Description of fast matrix multiplication algorithm: ⟨3×3×3:23⟩

Algorithm type

4 X^{2} Y^{2} Z^{2} + 2 X^{3} Y Z + 2 X Y^{3} Z + 2 X Y Z^{3} + 13 X Y Z

Algorithm definition

The algorithm ⟨3×3×3:23⟩ is taken from:

Julian David Laderman. A noncommutative algorithm for multiplying 3×3 matrices using 23 multiplications. Bulletin of the American Mathematical Society, 82(1):126--128, January 1976. [DOI]

Algorithm description

maple tensor representation (compressed by bzip2);
maple evaluation scheme (compressed by bzip2).

Algorithm symmetries

The following group of 24 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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