Description of fast matrix multiplication algorithm: ⟨22×32×32:12068⟩

Algorithm type

160 X^{8} Y^{8} Z^{8} + 3 X^{18} Y^{2} Z^{2} + 2 X^{2} Y^{18} Z^{2} + 3 X^{2} Y^{2} Z^{18} + 42 X^{12} Y^{4} Z^{4} + 42 X^{8} Y^{8} Z^{4} + 42 X^{4} Y^{12} Z^{4} + 52 X^{4} Y^{8} Z^{8} + 42 X^{4} Y^{4} Z^{12} + 5 X^{12} Y^{4} Z^{2} + 2 X^{8} Y^{8} Z^{2} + 4 X^{4} Y^{12} Z^{2} + 6 X^{2} Y^{12} Z^{4} + 4 X^{2} Y^{8} Z^{8} + 8 X^{2} Y^{4} Z^{12} + 4 X^{12} Y^{2} Z^{2} + 26 X^{8} Y^{4} Z^{4} + 90 X^{4} Y^{8} Z^{4} + 16 X^{4} Y^{4} Z^{8} + 15 X^{2} Y^{12} Z^{2} + X^{2} Y^{2} Z^{12} + 3 X^{8} Y^{4} Z^{2} + 5 X^{6} Y^{6} Z^{2} + 8 X^{6} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{6} + 15 X^{4} Y^{8} Z^{2} + 5 X^{4} Y^{4} Z^{6} + 26 X^{2} Y^{8} Z^{4} + 5 X^{2} Y^{6} Z^{6} + 2 X^{2} Y^{4} Z^{8} + X^{8} Y^{2} Z^{2} + 17 X^{6} Y^{4} Z^{2} + X^{6} Y^{2} Z^{4} + 3 X^{4} Y^{6} Z^{2} + 1327 X^{4} Y^{4} Z^{4} + 4 X^{4} Y^{2} Z^{6} + 22 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 17 X^{2} Y^{4} Z^{6} + 18 X^{9} Y Z + 12 X Y^{9} Z + 18 X Y Z^{9} + 322 X^{6} Y^{2} Z^{2} + 334 X^{4} Y^{4} Z^{2} + X^{4} Y^{2} Z^{4} + 321 X^{2} Y^{6} Z^{2} + 386 X^{2} Y^{4} Z^{4} + 322 X^{2} Y^{2} Z^{6} + 30 X^{6} Y^{2} Z + 12 X^{4} Y^{4} Z + 24 X^{2} Y^{6} Z + 36 X Y^{6} Z^{2} + 24 X Y^{4} Z^{4} + 48 X Y^{2} Z^{6} + 24 X^{6} Y Z + 192 X^{4} Y^{2} Z^{2} + 685 X^{2} Y^{4} Z^{2} + 129 X^{2} Y^{2} Z^{4} + 90 X Y^{6} Z + 6 X Y Z^{6} + 18 X^{4} Y^{2} Z + 30 X^{3} Y^{3} Z + 48 X^{3} Y^{2} Z^{2} + 36 X^{3} Y Z^{3} + 90 X^{2} Y^{4} Z + 30 X^{2} Y^{2} Z^{3} + 156 X Y^{4} Z^{2} + 30 X Y^{3} Z^{3} + 12 X Y^{2} Z^{4} + 6 X^{4} Y Z + 102 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 18 X^{2} Y^{3} Z + 2269 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 132 X Y^{4} Z + 6 X Y^{3} Z^{2} + 102 X Y^{2} Z^{3} + 420 X^{3} Y Z + 492 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 414 X Y^{3} Z + 444 X Y^{2} Z^{2} + 420 X Y Z^{3} + 216 X^{2} Y Z + 870 X Y^{2} Z + 198 X Y Z^{2} + 402 X Y Z

Algorithm definition

The algorithm ⟨22×32×32:12068⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨11×16×16:1724⟩.

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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