Description of fast matrix multiplication algorithm: ⟨10×28×30:4785⟩

Algorithm type

8 X^{4} Y^{8} Z^{6} + 472 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{8} Z^{4} + 8 X^{2} Y^{8} Z^{3} + 8 X^{4} Y^{4} Z^{4} + 688 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + X^{3} Y^{2} Z^{6} + 16 X Y^{8} Z^{2} + 152 X^{4} Y^{4} Z^{2} + 2 X^{3} Y^{2} Z^{5} + 96 X^{2} Y^{4} Z^{4} + 5 X^{2} Y^{2} Z^{6} + 216 X Y^{8} Z + 2 X^{4} Y^{2} Z^{3} + 5 X^{3} Y^{2} Z^{4} + 4 X^{2} Y^{2} Z^{5} + 6 X^{2} Y Z^{6} + 11 X Y^{2} Z^{6} + 3 X^{4} Y^{2} Z^{2} + 13 X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 152 X^{2} Y^{4} Z^{2} + 10 X^{2} Y^{2} Z^{4} + 4 X^{2} Y Z^{5} + 8 X Y^{4} Z^{3} + 4 X Y^{2} Z^{5} + X^{4} Y^{2} Z + 6 X^{4} Y Z^{2} + 13 X^{3} Y^{2} Z^{2} + 4 X^{3} Y Z^{3} + 152 X^{2} Y^{4} Z + 33 X^{2} Y^{2} Z^{3} + 9 X^{2} Y Z^{4} + 96 X Y^{4} Z^{2} + X Y^{3} Z^{3} + 9 X Y^{2} Z^{4} + 2 X^{4} Y Z + 4 X^{3} Y^{2} Z + 17 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 957 X^{2} Y^{2} Z^{2} + 31 X^{2} Y Z^{3} + 144 X Y^{4} Z + 4 X Y^{3} Z^{2} + 9 X Y^{2} Z^{3} + 19 X^{3} Y Z + 35 X^{2} Y Z^{2} + 4 X Y^{3} Z + 36 X Y^{2} Z^{2} + 23 X Y Z^{3} + 310 X^{2} Y Z + 432 X Y^{2} Z + 209 X Y Z^{2} + 304 X Y Z

Algorithm definition

The algorithm ⟨10×28×30:4785⟩ is serendipitous tensor product (⟨5×7×6:150⟩ - 10) ⊗ ⟨2×4×5:32⟩ +5⟨4×4×5:61⟩.

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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