Description of fast matrix multiplication algorithm: ⟨6×28×32:3212⟩

Algorithm type

6 X^{4} Y^{12} Z^{4} + 2 X^{2} Y^{16} Z^{2} + 32 X^{2} Y^{12} Z^{5} + 6 X Y^{16} Z + 24 X Y^{12} Z^{5} + 24 X Y^{11} Z^{5} + 15 X^{4} Y^{8} Z^{4} + 30 X^{2} Y^{12} Z^{2} + 72 X^{4} Y^{6} Z^{4} + 50 X Y^{12} Z + 42 X^{2} Y^{9} Z^{2} + 2 X^{2} Y^{8} Z^{3} + 186 X^{4} Y^{4} Z^{4} + 83 X^{2} Y^{8} Z^{2} + 10 X^{2} Y^{7} Z^{2} + 84 X Y^{9} Z + 2 X Y^{8} Z^{2} + 72 X^{4} Y^{2} Z^{4} + 251 X^{2} Y^{6} Z^{2} + 42 X Y^{8} Z + 2 X^{2} Y^{5} Z^{2} + 6 X^{2} Y^{4} Z^{3} + 8 X Y^{7} Z + 184 X^{2} Y^{4} Z^{2} + 88 X Y^{6} Z + 6 X Y^{4} Z^{3} + 192 X^{2} Y^{3} Z^{2} + 4 X Y^{5} Z + 16 X Y^{4} Z^{2} + 4 X Y^{3} Z^{3} + 495 X^{2} Y^{2} Z^{2} + 86 X Y^{4} Z + 8 X Y^{3} Z^{2} + 150 X^{2} Y Z^{2} + 370 X Y^{3} Z + 6 X Y Z^{3} + 300 X Y^{2} Z + 2 X Y Z^{2} + 250 X Y Z

Algorithm definition

The algorithm ⟨6×28×32:3212⟩ is serendipitous tensor product (⟨2×4×8:51⟩ - 17) ⊗ ⟨3×7×4:63⟩ +⟨3×7×12:188⟩ +7⟨3×7×8:126⟩.

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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