Description of fast matrix multiplication algorithm: ⟨12×13×15:1442⟩

Algorithm type

8 X^{6} Y^{4} Z^{8} + 16 X^{6} Y^{2} Z^{8} + 72 X^{4} Y^{4} Z^{8} + 16 X^{3} Y^{5} Z^{8} + 8 X^{6} Y^{5} Z^{4} + 8 X^{5} Y^{2} Z^{8} + 8 X^{3} Y^{4} Z^{8} + X^{6} Y^{6} Z^{2} + 16 X^{6} Y^{4} Z^{4} + 8 X^{5} Y^{5} Z^{4} + 4 X^{3} Y^{3} Z^{8} + 4 X^{9} Y^{2} Z^{2} + X^{8} Y^{3} Z^{2} + 5 X^{6} Y^{5} Z^{2} + 2 X Y^{10} Z^{2} + 7 X^{8} Y^{2} Z^{2} + 4 X^{6} Y^{4} Z^{2} + 8 X^{6} Y^{2} Z^{4} + 7 X^{4} Y^{6} Z^{2} + 2 X^{3} Y^{8} Z + 24 X^{3} Y Z^{8} + 2 X^{2} Y^{8} Z^{2} + 84 X^{2} Y^{2} Z^{8} + 12 X Y^{3} Z^{8} + 4 X^{9} Y Z + 2 X^{8} Y^{2} Z + 4 X^{8} Y Z^{2} + 2 X^{7} Y^{3} Z + 2 X^{6} Y^{3} Z^{2} + 2 X^{5} Y^{4} Z^{2} + 8 X^{5} Y^{2} Z^{4} + 13 X^{4} Y^{5} Z^{2} + 2 X^{3} Y^{7} Z + 15 X^{3} Y^{6} Z^{2} + 2 X^{2} Y^{8} Z + 4 X^{2} Y Z^{8} + 8 X Y^{9} Z + X Y^{8} Z^{2} + 10 X^{8} Y Z + 2 X^{7} Y^{2} Z + 4 X^{6} Y^{3} Z + 6 X^{6} Y^{2} Z^{2} + X^{5} Y^{4} Z + 5 X^{5} Y^{3} Z^{2} + 2 X^{3} Y^{6} Z + 12 X^{3} Y^{5} Z^{2} + 4 X^{3} Y^{3} Z^{4} + 2 X^{2} Y^{7} Z + 19 X^{2} Y^{6} Z^{2} + 6 X Y^{8} Z + X Y^{7} Z^{2} + 9 X^{6} Y^{2} Z + 4 X^{5} Y^{3} Z + 5 X^{5} Y^{2} Z^{2} + 5 X^{3} Y^{5} Z + 4 X^{3} Y^{4} Z^{2} + 2 X^{3} Y^{3} Z^{3} + 24 X^{3} Y^{2} Z^{4} + 10 X^{2} Y^{6} Z + 24 X^{2} Y^{5} Z^{2} + 4 X^{2} Y^{3} Z^{4} + 6 X Y^{7} Z + 6 X Y^{6} Z^{2} + X^{6} Y Z + 10 X^{5} Y^{2} Z + 8 X^{4} Y^{3} Z + 3 X^{3} Y^{4} Z + 24 X^{3} Y^{3} Z^{2} + 5 X^{3} Y^{2} Z^{3} + 12 X^{3} Y Z^{4} + 9 X^{2} Y^{5} Z + 9 X^{2} Y^{4} Z^{2} + 5 X^{2} Y^{3} Z^{3} + 48 X^{2} Y^{2} Z^{4} + 7 X Y^{6} Z + 12 X Y^{5} Z^{2} + 5 X^{5} Y Z + 41 X^{3} Y^{3} Z + 15 X^{3} Y^{2} Z^{2} + X^{3} Y Z^{3} + X^{2} Y^{4} Z + 33 X^{2} Y^{3} Z^{2} + X^{2} Y^{2} Z^{3} + 4 X^{2} Y Z^{4} + 5 X Y^{5} Z + 5 X Y^{3} Z^{3} + 58 X^{3} Y^{2} Z + 48 X^{3} Y Z^{2} + 33 X^{2} Y^{3} Z + 161 X^{2} Y^{2} Z^{2} + 2 X Y^{4} Z + 32 X Y^{3} Z^{2} + X Y^{2} Z^{3} + 48 X Y Z^{4} + 43 X^{3} Y Z + 9 X^{2} Y^{2} Z + 4 X^{2} Y Z^{2} + 24 X Y^{3} Z + 8 X Y^{2} Z^{2} + 6 X^{2} Y Z + 12 X Y^{2} Z + 116 X Y Z

Algorithm definition

The algorithm ⟨12×13×15:1442⟩ 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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