Description of fast matrix multiplication algorithm: ⟨14×24×25:4782⟩

Algorithm type

8 X^{4} Y^{12} Z^{4} + 472 X^{4} Y^{8} Z^{4} + 24 X^{2} Y^{12} Z^{2} + 16 X^{4} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 16 X Y^{12} Z + 600 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{8} Z + 8 X Y^{8} Z^{2} + 192 X^{4} Y^{4} Z^{2} + 128 X^{2} Y^{4} Z^{4} + 128 X Y^{8} Z + 6 X^{4} Y^{2} Z^{3} + 7 X^{3} Y^{2} Z^{4} + 9 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 136 X^{2} Y^{4} Z^{2} + 14 X^{2} Y^{2} Z^{4} + 3 X^{4} Y^{2} Z + 14 X^{4} Y Z^{2} + 22 X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 192 X^{2} Y^{4} Z + 16 X^{2} Y^{3} Z^{2} + 8 X^{2} Y^{2} Z^{3} + 9 X^{2} Y Z^{4} + 128 X Y^{4} Z^{2} + 14 X Y^{2} Z^{4} + 10 X^{4} Y Z + 5 X^{3} Y^{2} Z + 15 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 979 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 136 X Y^{4} Z + 4 X Y^{3} Z^{2} + 5 X Y^{2} Z^{3} + 35 X^{3} Y Z + 32 X^{2} Y^{2} Z + 25 X^{2} Y Z^{2} + 37 X Y^{3} Z + 28 X Y^{2} Z^{2} + 421 X^{2} Y Z + 264 X Y^{2} Z + 273 X Y Z^{2} + 294 X Y Z

Algorithm definition

The algorithm ⟨14×24×25:4782⟩ is serendipitous tensor product (⟨7×6×5:150⟩ - 12) ⊗ ⟨2×4×5:32⟩ +6⟨4×4×5:61⟩.

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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