Description of fast matrix multiplication algorithm: ⟨10×12×27:1976⟩

Algorithm type

144 X^{4} Y^{4} Z^{4} + 9 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 2 X^{4} Y^{2} Z^{3} + 19 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{2} Z^{3} + 342 X^{2} Y^{4} Z^{2} + 64 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 6 X^{4} Y Z^{2} + 3 X^{3} Y^{2} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 4 X^{2} Y Z^{4} + 12 X Y^{4} Z^{2} + X^{4} Y Z + 4 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 373 X^{2} Y^{2} Z^{2} + 4 X^{2} Y Z^{3} + 108 X Y^{4} Z + 12 X Y^{2} Z^{3} + 2 X Y Z^{4} + 7 X^{3} Y Z + 36 X^{2} Y^{2} Z + 13 X^{2} Y Z^{2} + 19 X Y^{3} Z + 132 X Y^{2} Z^{2} + 18 X Y Z^{3} + 48 X^{2} Y Z + 258 X Y^{2} Z + 138 X Y Z^{2} + 157 X Y Z

Algorithm definition

The algorithm ⟨10×12×27:1976⟩ is serendipitous tensor product (⟨5×4×9:132⟩ - 8) ⊗ ⟨2×3×3:15⟩ +4⟨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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