Description of fast matrix multiplication algorithm: ⟨14×18×20:2958⟩

Algorithm type

12 X^{4} Y^{8} Z^{6} + 3 X^{4} Y^{10} Z^{2} + 30 X^{4} Y^{8} Z^{4} + 3 X^{4} Y^{9} Z^{2} + 3 X^{3} Y^{10} Z^{2} + 15 X^{4} Y^{8} Z^{2} + 66 X^{4} Y^{4} Z^{6} + 8 X^{3} Y^{9} Z^{2} + 4 X^{2} Y^{4} Z^{8} + 5 X^{3} Y^{8} Z^{2} + 2 X^{2} Y^{10} Z + 5 X^{2} Y^{9} Z^{2} + 12 X^{2} Y^{8} Z^{3} + X Y^{11} Z + 2 X Y^{10} Z^{2} + 165 X^{4} Y^{4} Z^{4} + 3 X^{3} Y^{7} Z^{2} + 7 X^{2} Y^{9} Z + 39 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{4} Z^{6} + 22 X^{2} Y^{2} Z^{8} + X^{4} Y^{5} Z^{2} + 12 X^{2} Y^{8} Z + 48 X^{2} Y^{6} Z^{3} + X Y^{9} Z + 4 X^{4} Y^{5} Z + 66 X^{4} Y^{4} Z^{2} + 123 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 132 X^{2} Y^{2} Z^{6} + X^{4} Y^{4} Z + 8 X^{3} Y^{5} Z + 2 X^{3} Y^{4} Z^{2} + 48 X^{2} Y^{6} Z + 24 X^{2} Y^{4} Z^{3} + 4 X Y^{4} Z^{4} + 4 X^{3} Y^{4} Z + 9 X^{2} Y^{5} Z + 85 X^{2} Y^{4} Z^{2} + 132 X^{2} Y^{2} Z^{4} + 6 X Y^{5} Z^{2} + 24 X Y^{4} Z^{3} + 16 X Y^{3} Z^{4} + X^{3} Y^{3} Z + 36 X^{2} Y^{4} Z + 108 X^{2} Y^{2} Z^{3} + 6 X Y^{5} Z + 25 X Y^{4} Z^{2} + 96 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + X^{2} Y^{3} Z + 380 X^{2} Y^{2} Z^{2} + 24 X Y^{4} Z + 96 X Y^{3} Z^{2} + 48 X Y^{2} Z^{3} + 36 X Y Z^{4} + 108 X^{2} Y^{2} Z + 80 X Y^{3} Z + 48 X Y^{2} Z^{2} + 216 X Y Z^{3} + 40 X Y^{2} Z + 216 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨14×18×20:2958⟩ is serendipitous tensor product (⟨2×6×5:47⟩ - 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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