Description of fast matrix multiplication algorithm: ⟨3×7×7:111⟩

Algorithm type

2 X^{2} Y^{4} Z^{2} + 2 X^{2} Y^{3} Z^{2} + 4 X Y^{5} Z + 32 X^{2} Y^{2} Z^{2} + 4 X Y^{4} Z + 3 X Y^{3} Z^{2} + 6 X^{3} Y Z + X^{2} Y Z^{2} + 6 X Y^{3} Z + 9 X Y^{2} Z^{2} + 6 X Y Z^{3} + 16 X Y^{2} Z + 17 X Y Z^{2} + 3 X Y Z

Algorithm definition

The algorithm ⟨3×7×7:111⟩ is taken from:

Manuel Kauers and Issaac Wood. Exploring the meta flip graph for matrix multiplication. Technical Report 2510.19787, arXiv, October 2025. [ arXiv ]

Algorithm description

maple tensor representation (compressed by bzip2);
maple LRP 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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