changed an IsGeneratorsOfMagmaWithInverses method ...

[ThomasBreuer]

... that deals with collections of IsMagmaByMultiplicationTableObj:
Really check that the given elements are invertible. Up to now, the method was wrong.

I stumbled over the problem in the context of pull request #4373 and issue #4480.
Here is an example.

gap> M:= MagmaByMultiplicationTable( [[1,1],[1,1]] );
<magma with 2 generators>
gap> elms:= Elements( M );;
gap> IsGeneratorsOfMagmaWithInverses( elms );
true
gap> List( elms, IsMultiplicativeElementWithInverse );
[ true, true ]
gap> List( elms, Inverse );
[ fail, fail ]

Note that the filter IsMultiplicativeElementWithInverse does not mean that the element in question necessarily has an inverse, see the documentation.

After the change, the method can still give a wrong answer if it is called in the case of nonassociative multiplication. Currently (see issue #4480) there is a discussion how to deal with this situation.

(We have quite a few correct methods for IsGeneratorsOfMagmaWithInverses; the default method prints a warning if it cannot return false. The interpretation is that one should provide a meaningful method for the concrete situation if one sees this warning. The method which is now to be changed serves the purpose to avoid the warning. Eventually it would be good to turn it into a safe method.)

[wilfwilson]

I think this is a change for the better.

I think it would be nice if you added your (correct) example to a test file.