Description of fast matrix multiplication algorithm: ⟨15×18×20:3123⟩

Algorithm type

3 X^{4} Y^{4} Z^{8} + 6 X^{4} Y^{4} Z^{6} + 18 X^{6} Y^{2} Z^{4} + 306 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{6} + 18 X^{2} Y^{6} Z^{4} + 36 X^{2} Y^{2} Z^{8} + 90 X^{6} Y^{2} Z^{2} + 51 X^{4} Y^{2} Z^{4} + 90 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{6} + 18 X^{6} Y Z^{2} + 12 X^{4} Y^{2} Z^{3} + 18 X Y^{6} Z^{2} + 90 X^{6} Y Z + 324 X^{4} Y^{2} Z^{2} + 6 X^{4} Y Z^{3} + 324 X^{2} Y^{4} Z^{2} + 195 X^{2} Y^{2} Z^{4} + 90 X Y^{6} Z + 54 X^{4} Y Z^{2} + 18 X^{3} Y^{2} Z^{2} + 18 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 36 X^{2} Y Z^{4} + 36 X Y^{4} Z^{2} + 36 X Y^{2} Z^{4} + 18 X^{4} Y Z + 90 X^{3} Y^{2} Z + 90 X^{2} Y^{3} Z + 186 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 18 X Y^{4} Z + 36 X^{2} Y^{2} Z + 234 X^{2} Y Z^{2} + 162 X Y^{2} Z^{2} + 18 X Y Z^{3} + 120 X^{2} Y Z + 108 X Y^{2} Z + 54 X Y Z^{2} + 12 X Y Z

Algorithm definition

The algorithm ⟨15×18×20:3123⟩ is serendipitous tensor product (⟨5×3×5:58⟩ - 6) ⊗ ⟨3×6×4:54⟩ +3⟨6×6×4:105⟩.

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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