Description of fast matrix multiplication algorithm: ⟨26×32×32:14154⟩

Algorithm type

8 X^{16} Y^{16} Z^{16} + 8 X^{14} Y^{16} Z^{14} + 207 X^{8} Y^{8} Z^{8} + 15 X^{8} Y^{8} Z^{6} + 48 X^{7} Y^{8} Z^{7} + 7 X^{6} Y^{8} Z^{8} + 11 X^{12} Y^{4} Z^{4} + 9 X^{8} Y^{8} Z^{4} + 7 X^{6} Y^{8} Z^{6} + 10 X^{4} Y^{12} Z^{4} + 9 X^{4} Y^{8} Z^{8} + 11 X^{4} Y^{4} Z^{12} + X^{12} Y^{4} Z^{2} + 5 X^{10} Y^{4} Z^{4} + X^{8} Y^{8} Z^{2} + X^{6} Y^{8} Z^{4} + X^{4} Y^{8} Z^{6} + 5 X^{4} Y^{4} Z^{10} + 2 X^{2} Y^{12} Z^{4} + X^{2} Y^{8} Z^{8} + X^{2} Y^{4} Z^{12} + X^{10} Y^{4} Z^{2} + 3 X^{8} Y^{4} Z^{4} + X^{6} Y^{8} Z^{2} + 61 X^{4} Y^{8} Z^{4} + 4 X^{4} Y^{4} Z^{8} + X^{2} Y^{8} Z^{6} + X^{2} Y^{4} Z^{10} + X^{8} Y^{4} Z^{2} + X^{6} Y^{4} Z^{4} + 3 X^{4} Y^{8} Z^{2} + 2 X^{4} Y^{4} Z^{6} + X^{2} Y^{8} Z^{4} + X^{6} Y^{4} Z^{2} + 1576 X^{4} Y^{4} Z^{4} + X^{2} Y^{8} Z^{2} + 90 X^{4} Y^{4} Z^{3} + 42 X^{3} Y^{4} Z^{4} + 147 X^{6} Y^{2} Z^{2} + 110 X^{4} Y^{4} Z^{2} + 42 X^{3} Y^{4} Z^{3} + 114 X^{2} Y^{6} Z^{2} + 108 X^{2} Y^{4} Z^{4} + 147 X^{2} Y^{2} Z^{6} + 6 X^{6} Y^{2} Z + 30 X^{5} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z + 6 X^{3} Y^{4} Z^{2} + 6 X^{2} Y^{4} Z^{3} + 30 X^{2} Y^{2} Z^{5} + 12 X Y^{6} Z^{2} + 6 X Y^{4} Z^{4} + 6 X Y^{2} Z^{6} + 6 X^{5} Y^{2} Z + 45 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{4} Z + 663 X^{2} Y^{4} Z^{2} + 51 X^{2} Y^{2} Z^{4} + 6 X Y^{4} Z^{3} + 6 X Y^{2} Z^{5} + 6 X^{4} Y^{2} Z + 6 X^{3} Y^{2} Z^{2} + 18 X^{2} Y^{4} Z + 12 X^{2} Y^{2} Z^{3} + 6 X Y^{4} Z^{2} + 6 X^{3} Y^{2} Z + 4101 X^{2} Y^{2} Z^{2} + 6 X Y^{4} Z + 486 X^{3} Y Z + 336 X^{2} Y^{2} Z + 324 X Y^{3} Z + 324 X Y^{2} Z^{2} + 486 X Y Z^{3} + 162 X^{2} Y Z + 1782 X Y^{2} Z + 162 X Y Z^{2} + 2214 X Y Z

Algorithm definition

The algorithm ⟨26×32×32:14154⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨13×16×16:2022⟩.

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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