Description of fast matrix multiplication algorithm: ⟨12×14×15:1538⟩

Algorithm type

96 X^{4} Y^{4} Z^{8} + 32 X^{2} Y^{6} Z^{8} + 6 X^{8} Y^{4} Z^{2} + 4 X^{6} Y^{6} Z^{2} + 32 X^{4} Y^{6} Z^{4} + 12 X^{9} Y^{2} Z^{2} + 2 X^{8} Y^{4} Z + 6 X^{7} Y^{4} Z^{2} + X^{6} Y^{4} Z^{3} + 4 X^{9} Y^{2} Z + 14 X^{8} Y^{2} Z^{2} + 2 X^{7} Y^{4} Z + 21 X^{6} Y^{4} Z^{2} + X^{5} Y^{4} Z^{3} + 4 X^{4} Y^{6} Z^{2} + 2 X^{3} Y^{6} Z^{3} + 4 X^{2} Y^{9} Z + 18 X^{2} Y^{6} Z^{4} + 96 X^{2} Y^{2} Z^{8} + 32 X Y^{3} Z^{8} + 16 X^{9} Y Z + 2 X^{8} Y^{2} Z + 8 X^{7} Y^{3} Z + 10 X^{7} Y^{2} Z^{2} + 3 X^{6} Y^{3} Z^{2} + 9 X^{6} Y^{2} Z^{3} + 5 X^{5} Y^{4} Z^{2} + 4 X^{5} Y^{3} Z^{3} + 2 X^{3} Y^{7} Z + 24 X^{3} Y^{6} Z^{2} + 2 X^{3} Y^{4} Z^{4} + 2 X^{2} Y^{6} Z^{3} + 24 X^{8} Y Z + 6 X^{7} Y^{2} Z + 6 X^{6} Y^{3} Z + 19 X^{6} Y^{2} Z^{2} + 2 X^{5} Y^{3} Z^{2} + 9 X^{5} Y^{2} Z^{3} + 8 X^{4} Y^{4} Z^{2} + 4 X^{3} Y^{6} Z + 2 X^{3} Y^{4} Z^{3} + 14 X^{2} Y^{6} Z^{2} + 16 X^{7} Y Z + 19 X^{6} Y^{2} Z + 13 X^{6} Y Z^{2} + 6 X^{5} Y^{3} Z + 17 X^{5} Y^{2} Z^{2} + 2 X^{3} Y^{5} Z + 14 X^{3} Y^{4} Z^{2} + 6 X^{3} Y^{2} Z^{4} + X^{2} Y^{6} Z + 32 X^{2} Y^{3} Z^{4} + 4 X Y^{6} Z^{2} + 13 X^{6} Y Z + 12 X^{5} Y^{2} Z + 8 X^{5} Y Z^{2} + 3 X^{4} Y^{3} Z + 2 X^{3} Y^{4} Z + 6 X^{3} Y^{3} Z^{2} + 6 X^{3} Y^{2} Z^{3} + 2 X^{2} Y^{4} Z^{2} + 4 X^{2} Y^{3} Z^{3} + 56 X^{2} Y^{2} Z^{4} + 4 X Y^{6} Z + 16 X Y^{3} Z^{4} + 8 X^{5} Y Z + 5 X^{4} Y^{2} Z + 47 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + X^{2} Y^{4} Z + 2 X^{2} Y^{3} Z^{2} + 43 X^{3} Y^{2} Z + 89 X^{2} Y^{3} Z + 192 X^{2} Y^{2} Z^{2} + 64 X Y^{3} Z^{2} + 56 X Y Z^{4} + 23 X^{2} Y^{2} Z + 52 X Y^{3} Z + 112 X Y Z

Algorithm definition

The algorithm ⟨12×14×15:1538⟩ 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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