Description of fast matrix multiplication algorithm: ⟨10×18×28:2988⟩

Algorithm type

64 X^{4} Y^{11} Z^{5} + 32 X^{2} Y^{9} Z^{5} + 32 X^{2} Y^{8} Z^{5} + 4 X^{6} Y^{4} Z^{4} + 32 X^{2} Y^{7} Z^{5} + 236 X^{4} Y^{4} Z^{4} + 4 X^{3} Y^{6} Z^{2} + 64 X^{2} Y^{6} Z^{3} + 8 X^{6} Y^{2} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 236 X^{2} Y^{6} Z^{2} + 128 X^{2} Y^{5} Z^{3} + 8 X^{2} Y^{6} Z + 48 X Y^{5} Z^{3} + 72 X^{4} Y^{2} Z^{2} + 108 X^{2} Y^{4} Z^{2} + 80 X^{2} Y^{2} Z^{4} + 108 X Y^{6} Z + 176 X Y^{4} Z^{3} + 8 X^{3} Y^{3} Z + 4 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{3} Z^{2} + 64 X Y^{3} Z^{3} + 16 X^{4} Y Z + 64 X^{2} Y^{3} Z + 432 X^{2} Y^{2} Z^{2} + 80 X Y^{3} Z^{2} + 40 X^{3} Y Z + 8 X^{2} Y^{2} Z + 4 X^{2} Y Z^{2} + 104 X Y^{3} Z + 80 X^{2} Y Z + 244 X Y^{2} Z + 80 X Y Z^{2} + 296 X Y Z

Algorithm definition

The algorithm ⟨10×18×28:2988⟩ is serendipitous tensor product (⟨2×3×4:20⟩ - 8) ⊗ ⟨5×6×7:150⟩ +4⟨5×6×14:297⟩.

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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