Description of fast matrix multiplication algorithm: ⟨16×22×22:4487⟩

Algorithm type

33 X^{8} Y^{8} Z^{8} + 7 X^{8} Y^{6} Z^{8} + 7 X^{6} Y^{6} Z^{8} + X^{6} Y^{4} Z^{8} + 54 X^{4} Y^{8} Z^{4} + 7 X^{2} Y^{12} Z^{2} + 4 X^{4} Y^{8} Z^{2} + 17 X^{4} Y^{6} Z^{4} + 5 X^{2} Y^{10} Z^{2} + 4 X^{2} Y^{8} Z^{4} + 10 X^{6} Y^{4} Z^{2} + 361 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + 10 X^{2} Y^{4} Z^{6} + 42 X^{4} Y^{3} Z^{4} + 7 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{4} Z^{2} + 15 X^{4} Y^{2} Z^{4} + 42 X^{3} Y^{3} Z^{4} + 8 X^{2} Y^{6} Z^{2} + 30 X^{2} Y^{4} Z^{4} + 7 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{2} Z^{4} + 18 X^{4} Y^{2} Z^{2} + 398 X^{2} Y^{4} Z^{2} + 20 X^{2} Y^{2} Z^{4} + 42 X Y^{6} Z + 24 X^{2} Y^{4} Z + 102 X^{2} Y^{3} Z^{2} + 30 X Y^{5} Z + 24 X Y^{4} Z^{2} + 60 X^{3} Y^{2} Z + 1091 X^{2} Y^{2} Z^{2} + 18 X Y^{4} Z + 60 X Y^{2} Z^{3} + 42 X^{3} Y Z + 144 X^{2} Y^{2} Z + 90 X^{2} Y Z^{2} + 48 X Y^{3} Z + 180 X Y^{2} Z^{2} + 42 X Y Z^{3} + 108 X^{2} Y Z + 444 X Y^{2} Z + 120 X Y Z^{2} + 678 X Y Z

Algorithm definition

The algorithm ⟨16×22×22:4487⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×11:641⟩.

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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