Better inverses #1021

Tianrun-Y · 2024-07-02T14:53:19Z

Add a better method for finding inverses of a multiplicative element of a semigroup that can use Froidure-Pin.
Also add a new method called OneInverseOfSemigroupElement.

…or the argument of RightGreensMultiplierNC.

…e is no one but the method should work

gap/attributes/attr.gi

Co-authored-by: James Mitchell <james-d-mitchell@users.noreply.github.com>

gap/attributes/attr.gi

james-d-mitchell · 2024-07-29T12:20:08Z

gap/greens/froidure-pin.gi

  if path = fail then
    # This can occur when, for example, a = b and S is not a monoid.
-    return One(gens);
+    if IsMultiplicativeElement(a) and IsMultiplicativeElement(b) then


I don't think this does exactly what you want it to, maybe you meant not IsMultiplicativeElementWithOne(a) and similar for b?

Still missing, and the documentation for Left/RightGreensMultiplier should be updated to include:

If S is a semigroup but not a monoid, then the return value is either of the same type as the elements of S or an adjoined identity.

Missing "WithOne" fixed. The documentation is possibly more delicate than that, as an fp semigroup can be a monoid but GAP cannot recognise it as one. One example is < s1, s2 | s1^2=s1, s2^2=s2, s1s2=s2, s2s1=s2>. s1 is a "one" but GAP does not know that.

james-d-mitchell · 2024-07-29T12:20:26Z

gap/greens/froidure-pin.gi

+    if IsMultiplicativeElement(a) and IsMultiplicativeElement(b) then
+      return One(gens);
+    else 
+      return SEMIGROUPS.UniversalFakeOne;


Probably should add some tests for this too?

…to better-inverses

Co-authored-by: James Mitchell <james-d-mitchell@users.noreply.github.com>

gap/attributes/attr.gi

james-d-mitchell

Looks good, a few specific comments, you'll need to:

add more test for everything
a non-no-check version of OneInverseOfSemigroupElementNC
doc for OneInverseOfSemigroupElement
fix IsMultiplicativeElementWithOne in the other place indicated.

james-d-mitchell

And tests for code coverage as indicated during our meeting just now using:

etc/code-coverage-test-gap.py --gap-root /Users/jdm/gap tst/standard/main/froidure-pin.tst

from inside the semigroups package directory where you are doing your development.

Co-authored-by: James Mitchell <james-d-mitchell@users.noreply.github.com>

Tianrun-Y

Don't know which chapter of the documentation this should go to.
Also, might expand the description if needed. example?

gap/attributes/attr.gi

gap/greens/froidure-pin.gi

  if path = fail then
    # This can occur when, for example, a = b and S is not a monoid.
-    return One(gens);
+    if IsMultiplicativeElement(a) and IsMultiplicativeElement(b) then


gap/attributes/attr.gi

Tianrun-Y · 2024-07-31T10:36:43Z

currently no test for finding inverse of a semigroup that cannot use Froidure-Pin.

james-d-mitchell · 2024-07-31T15:46:28Z

doc/attr.xml

+  <Description>
+    <C>OneInverseOfSemigroupElement</C> returns one inverse of the element 
+    <C>x</C> in the semigroup <A>S</A>.
+  </Description>


Example please!

Tianrun-Y · 2024-07-31T15:56:41Z

currently no test for finding inverse of a semigroup that cannot use Froidure-Pin.

found one using Semigroup(SEMIGROUPS.UniversalFakeOne). Resolved

james-d-mitchell · 2024-08-07T14:46:29Z

doc/attr.xml

+  <Returns> One inverse of an element of a semigroup.</Returns>
+  <Description>
+    <C>OneInverseOfSemigroupElement</C> returns one inverse of the element 
+    <C>x</C> in the semigroup <A>S</A>.


What happens if there is no inverse?

doc/attr.xml

gap/attributes/attr.gi

Co-authored-by: James Mitchell <james-d-mitchell@users.noreply.github.com>

james-d-mitchell

Nice one, sorry for the long delay!

james-d-mitchell and others added 11 commits June 25, 2024 14:29

Stub

5065769

Add possibly better method for InversesOfSemigroupElementNC

56b10cb

delete Nambooripad Method for Transformation Semigroup

e874b8f

change inverses to a set

d42b687

change filter into IsMultiplicativeElementWithOne as it is required f…

073e25a

…or the argument of RightGreensMultiplierNC.

add the AsSet to the test rather than the method

d8dd7e1

fix consecutive empty lines

f40c494

fix RightGreensMultiplierNC does not work on fp semigroups where ther…

a7ab1d3

…e is no one but the method should work

fix comment

1f5b58f

add OneInverseOfSemigroupElement and fix small issues

99c1fc6

fix declaration and filter problem

b86b177

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Update gap/attributes/attr.gi

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Tianrun-Y and others added 5 commits July 29, 2024 13:33

fix formatting for gaplint

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Merge branch 'better-inverses' of github.com:/Tianrun-Y/Semigroups in…

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…to better-inverses

fix issue

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Update gap/attributes/attr.gi

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Co-authored-by: James Mitchell <james-d-mitchell@users.noreply.github.com>

Update gap/attributes/attr.gi

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Tianrun-Y and others added 2 commits July 30, 2024 18:41

fix issue

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Update gap/attributes/attr.gi

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Co-authored-by: James Mitchell <james-d-mitchell@users.noreply.github.com>

Tianrun-Y commented Jul 30, 2024

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Tianrun-Y added 3 commits July 31, 2024 11:00

fix formatting for gaplint

c969b11

fix syntax error

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add test for OneInverseOfSemigroupElement

80b17ec

Tianrun-Y added 7 commits July 31, 2024 14:30

addMultiplicativeNeutralElement as a return

60ed671

addMultiplicativeNeutralElement as a return for the other one

a695534

update documentation for LeftGreensMultiplier

0367685

fix filter problem

554e0dd

fix filter problem and also add test

513712b

fix test problems

82d81bd

fix gaplint

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fix test

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add example in documentation

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Tianrun-Y and others added 8 commits August 7, 2024 15:49

Update doc/attr.xml

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Co-authored-by: James Mitchell <james-d-mitchell@users.noreply.github.com>

if there is no inverse

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merge

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delete merge remnants

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add to chapter

bf02a27

fix small issue

2b441e0

fix example format

7f989c0

Merge branch 'main' into better-inverses

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james-d-mitchell approved these changes Nov 8, 2024

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james-d-mitchell merged commit 4f732b7 into semigroups:main Nov 8, 2024
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Better inverses #1021

Better inverses #1021

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Better inverses #1021

Better inverses #1021

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