Description of fast matrix multiplication algorithm: ⟨14×18×24:3525⟩

Algorithm type

18 X^{4} Y^{8} Z^{6} + 45 X^{4} Y^{8} Z^{4} + 4 X^{4} Y^{9} Z^{2} + 6 X^{2} Y^{10} Z^{3} + 29 X^{4} Y^{8} Z^{2} + 78 X^{4} Y^{4} Z^{6} + 4 X^{3} Y^{9} Z^{2} + 15 X^{2} Y^{10} Z^{2} + 6 X^{2} Y^{4} Z^{8} + 15 X^{3} Y^{8} Z^{2} + 6 X^{2} Y^{10} Z + 4 X^{2} Y^{9} Z^{2} + 42 X^{2} Y^{8} Z^{3} + 195 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{9} Z + 105 X^{2} Y^{8} Z^{2} + 36 X^{2} Y^{4} Z^{6} + 26 X^{2} Y^{2} Z^{8} + X^{5} Y^{5} Z + 4 X^{4} Y^{5} Z^{2} + 47 X^{2} Y^{8} Z + 54 X^{2} Y^{6} Z^{3} + 8 X^{4} Y^{5} Z + 80 X^{4} Y^{4} Z^{2} + 135 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 156 X^{2} Y^{2} Z^{6} + 2 X Y^{5} Z^{4} + 3 X^{4} Y^{4} Z + 3 X^{3} Y^{5} Z + 54 X^{2} Y^{6} Z + 7 X^{2} Y^{5} Z^{2} + 24 X^{2} Y^{4} Z^{3} + 12 X Y^{5} Z^{3} + 14 X Y^{4} Z^{4} + 6 X^{3} Y^{4} Z + 10 X^{2} Y^{5} Z + 98 X^{2} Y^{4} Z^{2} + 156 X^{2} Y^{2} Z^{4} + 12 X Y^{5} Z^{2} + 84 X Y^{4} Z^{3} + 18 X Y^{3} Z^{4} + 34 X^{2} Y^{4} Z + 102 X^{2} Y^{2} Z^{3} + 12 X Y^{5} Z + 87 X Y^{4} Z^{2} + 108 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + X^{4} Y Z + 385 X^{2} Y^{2} Z^{2} + 75 X Y^{4} Z + 108 X Y^{3} Z^{2} + 48 X Y^{2} Z^{3} + 34 X Y Z^{4} + 102 X^{2} Y^{2} Z + 90 X Y^{3} Z + 48 X Y^{2} Z^{2} + 204 X Y Z^{3} + X^{2} Y Z + 40 X Y^{2} Z + 204 X Y Z^{2} + 170 X Y Z

Algorithm definition

The algorithm ⟨14×18×24:3525⟩ is serendipitous tensor product (⟨2×6×6:56⟩ - 2) ⊗ ⟨7×3×4:63⟩ +⟨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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