Description of fast matrix multiplication algorithm: ⟨18×20×24:4676⟩

Algorithm type

64 X^{8} Y^{12} Z^{12} + 44 X^{6} Y^{12} Z^{12} + 48 X^{4} Y^{12} Z^{12} + 4 X^{2} Y^{12} Z^{12} + 32 X^{10} Y^{6} Z^{6} + 64 X^{8} Y^{6} Z^{6} + 21 X^{10} Y^{4} Z^{4} + 176 X^{6} Y^{6} Z^{6} + 15 X^{8} Y^{4} Z^{4} + 476 X^{4} Y^{6} Z^{6} + 264 X^{3} Y^{6} Z^{6} + 324 X^{2} Y^{6} Z^{6} + 24 X Y^{6} Z^{6} + 24 X^{6} Y^{4} Z^{2} + 24 X^{6} Y^{2} Z^{4} + 192 X^{5} Y^{3} Z^{3} + 6 X^{4} Y^{4} Z^{2} + 384 X^{4} Y^{3} Z^{3} + 6 X^{4} Y^{2} Z^{4} + 126 X^{5} Y^{2} Z^{2} + 1056 X^{3} Y^{3} Z^{3} + 90 X^{4} Y^{2} Z^{2} + 6 X^{2} Y^{4} Z^{2} + 552 X^{2} Y^{3} Z^{3} + 6 X^{2} Y^{2} Z^{4} + 216 X Y^{3} Z^{3} + 144 X^{3} Y^{2} Z + 144 X^{3} Y Z^{2} + 36 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 36 X Y^{2} Z + 36 X Y Z^{2}

Algorithm definition

The algorithm ⟨18×20×24:4676⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×10×12:668⟩.

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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