I think that google would expect a link to the actual report
Okay!
Computation of various subgroups of infinite finitely presented groups
Can you elaborate on this?
Computation of Galois groups for a given polynomial
This is a whole new world, theory of algebraic numbers, not much group theory.
Finding kernels of homomorphisms with infinite domains
Do you have some idea of how?
Extend functionalities of polycyclic groups
Can you elaborate?
Quotient groups
Of what kind of groups?
Automorphism groups
Of what kind of structures?
Triple Product Property (https://en.wikipedia.org/wiki/Triple_product_property) we can do it for both groups and set
Is there something to implement?
Intersection of subgroups
This could be useful though I don't know of algorithms.
Triple Product Property (https://en.wikipedia.org/wiki/Triple_product_property) we can do it for both groups and set.
Is there something to implement?
As Triple Product Property is a property we have to just implement test for this.I have seen the various algorithms for this property here (https://arxiv.org/pdf/1104.5097.pdf) to save your time you can directly head over to page no. 6 and 7 and page 8 to see the efficiency of each algorithms.
I think to implement this it would not take much time except few problems I am having :
I have thoughts like:
a[i, j]
and b[i, j]
. The entries of their product are sums of n products. That makes n^3 products altogether, and there is no way to reduce the exponent 3.
The application of the triple product property seems to be to multiplication of numerical matrices. I think that NumPy implements that kind of algorithms. SymPy's matrices are typically symbolic which means that the acceleration methods devised for numerical matrices are generally not useful in SymPy. Consider, for example, two nxn matrices with entries
a[i, j]
andb[i, j]
. The entries of their product are sums of n products. That makes n^3 products altogether, and there is no way to reduce the exponent 3.
Yes It exactly focus on fast matrix multiplication and you seems right too.