Description of fast matrix multiplication algorithm: ⟨10×25×30:4356⟩

Algorithm type

2 X^{2} Y^{12} Z^{4} + 2 X^{6} Y^{8} Z^{2} + 64 X^{4} Y^{8} Z^{4} + 4 X Y^{12} Z^{2} + 2 X^{4} Y^{8} Z^{2} + 2 X^{2} Y^{8} Z^{4} + 11 X^{6} Y^{4} Z^{2} + 352 X^{4} Y^{4} Z^{4} + 4 X^{4} Y^{2} Z^{6} + 4 X^{3} Y^{8} Z + 150 X^{2} Y^{8} Z^{2} + 11 X^{2} Y^{6} Z^{4} + 8 X Y^{9} Z^{2} + 10 X^{4} Y^{2} Z^{5} + 7 X^{3} Y^{2} Z^{6} + 4 X^{2} Y^{8} Z + 4 X Y^{8} Z^{2} + 33 X^{4} Y^{4} Z^{2} + 8 X^{3} Y^{6} Z + 11 X^{3} Y^{2} Z^{5} + 256 X^{2} Y^{6} Z^{2} + 31 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 44 X Y^{8} Z + 2 X^{5} Y Z^{3} + 5 X^{3} Y^{2} Z^{4} + 8 X^{2} Y^{6} Z + X^{2} Y^{2} Z^{5} + 8 X^{2} Y Z^{6} + 12 X Y^{6} Z^{2} + 124 X^{4} Y^{2} Z^{2} + 4 X^{4} Y Z^{3} + 4 X^{3} Y^{4} Z + 18 X^{3} Y^{2} Z^{3} + 289 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 110 X^{2} Y^{2} Z^{4} + 6 X^{2} Y Z^{5} + 88 X Y^{6} Z + X Y Z^{6} + 2 X^{4} Y Z^{2} + 5 X^{3} Y^{2} Z^{2} + 8 X^{3} Y Z^{3} + 48 X^{2} Y^{4} Z + 17 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + 44 X Y^{4} Z^{2} + X Y^{3} Z^{3} + X Y Z^{5} + X^{4} Y Z + 18 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 89 X^{2} Y^{3} Z + 811 X^{2} Y^{2} Z^{2} + 22 X^{2} Y Z^{3} + 124 X Y^{4} Z + 98 X Y^{3} Z^{2} + 3 X Y^{2} Z^{3} + X^{3} Y Z + 65 X^{2} Y^{2} Z + 13 X^{2} Y Z^{2} + 160 X Y^{3} Z + 67 X Y^{2} Z^{2} + 8 X Y Z^{3} + 203 X^{2} Y Z + 281 X Y^{2} Z + 188 X Y Z^{2} + 362 X Y Z

Algorithm definition

The algorithm ⟨10×25×30:4356⟩ is serendipitous tensor product (⟨5×5×5:93⟩ - 5) ⊗ ⟨2×5×6:47⟩ +⟨6×5×6:130⟩ +⟨4×5×6:90⟩.

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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