Description of fast matrix multiplication algorithm: ⟨14×15×32:3965⟩

Algorithm type

6 X^{4} Y^{10} Z^{6} + 15 X^{4} Y^{10} Z^{4} + 24 X^{4} Y^{8} Z^{6} + 6 X^{4} Y^{10} Z^{2} + 60 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{6} Z^{6} + 42 X^{2} Y^{10} Z^{3} + 2 X^{2} Y^{5} Z^{8} + 24 X^{4} Y^{8} Z^{2} + 15 X^{4} Y^{6} Z^{4} + 66 X^{4} Y^{4} Z^{6} + 105 X^{2} Y^{10} Z^{2} + 8 X^{2} Y^{4} Z^{8} + 42 X^{2} Y^{10} Z + 36 X^{2} Y^{8} Z^{3} + 12 X^{2} Y^{5} Z^{6} + 2 X^{2} Y^{3} Z^{8} + 6 X^{4} Y^{6} Z^{2} + 165 X^{4} Y^{4} Z^{4} + 90 X^{2} Y^{8} Z^{2} + 32 X^{2} Y^{7} Z^{3} + 48 X^{2} Y^{4} Z^{6} + 22 X^{2} Y^{2} Z^{8} + 36 X^{2} Y^{8} Z + 48 X^{2} Y^{6} Z^{3} + 12 X^{2} Y^{5} Z^{4} + 12 X^{2} Y^{3} Z^{6} + 48 X Y^{7} Z^{3} + 66 X^{4} Y^{4} Z^{2} + 120 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{4} Z^{4} + 132 X^{2} Y^{2} Z^{6} + 14 X Y^{5} Z^{4} + 48 X^{2} Y^{6} Z + 10 X^{2} Y^{5} Z^{2} + 24 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{3} Z^{4} + 84 X Y^{5} Z^{3} + 12 X Y^{4} Z^{4} + 162 X^{2} Y^{4} Z^{2} + 132 X^{2} Y^{2} Z^{4} + X Y^{6} Z + 84 X Y^{5} Z^{2} + 72 X Y^{4} Z^{3} + 16 X Y^{3} Z^{4} + 24 X^{2} Y^{4} Z + 27 X^{2} Y^{3} Z^{2} + 96 X^{2} Y^{2} Z^{3} + 70 X Y^{5} Z + 74 X Y^{4} Z^{2} + 96 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + X^{3} Y^{2} Z + 355 X^{2} Y^{2} Z^{2} + 98 X Y^{4} Z + 100 X Y^{3} Z^{2} + 48 X Y^{2} Z^{3} + 32 X Y Z^{4} + 123 X^{2} Y^{2} Z + 84 X Y^{3} Z + 84 X Y^{2} Z^{2} + 192 X Y Z^{3} + 66 X Y^{2} Z + 200 X Y Z^{2} + 160 X Y Z

Algorithm definition

The algorithm ⟨14×15×32:3965⟩ is serendipitous tensor product (⟨2×5×8:63⟩ - 21) ⊗ ⟨7×3×4:63⟩ +⟨7×3×12:188⟩ +8⟨7×3×8:126⟩ +⟨7×6×4:123⟩.

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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