Description of fast matrix multiplication algorithm: ⟨20×20×27:6032⟩

Algorithm type

4 X^{6} Y^{12} Z^{3} + 68 X^{6} Y^{8} Z^{6} + 8 X^{12} Y^{4} Z^{3} + 4 X^{6} Y^{4} Z^{9} + 20 X^{3} Y^{12} Z^{3} + 8 X^{6} Y^{8} Z^{3} + 4 X^{9} Y^{4} Z^{3} + 8 X^{6} Y^{4} Z^{6} + 20 X^{3} Y^{4} Z^{9} + 4 X^{2} Y^{12} Z + 4 X^{3} Y^{8} Z^{3} + 20 X Y^{12} Z + 52 X^{6} Y^{4} Z^{3} + 4 X^{3} Y^{4} Z^{6} + 64 X^{8} Y^{2} Z^{2} + 32 X^{4} Y^{6} Z^{2} + 544 X^{4} Y^{4} Z^{4} + 32 X^{4} Y^{2} Z^{6} + 68 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z + 32 X^{6} Y^{2} Z^{2} + 64 X^{4} Y^{4} Z^{2} + 64 X^{4} Y^{2} Z^{4} + 28 X^{3} Y^{4} Z^{3} + 160 X^{2} Y^{6} Z^{2} + 160 X^{2} Y^{2} Z^{6} + 4 X Y^{8} Z + 8 X^{4} Y^{4} Z + 4 X^{2} Y^{4} Z^{3} + 416 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 40 X^{2} Y^{4} Z^{2} + 32 X^{2} Y^{2} Z^{4} + 20 X Y^{4} Z^{3} + 52 X^{2} Y^{4} Z + 4 X Y^{4} Z^{2} + 128 X^{4} Y Z + 64 X^{2} Y^{3} Z + 1312 X^{2} Y^{2} Z^{2} + 64 X^{2} Y Z^{3} + 28 X Y^{4} Z + 64 X^{3} Y Z + 128 X^{2} Y^{2} Z + 128 X^{2} Y Z^{2} + 320 X Y^{3} Z + 320 X Y Z^{3} + 832 X^{2} Y Z + 64 X Y^{2} Z + 64 X Y Z^{2} + 448 X Y Z

Algorithm definition

The algorithm ⟨20×20×27:6032⟩ is the (Kronecker) tensor product of ⟨5×5×3:58⟩ with ⟨4×4×9:104⟩.

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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