Description of fast matrix multiplication algorithm: ⟨3×5×5:58⟩

Algorithm type

X^{3} Y^{2} Z + 17 X^{2} Y^{2} Z^{2} + 2 X Y^{4} Z + X Y^{2} Z^{3} + 5 X^{3} Y Z + 2 X^{2} Y^{2} Z + X Y^{3} Z + 2 X Y^{2} Z^{2} + 5 X Y Z^{3} + X^{2} Y Z + 13 X Y^{2} Z + X Y Z^{2} + 7 X Y Z

Algorithm definition

The algorithm ⟨3×5×5:58⟩ is taken from:

Alexandre Sedoglavic and Alexey Vladimirovich Smirnov. The tensor rank of 5×5 matrices multiplication is bounded by 98 and its border rank by 89. Technical Report 2101.12568, arXiv, January 2021.

Algorithm description

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