Description of fast matrix multiplication algorithm: ⟨9×16×21:1827⟩

Algorithm type

42 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} + 105 X^{4} Y^{4} Z^{4} + 14 X^{2} Y^{8} Z^{2} + 12 X^{6} Y^{3} Z^{2} + 4 X^{2} Y^{8} Z + 6 X^{2} Y^{3} Z^{6} + 24 X Y^{9} Z + 30 X^{6} Y^{2} Z^{2} + 30 X^{4} Y^{4} Z^{2} + 42 X^{4} Y^{2} Z^{4} + 138 X^{2} Y^{6} Z^{2} + 15 X^{2} Y^{2} Z^{6} + 8 X Y^{8} Z + 12 X^{6} Y Z^{2} + 24 X^{4} Y^{3} Z^{2} + 24 X^{2} Y^{6} Z + 6 X^{2} Y Z^{6} + 72 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 144 X^{2} Y^{4} Z^{2} + 72 X Y^{6} Z + 2 X Y^{4} Z^{3} + 24 X^{4} Y Z^{2} + 24 X^{3} Y^{3} Z + 32 X^{2} Y^{4} Z + 54 X^{2} Y^{3} Z^{2} + 12 X Y^{3} Z^{3} + 24 X^{3} Y^{2} Z + 48 X^{2} Y^{3} Z + 199 X^{2} Y^{2} Z^{2} + 62 X Y^{4} Z + 12 X Y^{2} Z^{3} + 20 X^{3} Y Z + 68 X^{2} Y^{2} Z + 42 X^{2} Y Z^{2} + 104 X Y^{3} Z + 10 X Y Z^{3} + 40 X^{2} Y Z + 124 X Y^{2} Z + 70 X Y Z

Algorithm definition

The algorithm ⟨9×16×21:1827⟩ is the (Kronecker) tensor product of ⟨3×4×3:29⟩ with ⟨3×4×7:63⟩.

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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