Description of fast matrix multiplication algorithm: ⟨4×5×8:122⟩

Algorithm type

2X4Y2Z+2X3Y2Z2+12X2Y2Z3+2X3Y2Z+4X3YZ2+18X2Y2Z2+4XY2Z3+8X2Y2Z+8X2YZ2+4XY3Z+16XYZ3+4XY2Z+20XYZ2+18XYZ2X4Y2Z2X3Y2Z212X2Y2Z32X3Y2Z4X3YZ218X2Y2Z24XY2Z38X2Y2Z8X2YZ24XY3Z16XYZ34XY2Z20XYZ218XYZ2*X^4*Y^2*Z+2*X^3*Y^2*Z^2+12*X^2*Y^2*Z^3+2*X^3*Y^2*Z+4*X^3*Y*Z^2+18*X^2*Y^2*Z^2+4*X*Y^2*Z^3+8*X^2*Y^2*Z+8*X^2*Y*Z^2+4*X*Y^3*Z+16*X*Y*Z^3+4*X*Y^2*Z+20*X*Y*Z^2+18*X*Y*Z

Algorithm definition

The algorithm ⟨4×5×8:122⟩ is the (Kronecker) tensor product of ⟨4×5×4:61⟩ with ⟨1×1×2:2⟩.

Algorithm description

Algorithm symmetries

The following group of 2 isotropies acts as a permutation group on algorithm tensor representation:

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.


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