Description of fast matrix multiplication algorithm: ⟨15×17×18:2720⟩

Algorithm type

16 X^{6} Y^{6} Z^{6} + 16 X^{6} Y^{5} Z^{6} + 32 X^{2} Y^{9} Z^{6} + 32 X^{2} Y^{6} Z^{9} + 48 X^{4} Y^{9} Z^{3} + 208 X^{4} Y^{6} Z^{6} + 48 X Y^{9} Z^{6} + 48 X Y^{6} Z^{9} + 80 X^{4} Y^{5} Z^{6} + 24 X^{3} Y^{6} Z^{6} + 32 X^{8} Y^{3} Z^{3} + 24 X^{3} Y^{5} Z^{6} + 120 X^{2} Y^{9} Z^{3} + 312 X^{2} Y^{6} Z^{6} + 96 X^{2} Y^{3} Z^{9} + 48 X^{4} Y^{3} Z^{6} + 16 X^{2} Y^{8} Z^{3} + 120 X^{2} Y^{5} Z^{6} + 72 X Y^{9} Z^{3} + 144 X Y^{3} Z^{9} + 48 X^{6} Y^{3} Z^{3} + 16 X^{4} Y^{2} Z^{6} + 24 X Y^{8} Z^{3} + 32 X^{6} Y^{2} Z^{3} + 184 X^{2} Y^{3} Z^{6} + 176 X^{4} Y^{3} Z^{3} + 40 X^{2} Y^{2} Z^{6} + 168 X Y^{3} Z^{6} + 72 X^{3} Y^{3} Z^{3} + 24 X Y^{2} Z^{6} + 48 X^{3} Y^{2} Z^{3} + 256 X^{2} Y^{3} Z^{3} + 96 X Y^{3} Z^{3}

Algorithm definition

The algorithm ⟨15×17×18:2720⟩ is the projection [[0, 18], [0]] of ⟨15×18×18:2720⟩.

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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