Description of fast matrix multiplication algorithm: ⟨12×16×21:2385⟩

Algorithm type

60 X^{4} Y^{6} Z^{4} + 6 X Y^{12} Z + 18 X^{2} Y^{9} Z^{2} + 12 X^{4} Y^{6} Z^{2} + 150 X^{4} Y^{4} Z^{4} + 20 X^{2} Y^{8} Z^{2} + 12 X^{6} Y^{3} Z^{2} + 12 X^{4} Y^{3} Z^{4} + 4 X^{2} Y^{8} Z + 18 X^{2} Y^{3} Z^{6} + 36 X Y^{9} Z + 39 X^{6} Y^{2} Z^{2} + 30 X^{4} Y^{4} Z^{2} + 108 X^{4} Y^{2} Z^{4} + 171 X^{2} Y^{6} Z^{2} + 45 X^{2} Y^{2} Z^{6} + 2 X Y^{8} Z + 2 X^{6} Y^{2} Z + 12 X^{6} Y Z^{2} + 9 X^{5} Y^{2} Z^{2} + 36 X^{4} Y^{3} Z^{2} + 29 X^{4} Y^{2} Z^{3} + 12 X^{4} Y Z^{4} + 24 X^{2} Y^{6} Z + 6 X^{2} Y^{3} Z^{4} + 18 X^{2} Y Z^{6} + 3 X^{6} Y Z + 134 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 9 X^{3} Y^{2} Z^{3} + 139 X^{2} Y^{4} Z^{2} + 17 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 6 X Y^{4} Z^{3} + 8 X^{5} Y Z + 4 X^{4} Y^{2} Z + 52 X^{4} Y Z^{2} + 24 X^{3} Y^{3} Z + 30 X^{3} Y^{2} Z^{2} + X^{3} Y Z^{3} + 36 X^{2} Y^{4} Z + 54 X^{2} Y^{3} Z^{2} + 4 X^{2} Y^{2} Z^{3} + 16 X^{2} Y Z^{4} + 2 X Y^{4} Z^{2} + 36 X Y^{3} Z^{3} + 3 X^{4} Y Z + 30 X^{3} Y^{2} Z + 18 X^{3} Y Z^{2} + 72 X^{2} Y^{3} Z + 171 X^{2} Y^{2} Z^{2} + 25 X^{2} Y Z^{3} + 16 X Y^{4} Z + 12 X Y^{3} Z^{2} + 36 X Y^{2} Z^{3} + 33 X^{3} Y Z + 108 X^{2} Y^{2} Z + 80 X^{2} Y Z^{2} + 54 X Y^{3} Z + 13 X Y^{2} Z^{2} + 31 X Y Z^{3} + 83 X^{2} Y Z + 38 X Y^{2} Z + 17 X Y Z^{2} + 27 X Y Z

Algorithm definition

The algorithm ⟨12×16×21:2385⟩ is serendipitous tensor product (⟨4×4×3:38⟩ - 6) ⊗ ⟨3×4×7:63⟩ +3⟨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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