Description of fast matrix multiplication algorithm: ⟨15×28×28:6543⟩

Algorithm type

216 X^{4} Y^{6} Z^{4} + 12 X^{4} Y^{6} Z^{2} + 540 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{8} Z + 30 X^{4} Y^{4} Z^{2} + 222 X^{4} Y^{2} Z^{4} + 528 X^{2} Y^{6} Z^{2} + 32 X Y^{8} Z + 108 X^{4} Y^{3} Z^{2} + 11 X^{4} Y^{2} Z^{3} + 5 X^{3} Y^{2} Z^{4} + 24 X^{2} Y^{6} Z + 42 X^{2} Y^{3} Z^{4} + X^{6} Y Z + 304 X^{4} Y^{2} Z^{2} + 23 X^{3} Y^{2} Z^{3} + 672 X^{2} Y^{4} Z^{2} + 116 X^{2} Y^{2} Z^{4} + X^{2} Y Z^{5} + 192 X Y^{6} Z + 6 X^{4} Y^{2} Z + 113 X^{4} Y Z^{2} + 34 X^{3} Y^{2} Z^{2} + 60 X^{2} Y^{4} Z + 114 X^{2} Y^{3} Z^{2} + 8 X^{2} Y^{2} Z^{3} + 48 X^{2} Y Z^{4} + 14 X Y^{4} Z^{2} + 9 X^{4} Y Z + 12 X^{3} Y Z^{2} + 216 X^{2} Y^{3} Z + 763 X^{2} Y^{2} Z^{2} + 22 X^{2} Y Z^{3} + 230 X Y^{4} Z + 84 X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 4 X Y Z^{4} + 4 X^{3} Y Z + 256 X^{2} Y^{2} Z + 160 X^{2} Y Z^{2} + 228 X Y^{3} Z + 96 X Y^{2} Z^{2} + 6 X Y Z^{3} + 210 X^{2} Y Z + 392 X Y^{2} Z + 97 X Y Z^{2} + 200 X Y Z

Algorithm definition

The algorithm ⟨15×28×28:6543⟩ is serendipitous tensor product (⟨5×7×4:104⟩ - 6) ⊗ ⟨3×4×7:63⟩ +3⟨6×4×7:123⟩.

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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