Description of fast matrix multiplication algorithm: ⟨10×28×32:5356⟩

Algorithm type

6 X^{8} Y^{8} Z^{8} + 2 X Y^{18} Z^{2} + 6 X^{8} Y^{8} Z^{4} + 24 X^{6} Y^{8} Z^{6} + 12 X^{6} Y^{6} Z^{8} + 2 X^{4} Y^{12} Z^{4} + 2 X^{2} Y^{15} Z^{2} + 12 X^{10} Y^{4} Z^{4} + 18 X^{6} Y^{6} Z^{6} + 2 X^{4} Y^{12} Z^{2} + 6 X^{4} Y^{10} Z^{4} + 6 X^{4} Y^{4} Z^{10} + 8 X^{3} Y^{12} Z^{3} + 6 X^{2} Y^{12} Z^{4} + 6 X^{10} Y^{4} Z^{2} + 6 X^{6} Y^{8} Z^{2} + 20 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{2} Z^{10} + 2 X^{3} Y^{12} Z + 4 X^{3} Y^{9} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 6 X^{2} Y^{6} Z^{8} + 6 X^{2} Y^{4} Z^{10} + 6 X^{3} Y^{9} Z^{3} + 2 X^{2} Y^{12} Z + 8 X Y^{12} Z^{2} + 14 X^{4} Y^{8} Z^{2} + 30 X^{4} Y^{6} Z^{4} + 6 X^{4} Y^{4} Z^{6} + 32 X^{3} Y^{8} Z^{3} + 8 X^{2} Y^{10} Z^{2} + 6 X^{2} Y^{6} Z^{6} + 2 X Y^{12} Z + 2 X Y^{9} Z^{4} + 4 X^{5} Y^{6} Z^{2} + 16 X^{3} Y^{6} Z^{4} + 10 X^{2} Y^{9} Z^{2} + 2 X^{2} Y^{6} Z^{5} + 2 X Y^{9} Z^{3} + 6 X^{6} Y^{4} Z^{2} + 2 X^{5} Y^{6} Z + 256 X^{4} Y^{4} Z^{4} + 8 X^{3} Y^{8} Z + 24 X^{3} Y^{6} Z^{3} + 22 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{4} + 4 X Y^{9} Z^{2} + 2 X Y^{6} Z^{5} + 16 X^{5} Y^{4} Z^{2} + 8 X^{2} Y^{8} Z + 2 X^{2} Y^{6} Z^{3} + 8 X^{2} Y^{4} Z^{5} + 28 X Y^{9} Z + 8 X Y^{6} Z^{4} + 30 X^{6} Y^{2} Z^{2} + 8 X^{5} Y^{4} Z + 22 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{6} Z + 40 X^{3} Y^{4} Z^{3} + 20 X^{3} Y^{3} Z^{4} + 206 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{3} Z^{5} + 42 X^{2} Y^{2} Z^{6} + 8 X Y^{8} Z + 8 X Y^{6} Z^{3} + 8 X Y^{4} Z^{5} + 20 X^{5} Y^{2} Z^{2} + 30 X^{3} Y^{3} Z^{3} + 4 X^{2} Y^{6} Z + 10 X^{2} Y^{5} Z^{2} + 8 X^{2} Y^{4} Z^{3} + 18 X^{2} Y^{2} Z^{5} + 38 X Y^{6} Z^{2} + 10 X^{5} Y^{2} Z + 12 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{4} Z + 558 X^{2} Y^{4} Z^{2} + 54 X^{2} Y^{2} Z^{4} + 10 X^{2} Y Z^{5} + 182 X Y^{6} Z + 10 X Y^{3} Z^{4} + 10 X Y^{2} Z^{5} + 10 X^{3} Y^{3} Z + 26 X^{2} Y^{4} Z + 52 X^{2} Y^{3} Z^{2} + 10 X^{2} Y^{2} Z^{3} + 48 X Y^{4} Z^{2} + 24 X Y^{3} Z^{3} + 50 X^{3} Y^{2} Z + 4 X^{2} Y^{3} Z + 712 X^{2} Y^{2} Z^{2} + 290 X Y^{4} Z + 38 X Y^{3} Z^{2} + 56 X Y^{2} Z^{3} + 50 X^{3} Y Z + 36 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 238 X Y^{3} Z + 132 X Y^{2} Z^{2} + 70 X Y Z^{3} + 20 X^{2} Y Z + 742 X Y^{2} Z + 90 X Y Z^{2} + 490 X Y Z

Algorithm definition

The algorithm ⟨10×28×32:5356⟩ is the (Kronecker) tensor product of ⟨2×4×4:26⟩ with ⟨5×7×8:206⟩.

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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