Description of fast matrix multiplication algorithm: ⟨7×15×16:1083⟩

Algorithm type

40 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{12} Z^{2} + 16 X^{3} Y^{8} Z^{3} + 16 X Y^{12} Z + 4 X^{4} Y^{4} Z^{5} + 20 X^{2} Y^{8} Z^{3} + 8 X^{6} Y^{4} Z^{2} + 4 X^{4} Y^{4} Z^{4} + 4 X^{3} Y^{4} Z^{5} + 52 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + 16 X^{5} Y^{4} Z^{2} + 4 X^{3} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z + 2 X^{2} Y^{6} Z^{3} + 16 X Y^{8} Z^{2} + 2 X^{5} Y^{2} Z^{3} + 11 X^{3} Y^{4} Z^{3} + X^{2} Y^{6} Z^{2} + 42 X^{2} Y^{4} Z^{4} + 5 X^{2} Y^{2} Z^{6} + 12 X Y^{8} Z + X Y^{6} Z^{3} + 4 X^{5} Y^{2} Z^{2} + 2 X^{4} Y^{2} Z^{3} + 3 X^{3} Y^{4} Z^{2} + 3 X^{2} Y^{6} Z + 19 X^{2} Y^{4} Z^{3} + 19 X^{2} Y^{2} Z^{5} + 7 X Y^{6} Z^{2} + 2 X^{5} Y^{2} Z + 3 X^{4} Y^{2} Z^{2} + 21 X^{3} Y^{4} Z + 3 X^{3} Y^{2} Z^{3} + 21 X^{2} Y^{4} Z^{2} + 20 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + 15 X Y^{4} Z^{3} + 6 X Y Z^{6} + X^{4} Y^{2} Z + 9 X^{3} Y^{2} Z^{2} + 8 X^{3} Y Z^{3} + 6 X^{2} Y^{4} Z + 30 X^{2} Y^{2} Z^{3} + 36 X Y^{4} Z^{2} + 7 X Y^{3} Z^{3} + 6 X Y^{2} Z^{4} + 2 X Y Z^{5} + 3 X^{3} Y^{2} Z + 2 X^{3} Y Z^{2} + 115 X^{2} Y^{2} Z^{2} + 16 X^{2} Y Z^{3} + 15 X Y^{4} Z + 29 X Y^{2} Z^{3} + 8 X Y Z^{4} + 46 X^{3} Y Z + 15 X^{2} Y^{2} Z + 3 X^{2} Y Z^{2} + 53 X Y^{3} Z + 58 X Y^{2} Z^{2} + 52 X Y Z^{3} + 13 X^{2} Y Z + 36 X Y^{2} Z + 46 X Y Z^{2} + 14 X Y Z

Algorithm definition

The algorithm ⟨7×15×16:1083⟩ is taken from:

Andrew I. Perminov. FastMatrixMultiplication, GitHub, February 2026. [ GitHub repository ]

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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