The answer says "For rings in which division by 2 is permitted". Is there the same constraint for AlphaEvolve's algorithm?
Edit2: Z_2 has characteristics 2.
Edit: AlphaEvolve claims it works over any field with characteristic 0. It appears Waksman's could be an existing work. From the AlphaEvolve paper: "For 56 years, designing an algorithm with fewer than 49 multiplications over any field with characteristic 0 was an open problem. AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications."
If you don't want to allow division by 2 then there is Winograd's algorithm from 1967 which works over any commutative ring and uses 48 multiplications for 4 x 4.
Edit2: Z_2 has characteristics 2.
Edit: AlphaEvolve claims it works over any field with characteristic 0. It appears Waksman's could be an existing work. From the AlphaEvolve paper: "For 56 years, designing an algorithm with fewer than 49 multiplications over any field with characteristic 0 was an open problem. AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications."