Description of fast matrix multiplication algorithm: ⟨6×16×20:1213⟩

Algorithm type

80 X^{4} Y^{8} Z^{4} + 17 X^{2} Y^{12} Z^{2} + 20 X^{4} Y^{8} Z^{2} + 2 X^{3} Y^{9} Z^{2} + 16 X^{2} Y^{8} Z^{4} + 22 X Y^{12} Z + 2 X^{3} Y^{8} Z^{2} + X^{2} Y^{9} Z^{2} + X Y^{11} Z + 24 X^{6} Y^{4} Z^{2} + 12 X^{2} Y^{9} Z + 130 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{4} Z^{6} + 2 X^{3} Y^{6} Z^{2} + 22 X^{2} Y^{8} Z + 2 X Y^{9} Z + 16 X Y^{8} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 3 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 50 X Y^{8} Z + 14 X^{3} Y^{4} Z^{2} + 10 X^{2} Y^{6} Z + 3 X^{2} Y^{5} Z^{2} + 10 X Y^{7} Z + 24 X^{3} Y^{4} Z + 29 X^{2} Y^{4} Z^{2} + 6 X Y^{6} Z + 24 X Y^{4} Z^{3} + 20 X^{2} Y^{4} Z + 2 X^{2} Y^{3} Z^{2} + 7 X Y^{5} Z + 8 X Y^{4} Z^{2} + 162 X^{2} Y^{2} Z^{2} + 26 X Y^{4} Z + 48 X^{3} Y Z + 58 X^{2} Y^{2} Z + 41 X Y^{3} Z + 32 X Y^{2} Z^{2} + 48 X Y Z^{3} + 16 X^{2} Y Z + 110 X Y^{2} Z + 16 X Y Z^{2} + 37 X Y Z

Algorithm definition

The algorithm ⟨6×16×20:1213⟩ is serendipitous tensor product (⟨3×4×4:38⟩ - 6) ⊗ ⟨2×4×5:32⟩ +3⟨2×8×5:63⟩.

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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