Description of fast matrix multiplication algorithm: ⟨8×18×30:2535⟩

Algorithm type

3 X^{4} Y^{12} Z^{4} + 36 X^{4} Y^{8} Z^{4} + 6 X^{2} Y^{12} Z^{2} + 6 X^{4} Y^{8} Z^{2} + 198 X^{4} Y^{4} Z^{4} + 78 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{8} Z + 156 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 48 X Y^{8} Z + 270 X^{2} Y^{4} Z^{2} + 198 X^{2} Y^{2} Z^{4} + 156 X Y^{6} Z + 12 X^{2} Y^{4} Z + 36 X Y^{4} Z^{2} + 324 X^{2} Y^{2} Z^{2} + 84 X Y^{4} Z + 144 X Y^{3} Z^{2} + 12 X Y^{3} Z + 72 X Y^{2} Z^{2} + 324 X Y^{2} Z + 324 X Y Z^{2}

Algorithm definition

The algorithm ⟨8×18×30:2535⟩ is serendipitous tensor product (⟨2×6×5:47⟩ - 2) ⊗ ⟨4×3×6:54⟩ +⟨4×6×6:105⟩.

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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