Description of fast matrix multiplication algorithm: ⟨10×12×15:1122⟩

Algorithm type

2 X^{4} Y^{4} Z^{6} + 14 X^{4} Y^{4} Z^{5} + 12 X^{8} Y^{2} Z^{2} + 62 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 12 X^{2} Y^{8} Z^{2} + 2 X^{6} Y^{2} Z^{3} + X^{2} Y^{2} Z^{7} + 10 X^{6} Y^{2} Z^{2} + 11 X^{4} Y^{2} Z^{4} + 6 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 13 X^{4} Y^{2} Z^{3} + 2 X^{2} Y^{2} Z^{5} + 8 X^{2} Y Z^{6} + 13 X Y Z^{7} + 11 X^{4} Y^{2} Z^{2} + 84 X^{2} Y^{4} Z^{2} + 89 X^{2} Y^{2} Z^{4} + 10 X Y Z^{6} + 24 X^{4} Y^{2} Z + 16 X^{3} Y Z^{3} + 20 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + 48 X Y^{4} Z^{2} + 5 X Y^{3} Z^{3} + 11 X Y Z^{5} + 24 X^{4} Y Z + 110 X^{2} Y^{2} Z^{2} + 37 X^{2} Y Z^{3} + 48 X Y^{4} Z + 34 X Y Z^{4} + 8 X^{3} Y Z + 4 X^{2} Y Z^{2} + 7 X Y^{3} Z + 72 X Y^{2} Z^{2} + 62 X Y Z^{3} + 11 X^{2} Y Z + 48 X Y^{2} Z + 28 X Y Z^{2} + 46 X Y Z

Algorithm definition

The algorithm ⟨10×12×15:1122⟩ is serendipitous tensor product (⟨5×4×5:76⟩ - 36) ⊗ ⟨2×3×3:15⟩ +18⟨4×3×3:29⟩.

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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