Description of fast matrix multiplication algorithm: ⟨10×12×16:1222⟩

Algorithm type

78 X^{4} Y^{4} Z^{4} + 6 X Y^{9} Z + 24 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 44 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 2 X Y^{6} Z^{2} + 36 X^{4} Y^{2} Z^{2} + 122 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 30 X Y^{6} Z + 8 X^{3} Y^{3} Z + 4 X^{2} Y^{3} Z^{2} + 8 X Y^{4} Z^{2} + 4 X Y^{3} Z^{3} + 32 X^{3} Y^{2} Z + 12 X^{2} Y^{3} Z + 176 X^{2} Y^{2} Z^{2} + 24 X Y^{4} Z + 16 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 40 X^{3} Y Z + 48 X^{2} Y^{2} Z + 20 X^{2} Y Z^{2} + 40 X Y^{3} Z + 74 X Y^{2} Z^{2} + 20 X Y Z^{3} + 60 X^{2} Y Z + 70 X Y^{2} Z + 80 X Y Z^{2} + 50 X Y Z

Algorithm definition

The algorithm ⟨10×12×16:1222⟩ is the (Kronecker) tensor product of ⟨2×4×4:26⟩ with ⟨5×3×4:47⟩.

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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