Description of fast matrix multiplication algorithm: ⟨15×30×32:7761⟩

Algorithm type

1023 X^{4} Y^{4} Z^{4} + 18 X^{6} Y^{2} Z^{2} + 36 X^{2} Y^{6} Z^{2} + 54 X^{2} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{6} + 18 X^{6} Y Z + 1254 X^{4} Y^{2} Z^{2} + 1440 X^{2} Y^{4} Z^{2} + 384 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 54 X Y^{4} Z^{2} + 252 X^{4} Y Z + 18 X^{3} Y^{2} Z + 36 X^{2} Y^{3} Z + 402 X^{2} Y^{2} Z^{2} + 36 X^{2} Y Z^{3} + 432 X Y^{4} Z + 36 X Y^{2} Z^{3} + 612 X^{2} Y^{2} Z + 408 X^{2} Y Z^{2} + 360 X Y^{2} Z^{2} + 420 X^{2} Y Z + 288 X Y^{2} Z + 48 X Y Z^{2} + 60 X Y Z

Algorithm definition

The algorithm ⟨15×30×32:7761⟩ is serendipitous tensor product (⟨5×5×8:144⟩ - 10) ⊗ ⟨3×6×4:54⟩ +5⟨6×6×4:105⟩.

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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