I can confirm that changing in 
sage.matrix.matrix_generic_dense.Matrix_generic_dense._multiply_classical 
the line from left._entries[m+k]._mul_ to just
left._entries[m+k]* , the code works as expected. So the problem is 
probably the _mul_.

I think this is a general problem that was not discovered before: as far as 
I can see, it's legal for element types to have a cdef _mul_. However, in 
the matrix code, I think it ends up being looked up as a python method. I'm 
not sure that matrix elements always have to inherit from Element, so I'm 
not sure a cython typecast to it is warranted. Changing to "*" and just let 
the coercion framework figure it out is definitely valid, but it should be 
checked if that brings a performance penalty.

Someone should make a ticket and alert the coercion gurus to it.

On Thursday, 6 March 2025 at 16:30:27 UTC-8 Nils Bruin wrote:

> It's probably a matter that ExteriorAlgebraElement has a "cdef _mul_" now. 
> That means in cython code it can access the method if it has enough type 
> information. That's probably why `p*p` works. It looks like in 
> sage.matrix.matrix_generic_dense.Matrix_generic_dense._multiply_classical 
> not enough type info is available on left._entries[m+k] to look up this 
> _mul_ . It may be that the correct typecast, something like "(<Element> 
> left._entries[m+k])" perhaps, does the trick. Or perhaps _mul_ is supposed 
> to be "def" or "cpdef". I doubt the latter, though, since for the most 
> part, multiplication seems to work: the coercion framework can figure out 
> how to do it:
>
> sage: coercion_model.bin_op(p,p,operator.mul)
> 0
>
> it makes sense that matrix multiplication takes a shortcut to avoid the 
> overhead of the coercion framework. But perhaps it doesn't have enough type 
> info.
>
> On Thursday, 6 March 2025 at 15:43:02 UTC-8 Seth Chaiken wrote:
>
>> In Sage 10.4,
>> Ext=ExteriorAlgebra(QQ,['p'])
>> Ext.inject_variables()
>> Mp = matrix(1,1,[[p]])
>> Mp[0,0]*Mp[0,0]
>> -> 0
>> Mp*Mp 
>> FAILS!
>> (This did work in an older version.)
>>
>> --------------------------------------------------------------------------- 
>> TypeError Traceback (most recent call last) Cell In[10], line 1 ----> 1 
>> Mp*Mp File /data/Software/Sage/sage/src/sage/structure/element.pyx:4116, 
>> in sage.structure.element.Matrix.__mul__() 4114 # better be square for 
>> the product to be defined. 4115 if (<Matrix>left)._nrows == 
>> (<Matrix>left)._ncols: -> 4116 return 
>> (<Matrix>left)._matrix_times_matrix_(<Matrix>right) 4117 else: 4118 
>> parent = (<Matrix>left)._parent File 
>> /data/Software/Sage/sage/src/sage/matrix/matrix0.pyx:5675, in 
>> sage.matrix.matrix0.Matrix._matrix_times_matrix_() 5673 return 
>> self._multiply_strassen(right) 5674 else: -> 5675 return 
>> self._multiply_classical(right) 5676 5677 cdef bint 
>> _will_use_strassen(self, Matrix right) except -2: File 
>> /data/Software/Sage/sage/src/sage/matrix/matrix_generic_dense.pyx:323, 
>> in 
>> sage.matrix.matrix_generic_dense.Matrix_generic_dense._multiply_classical
>> () 321 m = i*snc 322 for k in range(snc): --> 323 z += 
>> left._entries[m+k]._mul_(right._entries[k*nc+j]) 324 v[p] = z 325 p += 1 
>> TypeError: 'NotImplementedType' object is not callable
>>
>

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