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Incorrect implications from IsMapping to IsNearRingElement, resp. IsGeneralMapping to IsNearAdditiveElementWithInverse #12
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@PMayr any thoughts on this? |
The intention for these definitions was clearly to capture only mappings whose domain and codomain are the same group, e.g., endomorphisms on a group, in order to be able to define a sum of these mappings. |
If you want the same domain and codomain, then, as you probably know So I guess one could use But even there I am a bit sceptical that this is the way to go. For starters, what is the sum of two mappings between multiplicative groups supposed to be? |
Since groups in GAP are multiplicative in general, we were sort of forced to define the addition of functions on groups as pointwise multiplication in Sonata. This is in line with the notation of nearrings of functions on groups as structures with addition (interpreted as pointwise multiplication) and multiplication (interpreted as composition of functions). I followed your suggestion to define
in grptfms.gd and adapted some other filters in grptfms.gi (I've not submitted them to github yet but I can if you want to see them). Anyways, something seems to go wrong with this implication in the example below. Although b is first not recognized as IsNearAdditiveElementWithInverse, it is
Although b is first not recognized as IsNearAdditive |
The above output means that |
Right, thanks. I can make the changes if you think this would rectify the existing problems outside of Sonata. Or is something else needed? |
That would be great, thank you. But I'll have to see and test the changes to be able to tell if they suffice (but I think this is very likely) |
@PMayr please let me know when you make the change, then I can test it from this side, and then perhaps a new release with the fix in it can be made. |
@PMayr any news on this? |
Sorry, I lost track of this but hope to be able to get back to it in
February.
Peter
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Getting back to the problem of the following declarations in sonata: InstallTrueMethod( IsNearRingElement, IsMapping ); As mentioned before these should capture mappings (not necessarily homomorphisms) whose domain and codomain are the same group. So I think IsMapping/IsGeneralMapping could safely be replaced by IsEndoMapping/IsEndoGeneralMapping. |
So I thought a bit about this... I think So, if that change results in working code for you, that'd be OK, I guess. |
The following lines of code in Sonata are incorrect and break other things in GAP (see gap-system/gap#2818)
They are incorrect because they essentially claim that all (general) mappings are near ring elements resp. near additive elements with inverse, which simply is not true. In particular, in general such mappings cannot be added.
I do not know enough about Sonata to suggest an appropriate fix, other than to remove the offending lines, but clearly that breaks other things in Sonata.
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