Description of fast matrix multiplication algorithm: ⟨4×18×32:1498⟩

Algorithm type

8 X^{2} Y^{18} Z^{2} + 8 X^{4} Y^{12} Z^{4} + 24 X Y^{18} Z + 16 X^{2} Y^{15} Z^{2} + 16 X^{4} Y^{10} Z^{4} + 39 X Y^{15} Z + 8 X^{4} Y^{8} Z^{4} + 33 X^{2} Y^{12} Z^{2} + 4 X^{4} Y^{6} Z^{4} + 40 X^{2} Y^{10} Z^{2} + 22 X Y^{12} Z + 6 X^{2} Y^{9} Z^{2} + 48 X^{4} Y^{4} Z^{4} + 20 X^{2} Y^{8} Z^{2} + 4 X Y^{10} Z + 2 X^{2} Y^{7} Z^{2} + 21 X Y^{9} Z + 88 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{5} Z^{2} + 4 X Y^{7} Z + 49 X^{2} Y^{4} Z^{2} + 8 X^{2} Y^{2} Z^{4} + 96 X Y^{6} Z + 16 X^{2} Y^{3} Z^{2} + 118 X Y^{5} Z + 220 X^{2} Y^{2} Z^{2} + 62 X Y^{4} Z + 8 X Y^{3} Z^{2} + 128 X Y^{3} Z + 82 X Y^{2} Z + 24 X Y Z^{2} + 228 X Y Z

Algorithm definition

The algorithm ⟨4×18×32:1498⟩ is serendipitous tensor product (⟨2×6×8:75⟩ - 4) ⊗ ⟨2×3×4:20⟩ +2⟨2×6×4:39⟩.

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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