Description of fast matrix multiplication algorithm: ⟨12×15×16:1725⟩

Algorithm type

5 X^{4} Y^{6} Z^{5} + 3 X^{4} Y^{2} Z^{9} + X^{6} Y^{2} Z^{6} + X^{4} Y^{6} Z^{4} + 16 X^{4} Y^{4} Z^{6} + 2 X^{4} Y^{2} Z^{8} + 3 X^{2} Y^{4} Z^{8} + 5 X^{6} Y^{2} Z^{5} + 21 X^{4} Y^{4} Z^{5} + X^{4} Y^{2} Z^{7} + 3 X^{2} Y^{8} Z^{3} + 5 X^{2} Y^{4} Z^{7} + 95 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + X^{2} Y^{4} Z^{6} + 7 X^{2} Y^{2} Z^{8} + 4 X^{2} Y Z^{9} + 5 X Y^{2} Z^{9} + 12 X^{9} Y Z + 15 X^{6} Y^{2} Z^{3} + 6 X^{6} Y Z^{4} + 6 X^{4} Y^{4} Z^{3} + 6 X^{4} Y^{3} Z^{4} + 5 X^{4} Y Z^{6} + 8 X^{2} Y^{6} Z^{3} + 5 X^{2} Y^{3} Z^{6} + 4 X^{2} Y^{2} Z^{7} + 6 X Y^{9} Z + X Y^{2} Z^{8} + 6 X Y Z^{9} + 66 X^{6} Y^{2} Z^{2} + 5 X^{6} Y Z^{3} + 18 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{3} Z^{3} + 38 X^{4} Y^{2} Z^{4} + 3 X^{4} Y Z^{5} + 11 X^{3} Y Z^{6} + 58 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{3} Z^{5} + 66 X^{2} Y^{2} Z^{6} + 3 X^{2} Y Z^{7} + 6 X Y^{2} Z^{7} + 6 X^{6} Y^{2} Z + 33 X^{6} Y Z^{2} + 72 X^{4} Y^{2} Z^{3} + 4 X^{4} Y Z^{4} + 6 X^{2} Y^{6} Z + 14 X^{2} Y^{4} Z^{3} + 5 X^{2} Y^{3} Z^{4} + 18 X^{2} Y^{2} Z^{5} + 9 X^{2} Y Z^{6} + 3 X Y^{2} Z^{6} + 9 X Y Z^{7} + 22 X^{6} Y Z + 76 X^{4} Y^{2} Z^{2} + X^{3} Y Z^{4} + 68 X^{2} Y^{4} Z^{2} + 86 X^{2} Y^{2} Z^{4} + 12 X^{2} Y Z^{5} + 24 X Y^{6} Z + 8 X Y^{4} Z^{3} + 2 X Y^{2} Z^{5} + 8 X Y Z^{6} + 6 X^{4} Y^{2} Z + 42 X^{4} Y Z^{2} + 18 X^{3} Y^{3} Z + 35 X^{3} Y Z^{3} + 2 X^{2} Y^{4} Z + 21 X^{2} Y^{3} Z^{2} + 38 X^{2} Y^{2} Z^{3} + 7 X^{2} Y Z^{4} + X Y^{4} Z^{2} + 28 X Y^{3} Z^{3} + X Y^{2} Z^{4} + 5 X Y Z^{5} + 6 X^{4} Y Z + 24 X^{3} Y^{2} Z + 20 X^{3} Y Z^{2} + 27 X^{2} Y^{3} Z + 102 X^{2} Y^{2} Z^{2} + 41 X^{2} Y Z^{3} + 3 X Y^{4} Z + 15 X Y^{3} Z^{2} + 30 X Y^{2} Z^{3} + 8 X Y Z^{4} + 29 X^{3} Y Z + 18 X^{2} Y^{2} Z + 46 X^{2} Y Z^{2} + 29 X Y^{3} Z + 30 X Y^{2} Z^{2} + 22 X Y Z^{3} + 4 X^{2} Y Z + 12 X Y^{2} Z + 26 X Y Z^{2}

Algorithm definition

The algorithm ⟨12×15×16:1725⟩ 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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