Description of fast matrix multiplication algorithm: ⟨9×20×28:2955⟩

Algorithm type

78 X^{4} Y^{6} Z^{4} + 4 X Y^{12} Z + 12 X^{2} Y^{9} Z^{2} + 12 X^{4} Y^{6} Z^{2} + 195 X^{4} Y^{4} Z^{4} + 26 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{6} Z^{4} + 24 X^{6} Y^{3} Z^{2} + 4 X^{2} Y^{8} Z + 18 X^{2} Y^{3} Z^{6} + 24 X Y^{9} Z + 2 X Y^{8} Z^{2} + 60 X^{6} Y^{2} Z^{2} + 30 X^{4} Y^{4} Z^{2} + 78 X^{4} Y^{2} Z^{4} + 234 X^{2} Y^{6} Z^{2} + 15 X^{2} Y^{4} Z^{4} + 45 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + 24 X^{6} Y Z^{2} + 36 X^{4} Y^{3} Z^{2} + 24 X^{2} Y^{6} Z + 12 X^{2} Y^{3} Z^{4} + 18 X^{2} Y Z^{6} + 12 X Y^{6} Z^{2} + 102 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 276 X^{2} Y^{4} Z^{2} + 50 X^{2} Y^{2} Z^{4} + 120 X Y^{6} Z + 6 X Y^{4} Z^{3} + 36 X^{4} Y Z^{2} + 48 X^{3} Y^{3} Z + 36 X^{2} Y^{4} Z + 24 X^{2} Y^{3} Z^{2} + 22 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + 16 X Y^{4} Z^{2} + 36 X Y^{3} Z^{3} + X Y^{2} Z^{4} + X Y Z^{5} + 48 X^{3} Y^{2} Z + 72 X^{2} Y^{3} Z + 262 X^{2} Y^{2} Z^{2} + 100 X Y^{4} Z + 24 X Y^{3} Z^{2} + 38 X Y^{2} Z^{3} + 7 X Y Z^{4} + 42 X^{3} Y Z + 96 X^{2} Y^{2} Z + 21 X^{2} Y Z^{2} + 44 X Y^{3} Z + 45 X Y^{2} Z^{2} + 45 X Y Z^{3} + 71 X^{2} Y Z + 120 X Y^{2} Z + 70 X Y Z^{2} + 47 X Y Z

Algorithm definition

The algorithm ⟨9×20×28:2955⟩ is serendipitous tensor product (⟨3×5×4:47⟩ - 4) ⊗ ⟨3×4×7:63⟩ +2⟨6×4×7:123⟩.

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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