Description of fast matrix multiplication algorithm: ⟨20×22×24:5950⟩

Algorithm type

33 X^{8} Y^{8} Z^{8} + 10 X^{8} Y^{6} Z^{8} + 2 X^{12} Y^{4} Z^{4} + X^{8} Y^{4} Z^{8} + 7 X^{6} Y^{6} Z^{8} + 2 X^{4} Y^{4} Z^{12} + X^{10} Y^{4} Z^{4} + 2 X^{4} Y^{10} Z^{4} + X^{4} Y^{6} Z^{8} + 15 X^{8} Y^{4} Z^{4} + 13 X^{4} Y^{8} Z^{4} + 13 X^{4} Y^{4} Z^{8} + X^{6} Y^{4} Z^{4} + 4 X^{4} Y^{6} Z^{4} + 3 X^{4} Y^{2} Z^{8} + 487 X^{4} Y^{4} Z^{4} + X^{2} Y^{6} Z^{4} + 60 X^{4} Y^{3} Z^{4} + 27 X^{6} Y^{2} Z^{2} + 14 X^{4} Y^{2} Z^{4} + 42 X^{3} Y^{3} Z^{4} + 15 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 27 X^{2} Y^{2} Z^{6} + 6 X^{5} Y^{2} Z^{2} + 12 X^{2} Y^{5} Z^{2} + 6 X^{2} Y^{3} Z^{4} + 174 X^{4} Y^{2} Z^{2} + 174 X^{2} Y^{4} Z^{2} + 165 X^{2} Y^{2} Z^{4} + 6 X^{3} Y^{2} Z^{2} + 24 X^{2} Y^{3} Z^{2} + 18 X^{2} Y Z^{4} + 1860 X^{2} Y^{2} Z^{2} + 6 X Y^{3} Z^{2} + 90 X^{3} Y Z + 48 X^{2} Y Z^{2} + 90 X Y^{3} Z + 36 X Y^{2} Z^{2} + 90 X Y Z^{3} + 504 X^{2} Y Z + 576 X Y^{2} Z + 522 X Y Z^{2} + 756 X Y Z

Algorithm definition

The algorithm ⟨20×22×24:5950⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×11×12:850⟩.

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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