Description of fast matrix multiplication algorithm: ⟨8×18×25:2209⟩

Algorithm type

26 X^{4} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z^{2} + 4 X^{2} Y^{8} Z^{4} + 16 X Y^{12} Z + 6 X^{6} Y^{4} Z^{2} + 145 X^{4} Y^{4} Z^{4} + 64 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 32 X Y^{9} Z + 8 X Y^{8} Z^{2} + 33 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 11 X^{4} Y^{2} Z^{4} + 148 X^{2} Y^{6} Z^{2} + 38 X^{2} Y^{4} Z^{4} + 22 X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 16 X Y^{6} Z^{2} + 33 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{4} Z + 132 X^{2} Y^{4} Z^{2} + 88 X^{2} Y^{2} Z^{4} + 64 X Y^{6} Z + 8 X Y^{4} Z^{3} + 24 X^{3} Y^{3} Z + 12 X^{2} Y^{4} Z + 8 X^{2} Y^{3} Z^{2} + 40 X Y^{4} Z^{2} + 16 X Y^{3} Z^{3} + 12 X^{3} Y^{2} Z + 24 X^{2} Y^{3} Z + 293 X^{2} Y^{2} Z^{2} + 44 X Y^{4} Z + 64 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 54 X^{3} Y Z + 12 X^{2} Y^{2} Z + 18 X^{2} Y Z^{2} + 112 X Y^{3} Z + 68 X Y^{2} Z^{2} + 36 X Y Z^{3} + 54 X^{2} Y Z + 128 X Y^{2} Z + 144 X Y Z^{2} + 90 X Y Z

Algorithm definition

The algorithm ⟨8×18×25:2209⟩ is the (Kronecker) tensor product of ⟨2×6×5:47⟩ with ⟨4×3×5:47⟩.

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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