Description of fast matrix multiplication algorithm: ⟨10×12×28:2052⟩

Algorithm type

4 X^{2} Y^{12} Z^{2} + 4 X^{2} Y^{11} Z^{2} + 12 X^{4} Y^{4} Z^{6} + 16 X^{2} Y^{10} Z^{2} + 8 X Y^{12} Z + 144 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{8} + 16 X Y^{10} Z + 4 X^{2} Y^{6} Z^{3} + 8 X Y^{9} Z + 12 X^{6} Y^{2} Z^{2} + 80 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 24 X^{2} Y^{2} Z^{6} + 16 X^{2} Y^{4} Z^{3} + 12 X Y^{6} Z^{2} + 12 X^{4} Y^{2} Z^{2} + 264 X^{2} Y^{4} Z^{2} + 84 X^{2} Y^{2} Z^{4} + 64 X Y^{6} Z + 4 X Y^{3} Z^{4} + 4 X^{3} Y^{3} Z + 20 X^{2} Y^{2} Z^{3} + 48 X Y^{4} Z^{2} + 8 X Y^{3} Z^{3} + 16 X Y^{2} Z^{4} + 16 X^{3} Y^{2} Z + 4 X^{2} Y^{3} Z + 252 X^{2} Y^{2} Z^{2} + 96 X Y^{4} Z + 28 X Y^{3} Z^{2} + 32 X Y^{2} Z^{3} + 20 X Y Z^{4} + 20 X^{3} Y Z + 16 X^{2} Y^{2} Z + 92 X Y^{3} Z + 172 X Y^{2} Z^{2} + 40 X Y Z^{3} + 20 X^{2} Y Z + 136 X Y^{2} Z + 140 X Y Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨10×12×28:2052⟩ is serendipitous tensor product (⟨5×3×7:79⟩ - 5) ⊗ ⟨2×4×4:26⟩ +⟨2×4×20:128⟩.

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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