * g = g. (The situation is slightly more complicated for Rees 0-matrix semigroups, but never mind).

For the special case that g is an element of a group (rather than of just a semigroup, in general), you can rearrange that equation to be g = mat[j][i] ^ -1; this is the condition that the old code checked. A better check would've been g * mat[j][i] = One(g), to avoid inversion.

The version I went with works in general (not just for groups), and doesn't seem to noticeably slow things down.

fingolfin · 2017-09-06T15:50:09Z

lib/reesmat.gi

-
+  if ForAny(Columns(R), j -> ForAll(Rows(R), i -> Matrix(R)[j][i] = 0))
+      or ForAny(Rows(R), i -> ForAll(Columns(R), j -> Matrix(R)[j][i] = 0)) then 
+    return false;


Minor optimization: perhaps store Matrix(R) into a local variable.

I'll make this change

fingolfin · 2017-09-06T15:54:38Z

I see that @markuspf also reviewed this, so I guess we can merge this once (or "if" ???) Travis finishes with it.

This is a very minor change which (in my opinion) makes the code more readable, and seems to have no effect on performance.

This is a very minor change, which means that the good method in `IsRegularSemigroup` applies to a slightly larger class of argument.

This commit fixes a bug that could lead to a break loop, and also replaces the statement `return Size(ParentAttr(R)) = 1;` with `return false`, since a Rees 0-matrix semigroup is never trivial.

This commit shortens a method for `IsZeroSimpleSemigroup`, so that it uses `ForAll` and `ForAny` instead of loops; I think this is more readable.

In IsReesMatrixSemigroup, this commit removes some code that I believe is unreachable for finite semigroups, and invalid for infinite semigroups. It had no test coverage previously.

This commit fixes a bug whereby an Enumerator of a Rees (0-)matrix semigroup believed that it contains elements from a different Rees (0-)matrix semigroup.

wilfwilson · 2017-09-06T16:08:56Z

My tests haven't even started running yet - so I may as well fix the minor things pointed out by @fingolfin and push them.

wilfwilson · 2017-09-06T16:13:06Z

Done that. Thanks for reviewing. Hopefully Travis will have started (and maybe even finished) by tomorrow.

codecov · 2017-09-06T16:24:45Z

Codecov Report

Merging #1676 into master will increase coverage by 0.06%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master    #1676      +/-   ##
==========================================
+ Coverage   64.35%   64.42%   +0.06%     
==========================================
  Files        1002     1002              
  Lines      326699   326705       +6     
  Branches    13218    13218              
==========================================
+ Hits       210244   210475     +231     
+ Misses     113585   113361     -224     
+ Partials     2870     2869       -1

Impacted Files	Coverage Δ
lib/reesmat.gi	`99.02% <100%> (+18%)`	⬆️
src/funcs.c	`72.25% <0%> (-0.41%)`	⬇️
src/system.c	`52.77% <0%> (-0.34%)`	⬇️
src/stats.c	`72.94% <0%> (-0.27%)`	⬇️
lib/combinat.gi	`67.92% <0%> (+0.06%)`	⬆️
src/hpc/traverse.c	`78.29% <0%> (+0.08%)`	⬆️
lib/grpperm.gi	`85.37% <0%> (+0.09%)`	⬆️
src/hpc/threadapi.c	`34.46% <0%> (+0.09%)`	⬆️
hpcgap/lib/coll.gi	`71.86% <0%> (+0.13%)`	⬆️
hpcgap/lib/hpc/stdtasks.g	`38.87% <0%> (+0.25%)`	⬆️
... and 7 more

wilfwilson added 2 commits September 6, 2017 16:09

markuspf approved these changes Sep 6, 2017

View reviewed changes

wilfwilson force-pushed the improve-reesmat branch from 05be26d to 88028b8 Compare September 6, 2017 14:30

wilfwilson mentioned this pull request Sep 6, 2017

Proposal: move Rees matrix semigroups from library to Semigroups package #1681

Open

fingolfin approved these changes Sep 6, 2017

View reviewed changes

wilfwilson added 8 commits September 6, 2017 17:55

reesmat: rewrite IsIdempotent

3d4b12e

This is a very minor change which (in my opinion) makes the code more readable, and seems to have no effect on performance.

reesmat: generalise IsRegularSemigroup method

82905f0

This is a very minor change, which means that the good method in `IsRegularSemigroup` applies to a slightly larger class of argument.

reesmat: fix IsReesZeroMatrixSemigroup

a7d3c10

This commit fixes a bug that could lead to a break loop, and also replaces the statement `return Size(ParentAttr(R)) = 1;` with `return false`, since a Rees 0-matrix semigroup is never trivial.

reesmat: improve arg checking in RZMS

b5229d4

reesmat: cleanup IsZeroSimpleSemigroup

7515953

This commit shortens a method for `IsZeroSimpleSemigroup`, so that it uses `ForAll` and `ForAny` instead of loops; I think this is more readable.

reesmat: remove redundant/invalid code from IsRMS

d694876

In IsReesMatrixSemigroup, this commit removes some code that I believe is unreachable for finite semigroups, and invalid for infinite semigroups. It had no test coverage previously.

reesmat: fix bug in Enumerator

1595a2f

This commit fixes a bug whereby an Enumerator of a Rees (0-)matrix semigroup believed that it contains elements from a different Rees (0-)matrix semigroup.

reesmat: increase code coverage

a914d63

wilfwilson force-pushed the improve-reesmat branch from 88028b8 to a914d63 Compare September 6, 2017 16:11

markuspf merged commit 32ea4f4 into gap-system:master Sep 7, 2017

wilfwilson deleted the improve-reesmat branch September 7, 2017 09:39

fingolfin mentioned this pull request Sep 7, 2017

Release notes for GAP 4.9 #1699

Closed

olexandr-konovalov added the gapdays2017-fall Issues and PRs that arose at https://www.gapdays.de/gapdays2017-fall label Sep 7, 2017

olexandr-konovalov added the release notes: added PRs introducing changes that have since been mentioned in the release notes label Jan 22, 2018

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Improvements to reesmat code and new tests #1676

Improvements to reesmat code and new tests #1676

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