Description of fast matrix multiplication algorithm: ⟨10×15×30:2668⟩

Algorithm type

3 X^{2} Y^{8} Z^{4} + 3 X^{4} Y^{6} Z^{2} + 216 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 3 X^{3} Y^{2} Z^{7} + X^{2} Y^{2} Z^{8} + 3 X^{4} Y^{2} Z^{5} + X^{2} Y^{2} Z^{7} + 6 X Y^{8} Z^{2} + 3 X^{4} Y^{4} Z^{2} + X^{4} Y^{2} Z^{4} + X^{3} Y^{2} Z^{5} + 6 X^{2} Y^{6} Z^{2} + X^{2} Y Z^{7} + X Y Z^{8} + 6 X^{2} Y^{6} Z + X^{2} Y^{3} Z^{4} + 3 X^{2} Y Z^{6} + 2 X Y Z^{7} + 2 X^{5} Y Z^{2} + 27 X^{4} Y^{2} Z^{2} + 4 X^{4} Y Z^{3} + X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 540 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 112 X^{2} Y^{2} Z^{4} + 3 X^{2} Y Z^{5} + 12 X Y^{6} Z + X^{4} Y Z^{2} + 3 X^{3} Y Z^{3} + 6 X^{2} Y^{4} Z + 8 X^{2} Y Z^{4} + 6 X Y^{4} Z^{2} + 6 X^{2} Y^{3} Z + 477 X^{2} Y^{2} Z^{2} + 8 X^{2} Y Z^{3} + 216 X Y^{4} Z + 2 X Y Z^{4} + 60 X^{2} Y^{2} Z + 2 X^{2} Y Z^{2} + 12 X Y^{3} Z + 222 X Y^{2} Z^{2} + 54 X^{2} Y Z + 306 X Y^{2} Z + 222 X Y Z^{2} + 90 X Y Z

Algorithm definition

The algorithm ⟨10×15×30:2668⟩ is serendipitous tensor product (⟨5×5×10:178⟩ - 4) ⊗ ⟨2×3×3:15⟩ +2⟨4×3×3:29⟩.

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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