Description of fast matrix multiplication algorithm: ⟨8×15×20:1498⟩

Algorithm type

104 X^{4} Y^{8} Z^{4} + 32 X^{2} Y^{12} Z^{2} + 16 X^{2} Y^{8} Z^{4} + 32 X Y^{12} Z + 16 X^{6} Y^{4} Z^{2} + 152 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{4} Z^{6} + 2 X^{6} Y^{2} Z^{3} + 2 X^{5} Y^{2} Z^{4} + 16 X Y^{8} Z^{2} + 5 X^{6} Y^{2} Z^{2} + 2 X^{6} Y Z^{3} + 2 X^{5} Y^{2} Z^{3} + 16 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 64 X^{2} Y^{4} Z^{4} + 48 X Y^{8} Z + 6 X^{6} Y^{2} Z + 3 X^{6} Y Z^{2} + 2 X^{5} Y^{2} Z^{2} + X^{4} Y^{2} Z^{3} + X^{4} Y Z^{4} + X^{3} Y^{2} Z^{4} + 2 X^{5} Y^{2} Z + 3 X^{5} Y Z^{2} + 2 X^{4} Y^{2} Z^{2} + 16 X^{3} Y^{4} Z + 6 X^{3} Y^{2} Z^{3} + 5 X^{3} Y Z^{4} + 32 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + 16 X Y^{4} Z^{3} + X^{4} Y^{2} Z + 2 X^{4} Y Z^{2} + X^{3} Y^{3} Z + 9 X^{3} Y^{2} Z^{2} + 5 X^{3} Y Z^{3} + 16 X^{2} Y^{4} Z + X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + 64 X Y^{4} Z^{2} + 4 X^{3} Y^{2} Z + 13 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 209 X^{2} Y^{2} Z^{2} + 7 X^{2} Y Z^{3} + 32 X Y^{4} Z + X Y^{2} Z^{3} + 37 X^{3} Y Z + 5 X^{2} Y Z^{2} + 65 X Y^{3} Z + 32 X Y^{2} Z^{2} + 36 X Y Z^{3} + 36 X^{2} Y Z + 96 X Y^{2} Z + 129 X Y Z^{2} + 68 X Y Z

Algorithm definition

The algorithm ⟨8×15×20:1498⟩ is serendipitous tensor product (⟨4×3×5:47⟩ - 4) ⊗ ⟨2×5×4:32⟩ +2⟨4×5×4:61⟩.

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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