Description of fast matrix multiplication algorithm: ⟨4×18×32:1500⟩

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} + 40 X Y^{15} Z + 8 X^{4} Y^{8} Z^{4} + 32 X^{2} Y^{12} Z^{2} + 4 X^{4} Y^{6} Z^{4} + 40 X^{2} Y^{10} Z^{2} + 20 X Y^{12} Z + 4 X^{2} Y^{9} Z^{2} + 48 X^{4} Y^{4} Z^{4} + 20 X^{2} Y^{8} Z^{2} + 16 X Y^{9} Z + 88 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{5} Z^{2} + 52 X^{2} Y^{4} Z^{2} + 8 X^{2} Y^{2} Z^{4} + 100 X Y^{6} Z + 12 X^{2} Y^{3} Z^{2} + 120 X Y^{5} Z + 224 X^{2} Y^{2} Z^{2} + 60 X Y^{4} Z + 8 X Y^{3} Z^{2} + 128 X Y^{3} Z + 84 X Y^{2} Z + 24 X Y Z^{2} + 240 X Y Z

Algorithm definition

The algorithm ⟨4×18×32:1500⟩ is the (Kronecker) tensor product of ⟨2×3×4:20⟩ with ⟨2×6×8:75⟩.

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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