Description of fast matrix multiplication algorithm: ⟨15×20×25:4371⟩

Algorithm type

3 X^{9} Y^{2} Z + 13 X^{6} Y^{4} Z^{2} + 416 X^{4} Y^{4} Z^{4} + 13 X^{4} Y^{2} Z^{6} + 13 X^{2} Y^{6} Z^{4} + 4 X^{2} Y Z^{9} + 2 X Y^{9} Z^{2} + X^{6} Y^{4} Z + 2 X Y^{6} Z^{4} + 96 X^{6} Y^{2} Z^{2} + 3 X^{6} Y Z^{3} + 45 X^{4} Y^{4} Z^{2} + 13 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{6} Z + 65 X^{2} Y^{6} Z^{2} + 77 X^{2} Y^{4} Z^{4} + 130 X^{2} Y^{2} Z^{6} + 4 X Y^{3} Z^{6} + 6 X^{6} Y^{2} Z + 3 X^{6} Y Z^{2} + X^{4} Y^{4} Z + X^{4} Y^{2} Z^{3} + 2 X^{3} Y^{4} Z^{2} + 2 X^{2} Y^{6} Z + 10 X^{2} Y Z^{6} + 10 X Y^{6} Z^{2} + 2 X Y^{4} Z^{4} + 4 X Y^{2} Z^{6} + 33 X^{6} Y Z + 240 X^{4} Y^{2} Z^{2} + 3 X^{4} Y Z^{3} + 8 X^{3} Y^{4} Z + 3 X^{3} Y^{3} Z^{2} + 4 X^{3} Y^{2} Z^{3} + 402 X^{2} Y^{4} Z^{2} + 2 X^{2} Y^{3} Z^{3} + 337 X^{2} Y^{2} Z^{4} + 22 X Y^{6} Z + 6 X Y^{3} Z^{4} + 44 X Y Z^{6} + 14 X^{4} Y^{2} Z + 3 X^{4} Y Z^{2} + 9 X^{3} Y^{2} Z^{2} + 19 X^{2} Y^{4} Z + 5 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 30 X Y^{4} Z^{2} + 28 X Y^{2} Z^{4} + 33 X^{4} Y Z + 38 X^{3} Y^{2} Z + 33 X^{3} Y Z^{2} + 22 X^{2} Y^{3} Z + 496 X^{2} Y^{2} Z^{2} + 49 X^{2} Y Z^{3} + 88 X Y^{4} Z + 27 X Y^{3} Z^{2} + 44 X Y^{2} Z^{3} + 66 X Y Z^{4} + 66 X^{3} Y Z + 148 X^{2} Y^{2} Z + 104 X^{2} Y Z^{2} + 44 X Y^{3} Z + 203 X Y^{2} Z^{2} + 88 X Y Z^{3} + 121 X^{2} Y Z + 231 X Y^{2} Z + 187 X Y Z^{2} + 110 X Y Z

Algorithm definition

The algorithm ⟨15×20×25:4371⟩ is the (Kronecker) tensor product of ⟨3×4×5:47⟩ with ⟨5×5×5:93⟩.

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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