Better inverses #1021
Better inverses #1021
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…or the argument of RightGreensMultiplierNC.
…e is no one but the method should work
james-d-mitchell
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performance
Co-authored-by: James Mitchell <[email protected]>
Co-authored-by: James Mitchell <[email protected]>
gap/greens/froidure-pin.gi
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| 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 |
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I don't think this does exactly what you want it to, maybe you meant not IsMultiplicativeElementWithOne(a) and similar for b?
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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.
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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.
gap/greens/froidure-pin.gi
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| if IsMultiplicativeElement(a) and IsMultiplicativeElement(b) then | ||
| return One(gens); | ||
| else | ||
| return SEMIGROUPS.UniversalFakeOne; |
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Probably should add some tests for this too?
…to better-inverses
Co-authored-by: James Mitchell <[email protected]>
Co-authored-by: James Mitchell <[email protected]>
Co-authored-by: James Mitchell <[email protected]>
gap/greens/froidure-pin.gi
Outdated
| 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 |
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|
currently no test for finding inverse of a semigroup that cannot use Froidure-Pin. |
| <Description> | ||
| <C>OneInverseOfSemigroupElement</C> returns one inverse of the element | ||
| <C>x</C> in the semigroup <A>S</A>. | ||
| </Description> |
found one using Semigroup(SEMIGROUPS.UniversalFakeOne). Resolved |
doc/attr.xml
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| <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>. |
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What happens if there is no inverse?
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.