attr: Add NambooripadPartialOrder & Leq methods#467
attr: Add NambooripadPartialOrder & Leq methods#467james-d-mitchell merged 1 commit intosemigroups:masterfrom
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This looks good, there are a couple of typos that you should correct (as indicated). The only substantive comment I have is that you should install a method for NambooripadWhatever for IsInverseSemigroup which just returns the natural partial order, since the Nambooripad order is a generalisation of this.
doc/attr.xml
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| <A>S</A> is defined by <C>s</C><M>\leq</M><C>t</C> if the principal right | ||
| ideal of <C>S</C> generated by <C>s</C> is contained in the principal right | ||
| ideal of <C>S</C> generated by <C>t</C> and there is an idempotent | ||
| <C>e</C> in the R-class of <C>s</C> such that <C>s</C><M>=</M><C>et</C>. The |
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This should be &R;-class so that it is displayed correctly.
doc/attr.xml
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| <Attr Name="NambooripadPartialOrder" Arg="S"/> | ||
| <Returns>The Nambooripad partial order on an regular semigroup.</Returns> | ||
| <Description> | ||
| The <E>Nambooripad partial order</E> <M>\leq</M> on an regular semigroup |
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"an regular" -> "a regular"
doc/attr.xml
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| ideal of <C>S</C> generated by <C>t</C> and there is an idempotent | ||
| <C>e</C> in the R-class of <C>s</C> such that <C>s</C><M>=</M><C>et</C>. The | ||
| Nambooripad partial order coincides with the natural partial order when | ||
| considering inverse semigroups. |
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Add a reference to NaturalPartialOrder here?
gap/attributes/attr.gi
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| "the argument is not a finite semigroup,"); | ||
| elif not IsRegularSemigroup(S) then | ||
| ErrorNoReturn("Semigroups: NambooripadPartialOrder: usage,\n", | ||
| "the argument is not an inverse semigroup,"); |
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"an inverse" -> "a regular"
gap/attributes/attr.gi
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| if not IsRegularSemigroup(S) then | ||
| ErrorNoReturn("Semigroups: NambooripadLeqRegularSemigroup: usage,\n", | ||
| "the argument is not an inverse semigroup,"); |
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"an inverse" -> "a regular"
gap/attributes/attr.gi
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| ErrorNoReturn("Semigroups: NambooripadLeqRegularSemigroup: usage,\n", | ||
| "the argument is not a finite semigroup,"); | ||
| fi; | ||
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Remove this blank line and replace the next if not IsRegular... by elif not IsRegular...
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One other comment would be to perhaps make an issue suggesting that specialised methods for |
The NambooripadPartialOrder is a generalization of the natural partial order for inverse semigroups to the class of regular semigroups. These functions are modelled on the fallback methods for NaturalPartialOrder and NaturalLeqInverseSemigroup. As I do not have a current use for this, I haven't specialized the methods for any particular representations of regular semigroups.
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Thanks @james-d-mitchell. I believe I have now fixed all these typos, added appropriate references to |
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| <C>NambooripadPartialOrder</C> returns the Nambooripad partial order on the | ||
| regular semigroup <A>S</A> as a list of sets of positive integers where | ||
| entry <C>i</C> in <C>NaturalPartialOrder(<A>S</A>)</C> is the set of |
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NaturalPartialOrder -> NambooripadPartialOrder
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The Nambooripad partial order is a generalization of the natural partial
order for inverse semigroups to the class of regular semigroups. These
functions are modelled on the fallback methods for NaturalPartialOrder
and NaturalLeqInverseSemigroup. As I do not have a current use for this,
I haven't specialized the methods for any particular representations of
regular semigroups.
The order is defined on a regular semigroup by is x <= y if the respective
R-classes satisfy R_x <= R_y, and there is an idempotent e in R_x such
that x = e * y.