Description of fast matrix multiplication algorithm: ⟨2×5×7:56⟩

Algorithm type

4 X^{2} Y^{3} Z^{2} + 10 X^{2} Y^{2} Z^{2} + 5 X Y^{4} Z + 11 X Y^{3} Z + 7 X Y^{2} Z + 19 X Y Z

Algorithm definition

The algorithm ⟨2×5×7:56⟩ is taken from:

John Edward Hopcroft and Leslie R. Kerr. On minimizing the number of multiplication necessary for matrix multiplication. SIAM Journal on Applied Mathematics, 20(1), January 1971. [DOI]

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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