Description of fast matrix multiplication algorithm: ⟨15×15×16:2132⟩

Algorithm type

12 X^{6} Y^{4} Z^{4} + 8 X Y^{12} Z + 8 X Y Z^{12} + 54 X^{5} Y^{4} Z^{4} + 126 X^{4} Y^{4} Z^{4} + 28 X^{2} Y^{8} Z^{2} + 28 X^{2} Y^{2} Z^{8} + 8 X Y^{8} Z^{2} + 8 X Y^{2} Z^{8} + 126 X^{6} Y^{2} Z^{2} + 56 X^{4} Y^{2} Z^{4} + 24 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 24 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + 16 X Y Z^{8} + 8 X^{6} Y Z^{2} + 36 X^{5} Y^{2} Z^{2} + 60 X^{3} Y^{4} Z^{2} + 16 X^{2} Y Z^{6} + 112 X^{6} Y Z + 190 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 4 X^{3} Y Z^{4} + 96 X^{2} Y^{4} Z^{2} + 92 X^{2} Y^{2} Z^{4} + 8 X Y^{4} Z^{3} + 8 X Y^{3} Z^{4} + 8 X Y Z^{6} + 16 X^{2} Y^{3} Z^{2} + 32 X^{2} Y Z^{4} + 16 X Y^{4} Z^{2} + 24 X Y^{2} Z^{4} + 84 X^{4} Y Z + 168 X^{3} Y^{2} Z + 4 X^{3} Y Z^{2} + 8 X^{2} Y^{3} Z + 164 X^{2} Y^{2} Z^{2} + 8 X^{2} Y Z^{3} + 28 X Y^{4} Z + 8 X Y^{3} Z^{2} + 44 X Y Z^{4} + 4 X^{3} Y Z + 16 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 8 X Y^{3} Z + 24 X Y^{2} Z^{2} + 8 X Y Z^{3} + 52 X^{2} Y Z + 64 X Y^{2} Z + 44 X Y Z^{2} + 28 X Y Z

Algorithm definition

The algorithm ⟨15×15×16:2132⟩ 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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