Wreath product #262

ffloresbrito · 2017-02-24T16:46:48Z

This pull request adds a method for the operationWreathProduct that computes the wreath product of a monoid and a permutation group as its embedding in the full transformation monoid. Documentation and tests are included.

james-d-mitchell

This looks ok, there are a few things to change in the documentation, you consistently say semigroup when I think you mean transformation semigroup or maybe transformation monoid. You also capitalise Wreath Product, which I wouldn't do.

james-d-mitchell · 2017-02-27T09:03:25Z

doc/semitrans.xml

+<#GAPDoc Label="WreathProduct">
+  <ManSection>
+    <Oper Name = "WreathProduct" Arg = "S, G"/>
+    <Returns>The Wreath Product of <A>S</A> and <A>G</A>.</Returns>


No capital letters of Wreath or Product

This comment applies in numerous places.

james-d-mitchell · 2017-02-27T09:03:46Z

doc/semitrans.xml

+    <Description>
+      For a monoid <A>S</A> and a permutation group <A>G</A>,
+      <C>WreathProduct(<A>S</A>, <A>G</A>)</C> outputs the semigroup Wreath
+      product of S and G in terms of its embedding in the full transformation


Missing <A> tags around S and G here.

james-d-mitchell · 2017-02-27T09:04:25Z

doc/semitrans.xml

+      For a monoid <A>S</A> and a permutation group <A>G</A>,
+      <C>WreathProduct(<A>S</A>, <A>G</A>)</C> outputs the semigroup Wreath
+      product of S and G in terms of its embedding in the full transformation
+      monoid. For example, the Wreath product of T3, the full transformation


Please don't use T3 or C2 (this is not a standard convention in the Semigroups package)

james-d-mitchell · 2017-02-27T09:04:57Z

doc/semitrans.xml

+      product of S and G in terms of its embedding in the full transformation
+      monoid. For example, the Wreath product of T3, the full transformation
+      monoid on three points, and C2, the group generated by the transposition
+      <C>(1,3)</C>, would be output as its emedding in the full transformation 


spelling mistake emedding

james-d-mitchell · 2017-02-27T09:06:20Z

gap/semigroups/semitrans.gi

+function(S, G)
+  local maps, gensS, next, reps, n, i, g, x, m;
+  if not IsMonoidAsSemigroup(S) then
+    ErrorNoReturn("S should be a monoid");


This error should be in the format: Semigroups: WreathProduct: usage..
please see other error messages in the package for the correct format.

james-d-mitchell · 2017-02-27T09:07:18Z

gap/semigroups/semitrans.gi

+  m := LargestMovedPoint(G);
+  maps := []; # the final generating set for the wreath product
+
+  gensS := ShallowCopy(GeneratorsOfSemigroup(S));


I don't think you need to take a ShallowCopy here.

We do need ShallowCopy because we later modify the list gensS which would otherwise be immutable as GeneratorsOfSemigroup(S) returns an immutable object.

james-d-mitchell · 2017-02-27T09:07:48Z

gap/semigroups/semitrans.gi

+      od;
+    od;
+  fi;
+  return Semigroup(maps);


Isn't the return value a monoid? If so, shouldn't we return Monoid(maps) here?

Even though it is a monoid, using Monoid(maps) adds the identity transformation, which may not be in the wreath product. That is why using Semigroup(maps) is the appropiate thing to do.

james-d-mitchell · 2017-02-27T09:10:18Z

gap/semigroups/semitrans.gi

@@ -735,6 +735,47 @@ function(S)
  return t;
 end);

+InstallMethod(WreathProduct, "for a monoid and a permutation group",


The string here is wrong, it should describe the arguments in the next line. So in this case it should be for a transformation semigroup and a permutation group.

mtorpey

I have some comments, mostly about the documentation.

mtorpey · 2017-06-21T13:42:36Z

gap/semigroups/semitrans.gi

+end);
+
+InstallMethod(WreathProduct,
+"for a transformation semigroup and a permutation group",


This string should be the other way around: "for a permutation group and a transformation semigroup"

mtorpey · 2017-06-21T13:45:38Z

doc/semitrans.xml

+<#GAPDoc Label="WreathProduct">
+  <ManSection>
+    <Oper Name = "WreathProduct" Arg = "S, G"/>
+    <Returns>The wreath product of <A>S</A> and <A>G</A>.</Returns>


The Returns statement should just be the type of object returned: A transformation semigroup.

mtorpey · 2017-06-21T13:53:23Z

doc/semitrans.xml

+    <Oper Name = "WreathProduct" Arg = "S, G"/>
+    <Returns>The wreath product of <A>S</A> and <A>G</A>.</Returns>
+    <Description>
+      For a transformation monoid <A>S</A> and a permutation group <A>G</A>,


Doesn't this work for any transformation semigroup?

mtorpey · 2017-06-21T13:55:24Z

doc/semitrans.xml

+
+<#GAPDoc Label="WreathProduct">
+  <ManSection>
+    <Oper Name = "WreathProduct" Arg = "S, G"/>


We should also have the version where Arg = "S, G". You can just add the line right below this.

mtorpey · 2017-06-21T14:02:29Z

gap/semigroups/semitrans.gi

+        rimage;
+  if not IsMonoidAsSemigroup(S) then
+    ErrorNoReturn("Semigroups: WreathProduct: usage,\n",
+                    "the first argument <S> should be a monoid,");


<S> is the second argument.

mtorpey · 2017-06-23T11:21:27Z

gap/semigroups/semitrans.gi

+end);
+
+InstallMethod(WreathProduct,
+"for two transformation semigroups",


Just one bad string here: you want "for a transformation monoid and a transformation semigroup"

Thank you for pointing that out. I have already fixed it!

mtorpey · 2017-06-23T11:22:56Z

I have one more suggestion: add a method for [IsPermGroup, IsPermGroup]. You have methods for the case where one of the arguments is a permutation group, but not one for both.

ffloresbrito · 2017-06-23T11:36:11Z

Michael, thank you for the suggestion to add the method for two permutation groups. GAP already has a method to do the wreath product of two groups, and if I were to add this method, there would appear the following warning: "method installed for WreathProduct matches more than one declaration". Should I add this method, regardless?

james-d-mitchell · 2017-06-23T11:38:03Z

@ffloresbrito no don't add the method for 2 perm groups, since it already exists in GAP there is no need.`

mtorpey · 2017-06-23T12:03:51Z

Aha! I'm glad to hear a method already exists. In that case, please ignore my suggestion.

…

On 23 June 2017 at 12:36, Fernando Flores Brito ***@***.***> wrote: Michael, thank you for the suggestion to add the method for two permutation groups. GAP already has a method to do the wreath product of two groups, and if I were to add this method, there would appear the following warning: "method installed for WreathProduct matches more than one declaration". Should I add this method, regardless? — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#262 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AFUy714in0FfQXt4e1WPW0nxztpz-E9sks5sG6MrgaJpZM4MLa-V> .[image: Web Bug from https://github.com/notifications/beacon/AFUy7_XhbBZ4lmu9unElh7spRVkkOtpdks5sG6MrgaJpZM4MLa-V.gif] {"api_version":"1.0","publisher":{"api_key":" 05dde50f1d1a384dd78767c55493e4bb","name":"GitHub"},"entity": {"external_key":"github/gap-packages/Semigroups","title":" gap-packages/Semigroups","subtitle":"GitHub repository","main_image_url":" https://cloud.githubusercontent.com/assets/143418/17495839/a5054eac-5d88- 11e6-95fc-7290892c7bb5.png","avatar_image_url":"https:// cloud.githubusercontent.com/assets/143418/15842166/ 7c72db34-2c0b-11e6-9aed-b52498112777.png","action":{"name":"Open in GitHub","url":"https://github.com/gap-packages/Semigroups"}} ***@***.*** in #262: Michael, thank you for the suggestion to add the method for two permutation groups. GAP already has a method to do the wreath product of two groups, and if I were to add this method, there would appear the following warning: \"method installed for WreathProduct matches more than one declaration\". Should I add this method, regardless? "}],"action":{"name":"View Pull Request","url":"https:// github.com/gap-packages/Semigroups/pull/262#issuecomment-310643488"}}}

james-d-mitchell

Looks good apart from the suggested changes.

james-d-mitchell · 2017-06-23T12:12:16Z

doc/semitrans.xml

+    <Description>
+      If <A>M</A> is a transformation monoid or a permutation group, and
+      <A>S</A> is a transformation semigroup or a permutation group, the
+      function <C>WreathProduct(<A>M</A>, <A>S</A>)</C> outputs the wreath


the function <C>WreathProduct(<A>M</A>, <A>S</A>)</C> outputs -> the operation <C>WreathProduct</C> returns for consistency with the rest of the manual.

james-d-mitchell · 2017-06-23T12:12:39Z

doc/semitrans.xml

+      <A>S</A> is a transformation semigroup or a permutation group, the
+      function <C>WreathProduct(<A>M</A>, <A>S</A>)</C> outputs the wreath
+      product of <A>M</A> and <A>S</A>, in terms of its embedding in the full
+      transformation monoid.


You could also be much more specific about what this embedding actually is.

But there is still no information about what the embedding actually is.

james-d-mitchell · 2017-06-23T12:13:09Z

doc/z-chap13.xml

+  <Section>
+
+    <Heading>
+      The wreath product of a transformation monoid and a permutation group


I think this should be in the same section as the documentation for the direct product, if that exists.

james-d-mitchell · 2017-06-23T12:13:47Z

gap/semigroups/semitrans.gi

+[IsTransformationMonoid, IsPermGroup],
+function(M, G)
+  local S;
+  S := AsMonoid(IsTransformationMonoid, G);


This could just be return WreathProduct(M, AsMonoid(IsTransformationMonoid, G))

james-d-mitchell · 2017-06-23T12:13:57Z

gap/semigroups/semitrans.gi

+function(G, S)
+  local M;
+  M := AsMonoid(IsTransformationMonoid, G);
+  return WreathProduct(M, S);


Same as previous comment.

james-d-mitchell · 2017-06-23T12:14:29Z

gap/semigroups/semitrans.gi

+        rimage;
+  if not IsMonoidAsSemigroup(S) then
+    ErrorNoReturn("Semigroups: WreathProduct: usage,\n",
+                    "the second argument <S> should be a monoid,");


"should be a monoid (as semigroup)"

james-d-mitchell · 2017-06-23T12:16:49Z

gap/semigroups/semitrans.gi

+  gensM := List(gensM, x -> OnTuples([1 .. m], x));
+  gensS := GeneratorsOfSemigroup(S);
+
+  orbs := List(ComponentsOfTransformationSemigroup(S), x -> Minimum(x));


Can't lines 779 to 787 be replaced with rimage := DigraphSources(DigraphOfActionOnPoints(S));?

james-d-mitchell · 2017-06-23T12:17:57Z

tst/standard/semitrans.tst

+#T# Test wreath product of perm. group and transf. semgp.
+gap> W := WreathProduct(Group((1, 2)), FullTransformationMonoid(3));;
+gap> Size(W);
+216


Can you maybe test some more things than just the size too?

…athProduct

mtorpey · 2017-07-19T14:47:29Z

gap/semigroups/semitrans.gi

+        rimage;
+  if not IsMonoidAsSemigroup(S) then
+    ErrorNoReturn("Semigroups: WreathProduct: usage,\n",
+                    "the second argument <S> should be a monoid (as ",


Lines 778 and 779 should be aligned correctly.

mtorpey · 2017-07-19T14:47:51Z

gap/semigroups/semitrans.gi

+        rimage;
+  if not IsMonoidAsSemigroup(S) then
+    ErrorNoReturn("Semigroups: WreathProduct: usage,\n",
+                    "the second argument <S> should be a monoid (as ",


Align lines 778 and 779 properly.

mtorpey · 2017-07-19T14:50:15Z

gap/semigroups/semitrans.gi

+  m := DegreeOfTransformationCollection(M);
+
+  gensM := ShallowCopy(GeneratorsOfMonoid(M));
+  gensM := List(gensM, x -> OnTuples([1 .. m], x));


I'd replace these 2 lines with

gensM := List(GeneratorsOfMonoid(M), x -> ImageListOfTransformation(x, m));

mtorpey · 2017-07-19T14:51:17Z

gap/semigroups/semitrans.gi

+  gensM := List(gensM, x -> OnTuples([1 .. m], x));
+  gensS := GeneratorsOfSemigroup(S);
+
+  orbs := List(ComponentsOfTransformationSemigroup(S), x -> Minimum(x));


This can be simplified! Replace x -> Minimum(x) with just Minimum

mtorpey · 2017-07-19T14:57:03Z

gap/semigroups/semitrans.gi

+
+  gen1 := gensS[1];
+  for i in orbs do
+    newmap := OnTuples([1 .. m * n], maps[1]);


As before, try changing this to newmap := ImageListOfTransformation(maps[1], m * n);

Issues resolved.

james-d-mitchell requested changes Feb 27, 2017

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ffloresbrito changed the base branch from unstable-3.0 to master March 29, 2017 14:53

ffloresbrito force-pushed the wreath-product branch from 08c6268 to 7ff5740 Compare March 29, 2017 14:59

mtorpey added the 3.1 label May 29, 2017

ffloresbrito force-pushed the wreath-product branch 3 times, most recently from c22d5c6 to e05def6 Compare June 14, 2017 17:27

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ffloresbrito force-pushed the wreath-product branch from f57db4e to 9b634e4 Compare June 23, 2017 11:01

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james-d-mitchell previously requested changes Jun 23, 2017

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ffloresbrito force-pushed the wreath-product branch from 883b2de to f173aa3 Compare July 5, 2017 14:12

ffloresbrito added 12 commits July 5, 2017 17:29

semitrans: add WreathProduct method

b5f8479

semitrans: add tests and documentation for Wreath product

3394d5f

semitrans: change tests and documentation for wreath product

96dbea9

semitrans.gi : change method specification

75c77a0

semitrans.gi: delete whitespace

b9ad431

z-chap15.xml: add section on wreath product

36943dd

semitrans.xml: linting

963ebff

semitrans: add new WreathProduct method

23a7ae8

semitrans.gi: fix WreathProduct second method

b06ff81

semitrans: linting

0842b1f

semitrans: linting

ab9ade4

semitrans.tst: add test for new WreathProduct method

4b3884b

ffloresbrito added 10 commits July 5, 2017 17:29

semitrans.xml: fix WreathProduct documentation

5b23e6f

semitrans.gi: fix error message on WreathProduct

9a866e8

semitrans: merge WreathProduct methods and fix documentation

f8868f4

semitrans.gi: fix WreathProduct, use monoid instead of semigroup

42b600d

semitrans.gi: change label on WreathProduct main method

33b2999

semitrans: fix according to James's comments

e5c700c

semitrans: emphasize embedding in documentation and add tests for Wre…

984f960

…athProduct

semitrans.xml: fix documentation

1566279

semitrans.xml: fix documentation of WP

2109ecf

z-chap06/13: move documentation to the correct file

17638ac

ffloresbrito force-pushed the wreath-product branch from 47358bc to 17638ac Compare July 5, 2017 18:09

mtorpey reviewed Jul 19, 2017

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mtorpey requested changes Jul 19, 2017

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ffloresbrito added 2 commits July 19, 2017 16:14

semitrans.gi: integrate Michael's suggestions

6a133c7

semitrans.gi: linting

0620941

mtorpey approved these changes Jul 19, 2017

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semitrans.gi: make mutable list

0561cb4

mtorpey merged commit 3e93ef1 into semigroups:master Jul 19, 2017

Wreath product #262

Wreath product #262

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ffloresbrito commented Feb 24, 2017 • edited by james-d-mitchell Loading

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mtorpey commented Jun 23, 2017

ffloresbrito commented Jun 23, 2017

james-d-mitchell commented Jun 23, 2017

mtorpey commented Jun 23, 2017 via email

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ffloresbrito commented Feb 24, 2017 •

edited by james-d-mitchell

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