Description of fast matrix multiplication algorithm: ⟨18×22×24:5166⟩

Algorithm type

12 X^{12} Y^{12} Z^{12} + 40 X^{10} Y^{12} Z^{12} + 12 X^{8} Y^{12} Z^{12} + 68 X^{6} Y^{12} Z^{12} + 28 X^{4} Y^{12} Z^{12} + 16 X^{12} Y^{6} Z^{6} + 44 X^{10} Y^{6} Z^{6} + 5 X^{12} Y^{4} Z^{4} + 16 X^{8} Y^{6} Z^{6} + 31 X^{10} Y^{4} Z^{4} + 160 X^{6} Y^{6} Z^{6} + 240 X^{5} Y^{6} Z^{6} + 51 X^{8} Y^{4} Z^{4} + 100 X^{4} Y^{6} Z^{6} + 408 X^{3} Y^{6} Z^{6} + 31 X^{6} Y^{4} Z^{4} + 176 X^{2} Y^{6} Z^{6} + 54 X^{6} Y^{4} Z^{2} + 96 X^{6} Y^{3} Z^{3} + 54 X^{6} Y^{2} Z^{4} + 8 X^{4} Y^{4} Z^{4} + 264 X^{5} Y^{3} Z^{3} + 30 X^{6} Y^{2} Z^{2} + 44 X^{4} Y^{4} Z^{2} + 96 X^{4} Y^{3} Z^{3} + 44 X^{4} Y^{2} Z^{4} + 186 X^{5} Y^{2} Z^{2} + 528 X^{3} Y^{3} Z^{3} + 306 X^{4} Y^{2} Z^{2} + 28 X^{2} Y^{4} Z^{2} + 168 X^{2} Y^{3} Z^{3} + 28 X^{2} Y^{2} Z^{4} + 186 X^{3} Y^{2} Z^{2} + 48 X Y^{3} Z^{3} + 324 X^{3} Y^{2} Z + 324 X^{3} Y Z^{2} + 48 X^{2} Y^{2} Z^{2} + 264 X^{2} Y^{2} Z + 264 X^{2} Y Z^{2} + 168 X Y^{2} Z + 168 X Y Z^{2}

Algorithm definition

The algorithm ⟨18×22×24:5166⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×11×12:738⟩.

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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