Description of fast matrix multiplication algorithm: ⟨10×20×32:3724⟩

Algorithm type

336 X^{4} Y^{4} Z^{4} + 4 X Y^{9} Z + 6 X^{6} Y^{2} Z^{2} + 16 X^{4} Y^{2} Z^{4} + 124 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 6 X Y^{6} Z^{2} + 74 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{2} Z^{3} + 592 X^{2} Y^{4} Z^{2} + 124 X^{2} Y^{2} Z^{4} + 64 X Y^{6} Z + 2 X^{3} Y^{3} Z + 8 X^{2} Y^{2} Z^{3} + 24 X Y^{4} Z^{2} + 4 X Y^{3} Z^{3} + 8 X^{3} Y^{2} Z + 20 X^{2} Y^{3} Z + 686 X^{2} Y^{2} Z^{2} + 192 X Y^{4} Z + 40 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 10 X^{3} Y Z + 80 X^{2} Y^{2} Z + 42 X^{2} Y Z^{2} + 52 X Y^{3} Z + 190 X Y^{2} Z^{2} + 20 X Y Z^{3} + 178 X^{2} Y Z + 368 X Y^{2} Z + 222 X Y Z^{2} + 178 X Y Z

Algorithm definition

The algorithm ⟨10×20×32:3724⟩ is serendipitous tensor product (⟨5×5×8:144⟩ - 10) ⊗ ⟨2×4×4:26⟩ +5⟨4×4×4:48⟩.

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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