Description of fast matrix multiplication algorithm: ⟨10×15×32:2878⟩

Algorithm type

X^{6} Y^{13} Z^{2} + X^{6} Y^{10} Z^{2} + 24 X^{4} Y^{8} Z^{6} + 8 X^{2} Y^{12} Z^{4} + 7 X^{3} Y^{13} Z + 216 X^{4} Y^{8} Z^{4} + 80 X^{2} Y^{12} Z^{2} + 8 X Y^{12} Z^{2} + 8 X^{6} Y^{6} Z^{2} + X^{3} Y^{10} Z + 49 X^{2} Y^{8} Z^{4} + 80 X Y^{12} Z + X^{6} Y^{5} Z^{2} + 2 X^{3} Y^{9} Z + 24 X^{2} Y^{8} Z^{3} + X^{2} Y^{7} Z^{4} + 4 X^{6} Y^{4} Z^{2} + 3 X^{3} Y^{8} Z + 328 X^{2} Y^{8} Z^{2} + 40 X^{2} Y^{4} Z^{6} + 6 X^{2} Y^{5} Z^{4} + 55 X Y^{8} Z^{2} + 2 X^{6} Y^{2} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 4 X^{3} Y^{6} Z + 125 X^{2} Y^{4} Z^{4} + 112 X Y^{8} Z + 3 X Y^{7} Z^{2} + 6 X^{3} Y^{5} Z + 2 X^{2} Y^{3} Z^{4} + 3 X Y^{6} Z^{2} + 6 X^{3} Y^{4} Z + 32 X^{2} Y^{4} Z^{2} + 2 X^{2} Y^{2} Z^{4} + 6 X Y^{5} Z^{2} + 40 X Y^{4} Z^{3} + 12 X^{3} Y^{3} Z + 8 X^{2} Y^{4} Z + 48 X^{2} Y^{2} Z^{3} + 127 X Y^{4} Z^{2} + 432 X^{2} Y^{2} Z^{2} + 32 X Y^{4} Z + 25 X Y^{3} Z^{2} + 5 X^{3} Y Z + 160 X Y^{3} Z + 102 X Y^{2} Z^{2} + 80 X Y Z^{3} + 16 X^{2} Y Z + 224 X Y^{2} Z + 245 X Y Z^{2} + 64 X Y Z

Algorithm definition

The algorithm ⟨10×15×32:2878⟩ is serendipitous tensor product (⟨5×3×8:90⟩ - 4) ⊗ ⟨2×5×4:32⟩ +2⟨2×5×8:63⟩.

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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