Description of fast matrix multiplication algorithm: ⟨10×25×32:4587⟩

Algorithm type

2 X^{2} Y^{12} Z^{3} + 448 X^{4} Y^{8} Z^{4} + 2 X^{2} Y^{11} Z^{3} + 3 X^{2} Y^{8} Z^{6} + 4 X^{2} Y^{9} Z^{4} + X^{2} Y^{8} Z^{5} + X^{2} Y^{7} Z^{6} + 12 X Y^{12} Z^{2} + 2 X^{2} Y^{9} Z^{3} + 4 X^{2} Y^{8} Z^{4} + X^{2} Y^{7} Z^{5} + 2 X Y^{12} Z + 2 X^{2} Y^{8} Z^{3} + 3 X^{2} Y^{7} Z^{4} + 2 X^{2} Y^{5} Z^{6} + 2 X Y^{10} Z^{2} + 8 X^{6} Y^{4} Z^{2} + 616 X^{2} Y^{8} Z^{2} + X^{2} Y^{7} Z^{3} + X^{2} Y^{5} Z^{5} + X^{2} Y^{4} Z^{6} + 6 X Y^{9} Z^{2} + 13 X Y^{8} Z^{3} + 6 X^{2} Y^{6} Z^{3} + 9 X^{2} Y^{5} Z^{4} + 3 X^{2} Y^{4} Z^{5} + 6 X^{2} Y^{3} Z^{6} + 4 X Y^{9} Z + 16 X Y^{8} Z^{2} + 4 X Y^{7} Z^{3} + 80 X^{4} Y^{4} Z^{2} + 4 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{5} Z^{3} + 154 X^{2} Y^{4} Z^{4} + X^{2} Y^{3} Z^{5} + 4 X^{2} Y^{2} Z^{6} + 171 X Y^{8} Z + 16 X Y^{7} Z^{2} + 5 X Y^{6} Z^{3} + 6 X^{4} Y^{2} Z^{3} + 2 X^{3} Y^{2} Z^{4} + 6 X^{2} Y^{4} Z^{3} + 8 X^{2} Y^{3} Z^{4} + 2 X Y^{7} Z + 11 X Y^{6} Z^{2} + 5 X Y^{5} Z^{3} + 11 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 8 X^{3} Y^{4} Z + 3 X^{3} Y^{2} Z^{3} + 132 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{3} Z^{3} + 12 X^{2} Y^{2} Z^{4} + 4 X Y^{6} Z + 18 X Y^{5} Z^{2} + 11 X Y^{4} Z^{3} + 16 X^{4} Y^{2} Z + 10 X^{4} Y Z^{2} + 7 X^{3} Y^{2} Z^{2} + X^{3} Y Z^{3} + 80 X^{2} Y^{4} Z + 22 X^{2} Y^{2} Z^{3} + 7 X^{2} Y Z^{4} + 3 X Y^{5} Z + 155 X Y^{4} Z^{2} + 11 X Y^{3} Z^{3} + 2 X Y^{2} Z^{4} + 6 X^{3} Y^{2} Z + 9 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 928 X^{2} Y^{2} Z^{2} + 16 X^{2} Y Z^{3} + 132 X Y^{4} Z + 31 X Y^{3} Z^{2} + 24 X Y^{2} Z^{3} + 9 X Y Z^{4} + 16 X^{3} Y Z + 8 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 11 X Y^{3} Z + 34 X Y^{2} Z^{2} + 37 X Y Z^{3} + 176 X^{2} Y Z + 341 X Y^{2} Z + 312 X Y Z^{2} + 277 X Y Z

Algorithm definition

The algorithm ⟨10×25×32:4587⟩ is serendipitous tensor product (⟨5×5×8:144⟩ - 22) ⊗ ⟨2×5×4:32⟩ +6⟨2×5×8:63⟩ +5⟨4×5×4:61⟩.

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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