Description of fast matrix multiplication algorithm: ⟨20×24×27:7056⟩

Algorithm type

8 X^{8} Y^{16} Z^{8} + 8 X^{6} Y^{16} Z^{4} + 8 X^{4} Y^{16} Z^{4} + 8 X^{9} Y^{8} Z^{6} + 8 X^{10} Y^{8} Z^{4} + 8 X^{6} Y^{8} Z^{8} + 8 X^{6} Y^{12} Z^{3} + 8 X^{3} Y^{16} Z^{2} + 8 X^{3} Y^{12} Z^{6} + 8 X^{8} Y^{8} Z^{4} + 8 X^{6} Y^{12} Z^{2} + 64 X^{6} Y^{8} Z^{6} + 8 X^{4} Y^{8} Z^{8} + 8 X^{3} Y^{8} Z^{9} + 8 X^{12} Y^{4} Z^{3} + 24 X^{6} Y^{8} Z^{4} + 16 X^{3} Y^{12} Z^{3} + 12 X^{9} Y^{4} Z^{3} + 12 X^{6} Y^{4} Z^{6} + 16 X^{4} Y^{8} Z^{4} + 8 X^{3} Y^{12} Z + 24 X^{3} Y^{4} Z^{9} + 8 X^{2} Y^{12} Z^{2} + 8 X^{5} Y^{8} Z^{2} + 8 X^{3} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z + 8 X Y^{12} Z^{2} + 70 X^{6} Y^{4} Z^{4} + 8 X^{4} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 24 X Y^{12} Z + 20 X^{6} Y^{4} Z^{3} + 32 X^{3} Y^{8} Z^{2} + 20 X^{3} Y^{4} Z^{6} + 64 X^{8} Y^{2} Z^{2} + 64 X^{6} Y^{4} Z^{2} + 76 X^{4} Y^{6} Z^{2} + 552 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{9} Z + 80 X^{2} Y^{8} Z^{2} + 64 X^{2} Y^{6} Z^{4} + 64 X^{2} Y^{4} Z^{6} + 8 X Y^{8} Z^{3} + 2 X^{3} Y^{6} Z^{2} + 126 X^{6} Y^{2} Z^{2} + 32 X^{4} Y^{4} Z^{2} + 124 X^{4} Y^{2} Z^{4} + 132 X^{2} Y^{6} Z^{2} + 32 X^{2} Y^{4} Z^{4} + 192 X^{2} Y^{2} Z^{6} + 12 X^{5} Y^{2} Z^{2} + 8 X^{4} Y^{4} Z + 20 X^{3} Y^{4} Z^{2} + 12 X^{3} Y^{2} Z^{4} + 16 X^{2} Y^{6} Z + 4 X^{5} Y Z^{2} + 184 X^{4} Y^{2} Z^{2} + 76 X^{3} Y^{4} Z + 4 X^{3} Y^{3} Z^{2} + 4 X^{3} Y Z^{4} + 52 X^{2} Y^{4} Z^{2} + 184 X^{2} Y^{2} Z^{4} + 24 X Y^{4} Z^{3} + 4 X^{4} Y Z^{2} + 26 X^{3} Y^{3} Z + 178 X^{3} Y^{2} Z^{2} + 52 X^{2} Y^{4} Z + 8 X^{2} Y^{3} Z^{2} + 4 X^{2} Y Z^{4} + 52 X Y^{4} Z^{2} + 128 X^{4} Y Z + 40 X^{3} Y^{2} Z + 8 X^{3} Y Z^{2} + 152 X^{2} Y^{3} Z + 1144 X^{2} Y^{2} Z^{2} + 8 X Y^{4} Z + 132 X Y^{3} Z^{2} + 128 X Y^{2} Z^{3} + 370 X^{3} Y Z + 16 X^{2} Y^{2} Z + 264 X^{2} Y Z^{2} + 284 X Y^{3} Z + 16 X Y^{2} Z^{2} + 384 X Y Z^{3} + 404 X^{2} Y Z + 48 X Y^{2} Z + 404 X Y Z^{2} + 76 X Y Z

Algorithm definition

The algorithm ⟨20×24×27:7056⟩ is serendipitous tensor product (⟨5×6×3:68⟩ - 16) ⊗ ⟨4×4×9:104⟩ +8⟨4×8×9:206⟩.

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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