Description of fast matrix multiplication algorithm: ⟨10×14×26:2275⟩

Algorithm type

3 X^{8} Y^{8} Z^{8} + X^{8} Y^{6} Z^{8} + 6 X^{6} Y^{10} Z^{6} + X^{4} Y^{14} Z^{4} + 2 X^{8} Y^{6} Z^{6} + X^{8} Y^{4} Z^{8} + 6 X^{6} Y^{8} Z^{6} + X^{4} Y^{12} Z^{4} + 3 X^{6} Y^{6} Z^{6} + X^{6} Y^{4} Z^{8} + X^{4} Y^{12} Z^{2} + 5 X^{4} Y^{10} Z^{4} + X^{2} Y^{14} Z^{2} + X^{8} Y^{2} Z^{6} + 3 X^{6} Y^{4} Z^{6} + 2 X^{4} Y^{10} Z^{2} + 6 X^{4} Y^{8} Z^{4} + 32 X^{4} Y^{6} Z^{6} + 2 X^{4} Y^{8} Z^{2} + 9 X^{4} Y^{6} Z^{4} + 3 X^{2} Y^{10} Z^{2} + 48 X^{2} Y^{6} Z^{6} + 2 X^{4} Y^{6} Z^{2} + 62 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{8} Z^{2} + 6 X^{4} Y^{3} Z^{4} + 36 X^{3} Y^{5} Z^{3} + 6 X^{2} Y^{7} Z^{2} + 12 X^{4} Y^{3} Z^{3} + 6 X^{4} Y^{2} Z^{4} + 36 X^{3} Y^{4} Z^{3} + 24 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 18 X^{3} Y^{3} Z^{3} + 6 X^{3} Y^{2} Z^{4} + 6 X^{2} Y^{6} Z + 30 X^{2} Y^{5} Z^{2} + 6 X Y^{7} Z + X^{4} Y^{2} Z^{2} + 6 X^{4} Y Z^{3} + 18 X^{3} Y^{2} Z^{3} + 12 X^{2} Y^{5} Z + 68 X^{2} Y^{4} Z^{2} + 192 X^{2} Y^{3} Z^{3} + 18 X^{2} Y^{2} Z^{4} + 12 X^{2} Y^{4} Z + 54 X^{2} Y^{3} Z^{2} + 18 X Y^{5} Z + 288 X Y^{3} Z^{3} + 12 X^{2} Y^{3} Z + 325 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 108 X Y^{3} Z + 18 X Y^{2} Z^{2} + 6 X^{2} Y Z + 192 X Y^{2} Z + 108 X Y Z^{2} + 366 X Y Z

Algorithm definition

The algorithm ⟨10×14×26:2275⟩ is the (Kronecker) tensor product of ⟨5×7×13:325⟩ with ⟨2×2×2:7⟩.

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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