Description of fast matrix multiplication algorithm: ⟨3×3×4:29⟩

Algorithm type

7 X^{2} Y^{2} Z^{2} + X^{3} Y Z + 2 X Y^{3} Z + 2 X Y^{2} Z^{2} + 2 X Y Z^{3} + 4 X Y^{2} Z + 4 X Y Z^{2} + 7 X Y Z

Algorithm definition

The algorithm ⟨3×3×4:29⟩ is taken from:

Alexey Vladimirovich Smirnov. The bilinear complexity and practical algorithms for matrix multiplication. Computational Mathematics and Mathematical Physics, 53(2):1781--1795, December 2013. [DOI]

Algorithm description

Algorithm symmetries

The following group of 2 isotropies acts as a permutation group on algorithm tensor representation:

maple tensor representation (compressed by bzip2);

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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