Description of fast matrix multiplication algorithm: ⟨10×13×15:1230⟩

Algorithm type

X^{8} Y^{3} Z^{2} + X^{6} Y^{3} Z^{4} + 15 X^{4} Y^{5} Z^{4} + X^{2} Y^{3} Z^{8} + 7 X^{8} Y^{2} Z^{2} + 60 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + X^{2} Y^{2} Z^{8} + X^{6} Y^{3} Z^{2} + 3 X^{4} Y^{3} Z^{4} + 18 X^{2} Y^{3} Z^{6} + 4 X Y^{9} Z + 4 X^{6} Y^{2} Z^{2} + 15 X^{4} Y^{2} Z^{4} + 22 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 11 X^{2} Y^{2} Z^{6} + 4 X Y^{8} Z + 2 X^{4} Y^{3} Z^{2} + 36 X^{2} Y^{5} Z^{2} + 9 X^{2} Y^{3} Z^{4} + 8 X Y^{7} Z + 9 X^{4} Y^{3} Z + 7 X^{4} Y^{2} Z^{2} + 99 X^{2} Y^{4} Z^{2} + 22 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + 8 X^{4} Y^{2} Z + 157 X^{2} Y^{3} Z^{2} + 8 X Y^{5} Z + 50 X Y^{3} Z^{3} + 15 X^{4} Y Z + 24 X^{2} Y^{3} Z + 101 X^{2} Y^{2} Z^{2} + 17 X Y^{4} Z + 20 X Y^{3} Z^{2} + 36 X Y^{2} Z^{3} + 26 X^{2} Y^{2} Z + 30 X^{2} Y Z^{2} + 123 X Y^{3} Z + 15 X Y^{2} Z^{2} + 10 X Y Z^{3} + 25 X^{2} Y Z + 82 X Y^{2} Z + 40 X Y Z^{2} + 60 X Y Z

Algorithm definition

The algorithm ⟨10×13×15:1230⟩ 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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