Description of fast matrix multiplication algorithm: ⟨10×14×15:1314⟩

Algorithm type

5 X^{4} Y^{6} Z^{4} + 3 X^{4} Y^{6} Z^{3} + 2 X^{2} Y^{8} Z^{3} + 48 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z^{2} + 2 X^{6} Y^{2} Z^{3} + 50 X^{4} Y^{4} Z^{3} + 2 X^{2} Y^{8} Z + 8 X^{2} Y^{6} Z^{3} + 10 X^{6} Y^{2} Z^{2} + 16 X^{4} Y^{4} Z^{2} + 8 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{3} Z^{5} + 4 X^{6} Y^{2} Z + 6 X^{4} Y^{4} Z + 4 X^{4} Y^{2} Z^{3} + 21 X^{2} Y^{4} Z^{3} + 5 X^{2} Y^{3} Z^{4} + 77 X^{2} Y^{2} Z^{5} + 4 X Y Z^{7} + 32 X^{4} Y^{2} Z^{2} + 32 X^{2} Y^{4} Z^{2} + 6 X^{2} Y^{3} Z^{3} + 94 X^{2} Y^{2} Z^{4} + 4 X Y^{4} Z^{3} + 12 X^{4} Y^{2} Z + 7 X^{3} Y Z^{3} + 7 X^{2} Y^{4} Z + 5 X^{2} Y^{3} Z^{2} + 109 X^{2} Y^{2} Z^{3} + 10 X Y^{4} Z^{2} + 20 X Y^{3} Z^{3} + 13 X Y Z^{5} + 21 X^{3} Y Z^{2} + 110 X^{2} Y^{2} Z^{2} + 38 X^{2} Y Z^{3} + 6 X Y^{4} Z + 10 X Y^{3} Z^{2} + 67 X Y^{2} Z^{3} + 6 X Y Z^{4} + 12 X^{3} Y Z + 22 X^{2} Y^{2} Z + 67 X^{2} Y Z^{2} + 10 X Y^{3} Z + 63 X Y^{2} Z^{2} + 71 X Y Z^{3} + 38 X^{2} Y Z + 50 X Y^{2} Z + 47 X Y Z^{2} + 42 X Y Z

Algorithm definition

The algorithm ⟨10×14×15:1314⟩ 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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