Description of fast matrix multiplication algorithm: ⟨16×20×20:3724⟩

Algorithm type

X^{8} Y^{12} Z^{8} + 4 X^{16} Y^{4} Z^{4} + 23 X^{8} Y^{8} Z^{8} + 4 X^{4} Y^{4} Z^{16} + 13 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{8} Z^{8} + 4 X^{4} Y^{8} Z^{4} + 4 X^{4} Y^{4} Z^{8} + 12 X^{4} Y^{6} Z^{4} + 48 X^{8} Y^{2} Z^{2} + 291 X^{4} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{8} + 156 X^{2} Y^{6} Z^{2} + 96 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 36 X^{2} Y^{3} Z^{2} + 144 X^{4} Y Z + 1008 X^{2} Y^{2} Z^{2} + 144 X Y Z^{4} + 468 X Y^{3} Z + 288 X Y^{2} Z^{2} + 144 X Y^{2} Z + 144 X Y Z^{2} + 540 X Y Z

Algorithm definition

The algorithm ⟨16×20×20:3724⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×10×10:532⟩.

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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