Description of fast matrix multiplication algorithm: ⟨10×12×32:2337⟩

Algorithm type

X^{6} Y^{10} Z^{2} + 4 X^{6} Y^{6} Z^{2} + 18 X^{4} Y^{4} Z^{6} + 2 X^{3} Y^{10} Z + X^{4} Y^{7} Z^{2} + X^{2} Y^{7} Z^{4} + 8 X^{6} Y^{4} Z^{2} + 162 X^{4} Y^{4} Z^{4} + 2 X^{3} Y^{8} Z + 6 X^{2} Y^{6} Z^{4} + 2 X Y^{9} Z^{2} + 7 X^{3} Y^{7} Z + 6 X^{2} Y^{6} Z^{3} + 2 X^{2} Y^{5} Z^{4} + 20 X Y^{9} Z + 2 X^{4} Y^{4} Z^{2} + X^{2} Y^{7} Z + 114 X^{2} Y^{6} Z^{2} + 38 X^{2} Y^{4} Z^{4} + 30 X^{2} Y^{2} Z^{6} + 2 X Y^{7} Z^{2} + X^{4} Y^{3} Z^{2} + X^{3} Y^{5} Z + X^{3} Y^{4} Z^{2} + X^{2} Y^{6} Z + 24 X^{2} Y^{4} Z^{3} + 4 X^{2} Y^{3} Z^{4} + 20 X Y^{6} Z^{2} + X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{3} Z^{2} + 3 X^{2} Y^{5} Z + 295 X^{2} Y^{4} Z^{2} + 94 X^{2} Y^{2} Z^{4} + 106 X Y^{6} Z + 5 X Y^{5} Z^{2} + 20 X^{3} Y^{3} Z + 2 X^{3} Y^{2} Z^{2} + 5 X^{2} Y^{4} Z + 30 X^{2} Y^{2} Z^{3} + 53 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 295 X^{2} Y^{2} Z^{2} + 106 X Y^{4} Z + 46 X Y^{3} Z^{2} + 40 X Y^{2} Z^{3} + 6 X^{3} Y Z + 12 X^{2} Y^{2} Z + 108 X Y^{3} Z + 194 X Y^{2} Z^{2} + 50 X Y Z^{3} + 6 X^{2} Y Z + 170 X Y^{2} Z + 156 X Y Z^{2} + 40 X Y Z

Algorithm definition

The algorithm ⟨10×12×32:2337⟩ is serendipitous tensor product (⟨5×3×8:90⟩ - 6) ⊗ ⟨2×4×4:26⟩ +2⟨2×4×8:51⟩ +⟨2×8×4:51⟩.

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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