Description of fast matrix multiplication algorithm: ⟨12×14×18:1845⟩

Algorithm type

135 X^{4} Y^{4} Z^{4} + 9 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{2} Z^{6} + 36 X^{4} Y^{2} Z^{2} + 81 X^{2} Y^{4} Z^{2} + 300 X^{2} Y^{2} Z^{4} + 6 X Y Z^{6} + 12 X^{2} Y Z^{4} + 354 X^{2} Y^{2} Z^{2} + 6 X Y^{3} Z^{2} + 60 X Y Z^{4} + 18 X^{2} Y^{2} Z + 84 X^{2} Y Z^{2} + 6 X Y^{3} Z + 162 X Y^{2} Z^{2} + 6 X Y Z^{3} + 72 X^{2} Y Z + 162 X Y^{2} Z + 192 X Y Z^{2} + 132 X Y Z

Algorithm definition

The algorithm ⟨12×14×18:1845⟩ is the (Kronecker) tensor product of ⟨3×2×3:15⟩ with ⟨4×7×6:123⟩.

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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