Description of fast matrix multiplication algorithm: ⟨14×14×22:2632⟩

Algorithm type

X^{12} Y^{12} Z^{14} + X^{8} Y^{10} Z^{14} + X^{8} Y^{12} Z^{8} + 4 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{6} + 3 X^{8} Y^{6} Z^{8} + 2 X^{6} Y^{8} Z^{8} + X^{8} Y^{6} Z^{6} + X^{6} Y^{8} Z^{6} + 5 X^{6} Y^{6} Z^{8} + X^{4} Y^{2} Z^{14} + 6 X^{6} Y^{6} Z^{7} + 3 X^{4} Y^{10} Z^{4} + X^{4} Y^{8} Z^{4} + 16 X^{4} Y^{6} Z^{6} + 6 X^{4} Y^{5} Z^{7} + 6 X^{6} Y^{4} Z^{4} + X^{4} Y^{8} Z^{2} + 7 X^{4} Y^{6} Z^{4} + X^{4} Y^{4} Z^{6} + 24 X^{2} Y^{6} Z^{6} + X^{2} Y^{4} Z^{8} + 2 X^{6} Y^{4} Z^{2} + 131 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{4} Z^{3} + 18 X^{4} Y^{3} Z^{4} + 12 X^{3} Y^{4} Z^{4} + 14 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{3} Z^{3} + 9 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{4} Z^{3} + 30 X^{3} Y^{3} Z^{4} + 8 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 6 X^{2} Y Z^{7} + 18 X^{2} Y^{5} Z^{2} + 16 X^{4} Y^{2} Z^{2} + 58 X^{2} Y^{4} Z^{2} + 96 X^{2} Y^{3} Z^{3} + 50 X^{2} Y^{2} Z^{4} + 36 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 144 X Y^{3} Z^{3} + 6 X Y^{2} Z^{4} + 12 X^{3} Y^{2} Z + 661 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 6 X Y^{2} Z^{3} + 84 X^{3} Y Z + 12 X^{2} Y^{2} Z + 54 X^{2} Y Z^{2} + 48 X Y^{3} Z + 72 X Y^{2} Z^{2} + 36 X Y Z^{3} + 96 X^{2} Y Z + 312 X Y^{2} Z + 300 X Y Z^{2} + 114 X Y Z

Algorithm definition

The algorithm ⟨14×14×22:2632⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×7×11:376⟩.

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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