Description of fast matrix multiplication algorithm: ⟨15×20×24:4104⟩

Algorithm type

18 X^{6} Y^{4} Z^{4} + 414 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{8} Z^{2} + 72 X^{2} Y^{2} Z^{8} + 234 X^{6} Y^{2} Z^{2} + 144 X^{4} Y^{2} Z^{4} + 72 X Y^{8} Z + 72 X Y Z^{8} + 18 X^{3} Y^{4} Z^{2} + 18 X^{3} Y^{2} Z^{4} + 72 X^{4} Y^{2} Z^{2} + 414 X^{2} Y^{4} Z^{2} + 486 X^{2} Y^{2} Z^{4} + 144 X^{2} Y Z^{4} + 72 X Y^{4} Z^{2} + 72 X Y^{2} Z^{4} + 234 X^{3} Y^{2} Z + 234 X^{3} Y Z^{2} + 414 X^{2} Y^{2} Z^{2} + 72 X Y Z^{4} + 72 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 72 X Y^{2} Z^{2} + 270 X Y^{2} Z + 270 X Y Z^{2}

Algorithm definition

The algorithm ⟨15×20×24:4104⟩ is the (Kronecker) tensor product of ⟨3×4×6:54⟩ with ⟨5×5×4:76⟩.

Algorithm description

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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