Description of fast matrix multiplication algorithm: ⟨12×18×27:3375⟩

Algorithm type

27 X^{8} Y^{8} Z^{8} + 108 X^{4} Y^{8} Z^{4} + 54 X^{4} Y^{4} Z^{8} + 162 X^{4} Y^{4} Z^{4} + 108 X^{2} Y^{8} Z^{2} + 216 X^{2} Y^{4} Z^{4} + 432 X^{2} Y^{4} Z^{2} + 216 X^{2} Y^{2} Z^{4} + 216 X Y^{4} Z^{2} + 324 X^{2} Y^{2} Z^{2} + 216 X Y^{4} Z + 432 X Y^{2} Z^{2} + 432 X Y^{2} Z + 216 X Y Z^{2} + 216 X Y Z

Algorithm definition

The algorithm ⟨12×18×27:3375⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨6×6×9:225⟩.

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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