Description of fast matrix multiplication algorithm: ⟨8×8×30:1232⟩

Algorithm type

6 X^{6} Y^{4} Z^{4} + X^{4} Y^{4} Z^{6} + X^{2} Y^{4} Z^{8} + 2 X^{6} Y^{4} Z^{2} + 54 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + X^{2} Y^{4} Z^{6} + 8 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 2 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 10 X^{4} Y^{2} Z^{2} + 32 X^{2} Y^{4} Z^{2} + 30 X^{2} Y^{2} Z^{4} + 36 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 6 X Y^{2} Z^{4} + 12 X^{3} Y^{2} Z + 343 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 6 X Y^{2} Z^{3} + 48 X^{3} Y Z + 24 X^{2} Y Z^{2} + 12 X Y^{3} Z + 24 X Y^{2} Z^{2} + 60 X^{2} Y Z + 192 X Y^{2} Z + 180 X Y Z^{2} + 114 X Y Z

Algorithm definition

The algorithm ⟨8×8×30:1232⟩ is the (Kronecker) tensor product of ⟨4×4×15:176⟩ with ⟨2×2×2:7⟩.

Algorithm description

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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