Description of fast matrix multiplication algorithm: ⟨16×24×28:5901⟩

Algorithm type

4 X^{8} Y^{12} Z^{8} + 16 X^{8} Y^{10} Z^{8} + 28 X^{8} Y^{8} Z^{8} + 16 X^{8} Y^{6} Z^{8} + 29 X^{4} Y^{12} Z^{4} + 18 X^{4} Y^{10} Z^{4} + 69 X^{4} Y^{8} Z^{4} + X^{2} Y^{12} Z^{2} + 128 X^{4} Y^{6} Z^{4} + X^{2} Y^{10} Z^{2} + 96 X^{4} Y^{5} Z^{4} + 2 X^{4} Y^{6} Z^{2} + 289 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z^{2} + 9 X^{2} Y^{6} Z^{4} + 96 X^{4} Y^{3} Z^{4} + 10 X^{4} Y^{4} Z^{2} + 305 X^{2} Y^{6} Z^{2} + 11 X^{2} Y^{4} Z^{4} + 108 X^{2} Y^{5} Z^{2} + 6 X^{4} Y^{2} Z^{2} + 600 X^{2} Y^{4} Z^{2} + 7 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + 624 X^{2} Y^{3} Z^{2} + 6 X Y^{5} Z + 12 X^{2} Y^{3} Z + 788 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 54 X Y^{3} Z^{2} + 60 X^{2} Y^{2} Z + 786 X Y^{3} Z + 66 X Y^{2} Z^{2} + 36 X^{2} Y Z + 1116 X Y^{2} Z + 42 X Y Z^{2} + 372 X Y Z

Algorithm definition

The algorithm ⟨16×24×28:5901⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×12×14:843⟩.

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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