Description of fast matrix multiplication algorithm: ⟨10×15×16:1482⟩

Algorithm type

32 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{12} Z^{2} + X^{4} Y^{8} Z^{3} + X^{4} Y^{6} Z^{5} + 4 X^{4} Y^{4} Z^{7} + X^{2} Y^{12} Z + 2 X^{4} Y^{8} Z^{2} + 2 X^{4} Y^{6} Z^{4} + 18 X^{4} Y^{4} Z^{6} + 16 X Y^{12} Z + 5 X^{4} Y^{6} Z^{3} + 15 X^{4} Y^{4} Z^{5} + 4 X^{4} Y^{2} Z^{7} + 2 X^{3} Y^{8} Z^{2} + X^{2} Y^{9} Z^{2} + 2 X^{2} Y^{6} Z^{5} + 24 X^{6} Y^{4} Z^{2} + 2 X^{4} Y^{6} Z^{2} + 18 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 2 X^{3} Y^{4} Z^{5} + X^{2} Y^{9} Z + 36 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{6} Z^{4} + 2 X Y^{9} Z^{2} + 4 X^{6} Y^{2} Z^{3} + 4 X^{4} Y^{4} Z^{3} + 2 X^{4} Y^{2} Z^{5} + 10 X^{3} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z + 13 X^{2} Y^{6} Z^{3} + 17 X^{2} Y^{4} Z^{5} + X^{2} Y^{3} Z^{6} + 16 X^{2} Y^{2} Z^{7} + X Y^{6} Z^{4} + 2 X^{6} Y^{2} Z^{2} + 10 X^{4} Y^{4} Z^{2} + 2 X^{3} Y^{4} Z^{3} + 2 X^{3} Y^{2} Z^{5} + 16 X^{2} Y^{6} Z^{2} + 73 X^{2} Y^{4} Z^{4} + X^{2} Y^{3} Z^{5} + 45 X^{2} Y^{2} Z^{6} + 4 X^{2} Y Z^{7} + 10 X Y^{6} Z^{3} + 4 X^{5} Y^{2} Z^{2} + 2 X^{4} Y^{2} Z^{3} + 4 X^{3} Y^{4} Z^{2} + 4 X^{2} Y^{6} Z + 37 X^{2} Y^{4} Z^{3} + 4 X^{2} Y^{3} Z^{4} + 48 X^{2} Y^{2} Z^{5} + 2 X^{2} Y Z^{6} + 7 X Y^{6} Z^{2} + 3 X Y^{4} Z^{4} + 2 X Y^{3} Z^{5} + 3 X Y^{2} Z^{6} + 12 X Y Z^{7} + 6 X^{4} Y^{2} Z^{2} + 26 X^{3} Y^{4} Z + 28 X^{2} Y^{4} Z^{2} + 8 X^{2} Y^{3} Z^{3} + 50 X^{2} Y^{2} Z^{4} + 6 X^{2} Y Z^{5} + 17 X Y^{4} Z^{3} + 7 X Y^{3} Z^{4} + 25 X Y^{2} Z^{5} + 25 X Y Z^{6} + 2 X^{4} Y^{2} Z + 2 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 10 X^{3} Y Z^{3} + 15 X^{2} Y^{4} Z + 38 X^{2} Y^{2} Z^{3} + 28 X Y^{4} Z^{2} + 11 X Y^{3} Z^{3} + 43 X Y^{2} Z^{4} + 25 X Y Z^{5} + 2 X^{3} Y^{2} Z + X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 103 X^{2} Y^{2} Z^{2} + 4 X^{2} Y Z^{3} + 9 X Y^{3} Z^{2} + 44 X Y^{2} Z^{3} + 30 X Y Z^{4} + 49 X^{3} Y Z + 15 X^{2} Y^{2} Z + 5 X^{2} Y Z^{2} + 42 X Y^{3} Z + 63 X Y^{2} Z^{2} + 25 X Y Z^{3} + 3 X^{2} Y Z + 30 X Y^{2} Z + 79 X Y Z^{2} + 14 X Y Z

Algorithm definition

The algorithm ⟨10×15×16:1482⟩ 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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