Description of fast matrix multiplication algorithm: ⟨8×15×28:2128⟩

Algorithm type

40 X^{4} Y^{6} Z^{4} + 15 X Y^{12} Z + 12 X^{2} Y^{9} Z^{2} + 100 X^{4} Y^{4} Z^{4} + 50 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{6} Z^{4} + 12 X^{6} Y^{3} Z^{2} + 8 X^{4} Y^{3} Z^{4} + 8 X^{2} Y^{3} Z^{6} + 33 X Y^{9} Z + 10 X Y^{8} Z^{2} + 30 X^{6} Y^{2} Z^{2} + 20 X^{4} Y^{2} Z^{4} + 144 X^{2} Y^{6} Z^{2} + 20 X^{2} Y^{4} Z^{4} + 20 X^{2} Y^{2} Z^{6} + 5 X Y^{8} Z + 4 X^{4} Y^{3} Z^{2} + 44 X^{2} Y^{3} Z^{4} + 22 X Y^{6} Z^{2} + 10 X^{4} Y^{2} Z^{2} + 15 X^{3} Y^{4} Z + 90 X^{2} Y^{4} Z^{2} + 110 X^{2} Y^{2} Z^{4} + 32 X Y^{6} Z + 10 X Y^{4} Z^{3} + 33 X^{3} Y^{3} Z + 5 X^{2} Y^{4} Z + 34 X^{2} Y^{3} Z^{2} + 69 X Y^{4} Z^{2} + 22 X Y^{3} Z^{3} + 21 X^{3} Y^{2} Z + 11 X^{2} Y^{3} Z + 234 X^{2} Y^{2} Z^{2} + 22 X Y^{4} Z + 121 X Y^{3} Z^{2} + 14 X Y^{2} Z^{3} + 57 X^{3} Y Z + 7 X^{2} Y^{2} Z + 38 X^{2} Y Z^{2} + 90 X Y^{3} Z + 115 X Y^{2} Z^{2} + 38 X Y Z^{3} + 19 X^{2} Y Z + 40 X Y^{2} Z + 209 X Y Z^{2} + 57 X Y Z

Algorithm definition

The algorithm ⟨8×15×28:2128⟩ is the (Kronecker) tensor product of ⟨2×5×7:56⟩ with ⟨4×3×4:38⟩.

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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