Description of fast matrix multiplication algorithm: ⟨9×28×32:4596⟩

Algorithm type

12 X^{4} Y^{12} Z^{4} + 4 X^{2} Y^{16} Z^{2} + 12 X^{2} Y^{12} Z^{6} + 4 X Y^{16} Z^{3} + 6 X Y^{16} Z + 24 X^{4} Y^{9} Z^{4} + 30 X^{4} Y^{8} Z^{4} + 36 X^{4} Y^{6} Z^{6} + 50 X^{2} Y^{12} Z^{2} + 30 X^{2} Y^{8} Z^{6} + 24 X Y^{12} Z^{3} + 24 X^{2} Y^{9} Z^{4} + 8 X Y^{12} Z^{2} + 120 X^{4} Y^{6} Z^{4} + 106 X^{4} Y^{4} Z^{6} + 30 X^{2} Y^{6} Z^{6} + 36 X Y^{12} Z + 3 X^{3} Y^{4} Z^{6} + 48 X^{2} Y^{9} Z^{2} + 12 X^{2} Y^{8} Z^{3} + X^{2} Y^{2} Z^{9} + 182 X^{4} Y^{4} Z^{4} + 36 X^{4} Y^{2} Z^{6} + 89 X^{2} Y^{8} Z^{2} + 60 X^{2} Y^{6} Z^{4} + 89 X^{2} Y^{4} Z^{6} + 48 X Y^{9} Z^{2} + 34 X Y^{8} Z^{3} + X^{6} Y^{2} Z^{3} + 2 X^{4} Y^{4} Z^{3} + 24 X^{4} Y^{3} Z^{4} + 72 X^{2} Y^{6} Z^{3} + 84 X^{2} Y^{3} Z^{6} + 3 X^{4} Y^{4} Z^{2} + 60 X^{4} Y^{2} Z^{4} + 3 X^{3} Y^{4} Z^{3} + 180 X^{2} Y^{6} Z^{2} + 244 X^{2} Y^{2} Z^{6} + 40 X Y^{8} Z + 60 X Y^{6} Z^{3} + X^{4} Y^{4} Z + 17 X^{4} Y^{2} Z^{3} + 80 X^{2} Y^{4} Z^{3} + 66 X^{2} Y^{3} Z^{4} + 84 X^{2} Y Z^{6} + 48 X Y^{6} Z^{2} + 4 X^{3} Y^{2} Z^{3} + 188 X^{2} Y^{4} Z^{2} + 111 X^{2} Y^{2} Z^{4} + 24 X Y^{6} Z + 108 X Y^{4} Z^{3} + 5 X^{4} Y^{2} Z + 4 X^{2} Y^{4} Z + 112 X^{2} Y^{3} Z^{2} + 77 X^{2} Y^{2} Z^{3} + 42 X^{2} Y Z^{4} + 14 X Y^{4} Z^{2} + 168 X Y^{3} Z^{3} + X^{3} Y^{2} Z + 292 X^{2} Y^{2} Z^{2} + 78 X Y^{4} Z + 124 X Y^{3} Z^{2} + 218 X Y^{2} Z^{3} + 5 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 144 X Y^{3} Z + 84 X Y^{2} Z^{2} + 140 X Y Z^{3} + 164 X Y^{2} Z + 70 X Y Z^{2} + 120 X Y Z

Algorithm definition

The algorithm ⟨9×28×32:4596⟩ is serendipitous tensor product (⟨3×4×8:73⟩ - 2) ⊗ ⟨3×7×4:63⟩ +⟨6×7×4:123⟩.

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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