Description of fast matrix multiplication algorithm: ⟨15×20×21:3654⟩

Algorithm type

6 X^{4} Y^{9} Z^{2} + 2 X^{2} Y^{12} Z + 102 X^{4} Y^{6} Z^{4} + 10 X Y^{12} Z + 12 X^{8} Y^{3} Z^{2} + 6 X^{4} Y^{3} Z^{6} + 30 X^{2} Y^{9} Z^{2} + 30 X^{8} Y^{2} Z^{2} + 27 X^{4} Y^{6} Z^{2} + 255 X^{4} Y^{4} Z^{4} + 15 X^{4} Y^{2} Z^{6} + 12 X^{2} Y^{9} Z + 34 X^{2} Y^{8} Z^{2} + 12 X^{8} Y Z^{2} + 6 X^{6} Y^{3} Z^{2} + 12 X^{4} Y^{3} Z^{4} + 6 X^{4} Y Z^{6} + 4 X^{2} Y^{8} Z + 30 X^{2} Y^{3} Z^{6} + 60 X Y^{9} Z + 15 X^{6} Y^{2} Z^{2} + 30 X^{4} Y^{4} Z^{2} + 132 X^{4} Y^{2} Z^{4} + 285 X^{2} Y^{6} Z^{2} + 75 X^{2} Y^{2} Z^{6} + 2 X Y^{8} Z + 6 X^{6} Y Z^{2} + 4 X^{4} Y^{4} Z + 84 X^{4} Y^{3} Z^{2} + 12 X^{4} Y Z^{4} + 36 X^{2} Y^{6} Z + 2 X^{2} Y^{4} Z^{3} + 6 X^{2} Y^{3} Z^{4} + 30 X^{2} Y Z^{6} + 24 X^{4} Y^{3} Z + 207 X^{4} Y^{2} Z^{2} + 2 X^{3} Y^{4} Z + 223 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 15 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 10 X Y^{4} Z^{3} + 24 X^{4} Y^{2} Z + 78 X^{4} Y Z^{2} + 12 X^{3} Y^{3} Z + 50 X^{2} Y^{4} Z + 96 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 2 X Y^{4} Z^{2} + 60 X Y^{3} Z^{3} + 20 X^{4} Y Z + 12 X^{3} Y^{2} Z + 166 X^{2} Y^{3} Z + 305 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 26 X Y^{4} Z + 12 X Y^{3} Z^{2} + 60 X Y^{2} Z^{3} + 10 X^{3} Y Z + 176 X^{2} Y^{2} Z + 62 X^{2} Y Z^{2} + 134 X Y^{3} Z + 12 X Y^{2} Z^{2} + 50 X Y Z^{3} + 130 X^{2} Y Z + 94 X Y^{2} Z + 10 X Y Z^{2} + 70 X Y Z

Algorithm definition

The algorithm ⟨15×20×21:3654⟩ is the (Kronecker) tensor product of ⟨3×4×7:63⟩ with ⟨5×5×3:58⟩.

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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