Description of fast matrix multiplication algorithm: ⟨15×25×28:5944⟩

Algorithm type

13 X^{6} Y^{4} Z^{4} + 4 X^{9} Y^{2} Z^{2} + 2 X^{6} Y^{4} Z^{2} + 611 X^{4} Y^{4} Z^{4} + 5 X^{2} Y^{6} Z^{4} + 12 X^{9} Y Z + 2 X^{3} Y^{6} Z^{2} + X^{3} Y^{4} Z^{4} + 3 X^{3} Y^{2} Z^{6} + 2 X^{2} Y^{6} Z^{3} + X^{2} Y^{5} Z^{4} + 233 X^{6} Y^{2} Z^{2} + 94 X^{4} Y^{4} Z^{2} + 13 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{2} Z^{5} + 94 X^{2} Y^{6} Z^{2} + X^{2} Y^{5} Z^{3} + 70 X^{2} Y^{4} Z^{4} + 145 X^{2} Y^{2} Z^{6} + 6 X^{6} Y^{2} Z + 4 X^{6} Y Z^{2} + 8 X^{3} Y^{4} Z^{2} + 3 X^{3} Y^{2} Z^{4} + 2 X^{3} Y Z^{5} + 2 X^{2} Y^{5} Z^{2} + 11 X^{2} Y^{4} Z^{3} + 44 X^{2} Y^{3} Z^{4} + 3 X^{2} Y Z^{6} + 8 X Y^{6} Z^{2} + 15 X Y^{4} Z^{4} + 54 X^{6} Y Z + 401 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{2} Z^{3} + 600 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 379 X^{2} Y^{2} Z^{4} + 2 X^{2} Y Z^{5} + 34 X Y^{6} Z + 4 X Y^{5} Z^{2} + 10 X Y^{4} Z^{3} + 2 X Y^{3} Z^{4} + 24 X Y^{2} Z^{5} + 52 X Y Z^{6} + 18 X^{4} Y^{2} Z + 6 X^{4} Y Z^{2} + 6 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 16 X^{3} Y Z^{3} + 34 X^{2} Y^{4} Z + 15 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 5 X^{2} Y Z^{4} + 6 X Y^{5} Z + 40 X Y^{4} Z^{2} + X Y^{3} Z^{3} + 51 X Y^{2} Z^{4} + 18 X Y Z^{5} + 54 X^{4} Y Z + 95 X^{3} Y^{2} Z + 73 X^{3} Y Z^{2} + 24 X^{2} Y^{3} Z + 578 X^{2} Y^{2} Z^{2} + 31 X^{2} Y Z^{3} + 143 X Y^{4} Z + 57 X Y^{3} Z^{2} + 66 X Y^{2} Z^{3} + 74 X Y Z^{4} + 99 X^{3} Y Z + 220 X^{2} Y^{2} Z + 130 X^{2} Y Z^{2} + 52 X Y^{3} Z + 226 X Y^{2} Z^{2} + 73 X Y Z^{3} + 170 X^{2} Y Z + 280 X Y^{2} Z + 158 X Y Z^{2} + 109 X Y Z

Algorithm definition

The algorithm ⟨15×25×28:5944⟩ is serendipitous tensor product (⟨5×5×7:127⟩ - 13) ⊗ ⟨3×5×4:47⟩ +⟨3×5×12:136⟩ +5⟨3×5×8:90⟩.

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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