Tietze transformations for semigroups by tomcontileslie · Pull Request #762 · semigroups/Semigroups

tomcontileslie · 2021-04-14T15:36:02Z

Authors: Ben Spiers (@bspiers) and Tom Conti-Leslie (@tomcontileslie)
Ready for review

This PR creates methods for a "semigroup Tietze" object which contains the generators and relations of an fp semigroup. Tietze transformations can be manually applied to the object to change the presentation, giving an fp semigroup isomorphic to the original. The idea is to also have a "SimplifyPresentation" operation which will intelligently apply transformations in order to reduce the overall length of the presentation.

Once transformations have been applied to the Tietze object to taste, it can be converted back into an fp semigroup and a mapping object can be produced which provides an isomorphism between the original fp semigroup and the modified version.

Still needs doing:

tomcontileslie · 2021-04-26T19:06:58Z

@@ -77,10 +77,11 @@
  <#Include SYSTEM "z-chap16.xml">  <!-- properties and attributes of inverse semigroups -->


I should specify I have shuffled doc chapters down so that this new "fp semigroups" chapter doesn't appear after the stuff on IO and visualising semigroups!

Co-authored-by: Ben Spiers <bspiers972@outlook.com> Co-authored-by: Tom Conti-Leslie <tom.contileslie@gmail.com>

james-d-mitchell

A host of minor corrections to the doc, but otherwise this looks awesome!

james-d-mitchell · 2021-05-26T12:30:01Z

+  <ManSection>
+    <Oper Name="StzPresentation" Arg="s"/>
+    <Returns>
+      A Semigroup Tietze (Stz) object.


Semigroup -> semigroup

Suggested change

A Semigroup Tietze (Stz) object.

A semigroup Tietze (Stz) object.

james-d-mitchell · 2021-05-26T12:30:19Z

+
+<#GAPDoc Label="StzPresentation">
+  <ManSection>
+    <Oper Name="StzPresentation" Arg="s"/>


s -> S

Suggested change

<Oper Name="StzPresentation" Arg="s"/>

<Oper Name="StzPresentation" Arg="S"/>

james-d-mitchell · 2021-05-26T12:30:33Z

+      A Semigroup Tietze (Stz) object.
+    </Returns>
+    <Description>
+      If <A>s</A> is a fp semigroup


"a fp semigroup" should be "an fp semigroup"

james-d-mitchell · 2021-05-26T12:31:16Z

+      Every semigroup Tietze object is an element of the category
+      <C>IsStzPresentation</C>. Internally, each Stz object contains a list
+      of generators (each represented as a string) and a list of relations
+      (each represented as a pair of LetterRep words, see


Suggested change

(each represented as a pair of LetterRep words, see

(each represented as a pair of <C>LetterRep</C> words, see

james-d-mitchell · 2021-05-26T13:30:36Z

+
+    <P/>

+    This object is analogous to the "Tietze object" implemented for fp groups


Reference not quotes

james-d-mitchell · 2021-05-26T13:30:50Z

+    in the main &GAP; distribution
+    (<Ref Chap="Presentations and Tietze Transformations" BookName="ref"/>),
+    but its features are semigroup-specific. Most of the functions used to
+    create, view and manipulate Semigroup Tietze objects are prefixed with


Suggested change

create, view and manipulate Semigroup Tietze objects are prefixed with

create, view and manipulate semigroup Tietze objects are prefixed with

james-d-mitchell · 2021-05-26T14:01:43Z

+      Converting a modified presentation into a semigroup
+    </Heading>
+
+    Now that a presentation object has been established, we need to cover how 


Again, this could be a bit clearer.

james-d-mitchell · 2021-05-26T14:51:09Z

+
+  return ObjectifyWithAttributes(out, type,
+                                  RelationsOfStzPresentation,
+                                  out!.rels,


I think to avoid duplication, you might want to rename these out!.rels -> out!.RelationsOfStzPresentation. Also if type doesn't belong to IsAttributeStoringRep, then does ObjectifyWithAttributes do anything?

james-d-mitchell · 2021-05-26T14:51:42Z

+    stz!.gens := newGens;
+end);
+
+# TODO: TCL: maybe better to call this StzIsomorphism?


Agreed, this is probably a more uniform name.

james-d-mitchell · 2021-05-26T14:55:54Z

+################################################################################
+
+DeclareOperation("StzPresentation", [IsFpSemigroup]);
+DeclareCategory("IsStzPresentation", IsList);


IsList -> IsRecord

I run into issues I'm not familiar with when trying to change the representation. Something about the implementation of StzPresentation fails! I'll avoid addressing this for now

Co-authored-by: James D. Mitchell <jdm3@st-andrews.ac.uk>

UnreducedSemigroupOfStzPresentation UnreducedFpSemigroupOfFpSemigroup both -> "UnreducedFpSemigroup"

stz!.rels -> stz!.RelationsOfStzPresentation stz!.gens -> stz!.GeneratorsOfStzPresentation stz!.unreducedSemigroup -> stz!.UnreducedFpSemigroup stz!.tietzeForwardMap -> stz!.TietzeForwardMap stz!.tietzeBackwardMap -> stz!.TietzeBackwardMap

TietzeIsomorphism -> StzIsomorphism

tomcontileslie · 2021-06-08T23:46:34Z

Since there hadn't been any action on this pull request for a couple weeks, I've attempted to address all of @james-d-mitchell's comments from the review. I believe that's everything sorted (mostly documentation and function renaming) except for changing DeclareCategory("IsStzPresentation", IsList); to DeclareCategory("IsStzPresentation", IsRecord); in gap/fp/tietze.gi which brought about unexpected issues.

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tomcontileslie commented Apr 26, 2021

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tomcontileslie commented Apr 30, 2021

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Comment thread tst/standard/isomorph.tst Outdated

wilfwilson force-pushed the tietze branch from 8a89425 to 7e2142a Compare May 20, 2021 12:44

Add Tietze transformations for semigroups

6435a07

Co-authored-by: Ben Spiers <bspiers972@outlook.com> Co-authored-by: Tom Conti-Leslie <tom.contileslie@gmail.com>

wilfwilson force-pushed the tietze branch from 7250e4d to 6435a07 Compare May 20, 2021 20:14

Re-link new ElementOfFpSemigroup doc entries into Chap 19

b6380fc

james-d-mitchell added the hackathon-may-2021 label May 26, 2021

james-d-mitchell requested review from flsmith and james-d-mitchell May 26, 2021 09:20

james-d-mitchell changed the title ~~Tietze Transformations for Semigroups~~ Tietze transformations for semigroups May 26, 2021

james-d-mitchell requested changes May 26, 2021

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james-d-mitchell reviewed May 26, 2021

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tomcontileslie and others added 4 commits June 9, 2021 00:05

Documentation review (JDM)

93f6fbb

Co-authored-by: James D. Mitchell <jdm3@st-andrews.ac.uk>

Code review (JDM): rename:

5fc72e1

UnreducedSemigroupOfStzPresentation UnreducedFpSemigroupOfFpSemigroup both -> "UnreducedFpSemigroup"

Code review (JDM) rename:

db21814

stz!.rels -> stz!.RelationsOfStzPresentation stz!.gens -> stz!.GeneratorsOfStzPresentation stz!.unreducedSemigroup -> stz!.UnreducedFpSemigroup stz!.tietzeForwardMap -> stz!.TietzeForwardMap stz!.tietzeBackwardMap -> stz!.TietzeBackwardMap

Code review (JDM): rename:

3047730

TietzeIsomorphism -> StzIsomorphism

james-d-mitchell merged commit 1e7754e into semigroups:master Nov 1, 2021

		@@ -77,10 +77,11 @@
		<#Include SYSTEM "z-chap16.xml"> <!-- properties and attributes of inverse semigroups -->

	A Semigroup Tietze (Stz) object.
	A semigroup Tietze (Stz) object.

	<Oper Name="StzPresentation" Arg="s"/>
	<Oper Name="StzPresentation" Arg="S"/>

	(each represented as a pair of LetterRep words, see
	(each represented as a pair of <C>LetterRep</C> words, see


		<P/>

		This object is analogous to the "Tietze object" implemented for fp groups

	create, view and manipulate Semigroup Tietze objects are prefixed with
	create, view and manipulate semigroup Tietze objects are prefixed with

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tomcontileslie commented Jun 8, 2021

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tomcontileslie commented Apr 14, 2021 •

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