Description of fast matrix multiplication algorithm: ⟨10×21×24:2984⟩

Algorithm type

4 X^{4} Y^{4} Z^{6} + 252 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z^{2} + 8 X^{3} Y^{4} Z^{4} + 68 X^{2} Y^{6} Z^{3} + 4 X^{4} Y^{2} Z^{4} + 44 X^{3} Y^{4} Z^{3} + 252 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 8 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + 96 X Y^{6} Z^{3} + 4 X^{3} Y^{3} Z^{3} + 8 X Y^{6} Z^{2} + 80 X^{4} Y^{2} Z^{2} + 168 X^{2} Y^{4} Z^{2} + 64 X^{2} Y^{3} Z^{3} + 84 X^{2} Y^{2} Z^{4} + 140 X Y^{6} Z + 24 X^{2} Y^{4} Z + 20 X^{2} Y^{3} Z^{2} + 28 X^{2} Y^{2} Z^{3} + 8 X Y^{4} Z^{2} + 104 X Y^{3} Z^{3} + 4 X Y^{2} Z^{4} + 80 X^{2} Y^{3} Z + 436 X^{2} Y^{2} Z^{2} + 40 X Y^{4} Z + 64 X Y^{3} Z^{2} + 24 X Y^{2} Z^{3} + 4 X^{2} Y Z^{2} + 120 X Y^{3} Z + 8 X Y^{2} Z^{2} + 8 X Y Z^{3} + 80 X^{2} Y Z + 300 X Y^{2} Z + 136 X Y Z^{2} + 184 X Y Z

Algorithm definition

The algorithm ⟨10×21×24:2984⟩ is serendipitous tensor product (⟨2×3×4:20⟩ - 8) ⊗ ⟨5×7×6:150⟩ +4⟨5×7×12:296⟩.

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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