Description of fast matrix multiplication algorithm: ⟨6×25×25:2309⟩

Algorithm type

8 X Y^{12} Z + 10 X^{6} Y^{4} Z^{2} + 170 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{8} Z^{2} + 10 X^{2} Y^{4} Z^{6} + 6 X^{2} Y^{7} Z^{2} + 4 X Y^{9} Z + 50 X^{6} Y^{2} Z^{2} + 20 X^{4} Y^{4} Z^{2} + 4 X^{3} Y^{6} Z + 78 X^{2} Y^{6} Z^{2} + 20 X^{2} Y^{4} Z^{4} + 50 X^{2} Y^{2} Z^{6} + 36 X Y^{8} Z + 2 X Y^{7} Z^{2} + 4 X Y^{6} Z^{3} + 8 X^{2} Y^{6} Z + 2 X^{2} Y^{5} Z^{2} + 8 X^{2} Y^{4} Z^{3} + 14 X Y^{7} Z + 12 X Y^{6} Z^{2} + 10 X^{4} Y^{2} Z^{2} + 10 X^{3} Y^{4} Z + 277 X^{2} Y^{4} Z^{2} + 10 X^{2} Y^{2} Z^{4} + 51 X Y^{6} Z + 4 X Y^{5} Z^{2} + 10 X Y^{4} Z^{3} + 20 X^{3} Y^{3} Z + 20 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 3 X Y^{5} Z + 20 X Y^{4} Z^{2} + 20 X Y^{3} Z^{3} + 8 X^{4} Y Z + 66 X^{3} Y^{2} Z + 20 X^{2} Y^{3} Z + 338 X^{2} Y^{2} Z^{2} + 131 X Y^{4} Z + 4 X Y^{3} Z^{2} + 66 X Y^{2} Z^{3} + 8 X Y Z^{4} + 80 X^{3} Y Z + 42 X^{2} Y^{2} Z + 39 X Y^{3} Z + 68 X Y^{2} Z^{2} + 80 X Y Z^{3} + 32 X^{2} Y Z + 228 X Y^{2} Z + 32 X Y Z^{2} + 54 X Y Z

Algorithm definition

The algorithm ⟨6×25×25:2309⟩ is serendipitous tensor product (⟨3×5×5:58⟩ - 10) ⊗ ⟨2×5×5:40⟩ +3⟨2×5×10:79⟩ +2⟨4×5×5:76⟩.

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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