Description of fast matrix multiplication algorithm: ⟨10×24×24:3368⟩

Algorithm type

X^{2} Y^{12} Z^{2} + X^{2} Y^{11} Z^{2} + X Y^{12} Z + X^{4} Y^{7} Z^{2} + X^{2} Y^{7} Z^{4} + X Y^{11} Z + X^{6} Y^{4} Z^{2} + 300 X^{4} Y^{4} Z^{4} + X Y^{10} Z + 4 X^{2} Y^{7} Z^{2} + 5 X Y^{9} Z + 13 X^{6} Y^{2} Z^{2} + 7 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 2 X^{2} Y^{7} Z + 108 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 10 X^{2} Y^{2} Z^{6} + 2 X Y^{8} Z + X Y^{7} Z^{2} + 7 X^{5} Y^{2} Z^{2} + 5 X^{2} Y^{6} Z + X^{2} Y^{5} Z^{2} + 5 X Y^{7} Z + 3 X Y^{6} Z^{2} + 90 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 5 X^{3} Y^{3} Z^{2} + 3 X^{2} Y^{5} Z + 503 X^{2} Y^{4} Z^{2} + 5 X^{2} Y^{3} Z^{3} + 103 X^{2} Y^{2} Z^{4} + 40 X Y^{6} Z + 3 X Y^{5} Z^{2} + 13 X^{3} Y^{3} Z + 11 X^{3} Y^{2} Z^{2} + 14 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 3 X^{2} Y^{2} Z^{3} + 14 X Y^{4} Z^{2} + 9 X Y^{3} Z^{3} + 43 X^{2} Y^{3} Z + 607 X^{2} Y^{2} Z^{2} + 134 X Y^{4} Z + 38 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 43 X^{3} Y Z + 127 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 65 X Y^{3} Z + 144 X Y^{2} Z^{2} + 29 X Y Z^{3} + 180 X^{2} Y Z + 285 X Y^{2} Z + 175 X Y Z^{2} + 159 X Y Z

Algorithm definition

The algorithm ⟨10×24×24:3368⟩ is serendipitous tensor product (⟨5×6×6:130⟩ - 24) ⊗ ⟨2×4×4:26⟩ +4⟨2×4×8:51⟩ +8⟨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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