Description of fast matrix multiplication algorithm: ⟨12×13×14:1370⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 23 X^{5} Y^{4} Z^{4} + 6 X^{3} Y^{4} Z^{6} + 49 X^{4} Y^{4} Z^{4} + X^{2} Y^{2} Z^{8} + 13 X^{3} Y^{4} Z^{4} + X Y^{2} Z^{8} + 23 X^{6} Y^{2} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{6} + 65 X^{5} Y^{2} Z^{2} + 15 X^{3} Y^{4} Z^{2} + 24 X^{3} Y^{2} Z^{4} + 3 X Y^{2} Z^{6} + 4 X^{6} Y Z + 3 X^{5} Y^{2} Z + 125 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{2} Z^{3} + 20 X^{2} Y^{4} Z^{2} + 21 X^{2} Y^{2} Z^{4} + 10 X^{5} Y Z + 6 X^{4} Y^{2} Z + 156 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + 4 X Y^{4} Z^{2} + 18 X^{4} Y Z + 58 X^{3} Y^{2} Z + 66 X^{3} Y Z^{2} + 76 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 2 X Y Z^{4} + 154 X^{3} Y Z + 43 X^{2} Y^{2} Z + 38 X^{2} Y Z^{2} + 9 X Y^{2} Z^{2} + 12 X Y Z^{3} + 131 X^{2} Y Z + 28 X Y^{2} Z + 30 X Y Z^{2} + 87 X Y Z

Algorithm definition

The algorithm ⟨12×13×14:1370⟩ 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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