Description of fast matrix multiplication algorithm: ⟨14×16×21:2835⟩

Algorithm type

6 X^{6} Y^{8} Z^{4} + 6 X^{6} Y^{6} Z^{4} + 15 X^{4} Y^{8} Z^{4} + 2 X^{8} Y^{4} Z^{2} + 54 X^{6} Y^{4} Z^{4} + 15 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{8} Z^{4} + 2 X^{8} Y^{3} Z^{2} + 24 X^{3} Y^{8} Z^{2} + 18 X^{8} Y^{2} Z^{2} + 12 X^{6} Y^{4} Z^{2} + 135 X^{4} Y^{4} Z^{4} + 60 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{6} Z^{4} + 12 X^{6} Y^{3} Z^{2} + 36 X^{3} Y^{6} Z^{2} + 24 X Y^{8} Z^{2} + 108 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 90 X^{2} Y^{6} Z^{2} + 54 X^{2} Y^{4} Z^{4} + 8 X^{4} Y^{4} Z + 12 X^{4} Y^{3} Z^{2} + 12 X^{3} Y^{4} Z^{2} + 36 X Y^{6} Z^{2} + 12 X^{4} Y^{3} Z + 108 X^{4} Y^{2} Z^{2} + 48 X^{3} Y^{4} Z + 40 X^{2} Y^{4} Z^{2} + 4 X^{4} Y^{2} Z + 72 X^{3} Y^{3} Z + 132 X^{3} Y^{2} Z^{2} + 48 X^{2} Y^{4} Z + 10 X^{2} Y^{3} Z^{2} + 12 X Y^{4} Z^{2} + 44 X^{4} Y Z + 24 X^{3} Y^{2} Z + 72 X^{2} Y^{3} Z + 420 X^{2} Y^{2} Z^{2} + 40 X Y^{4} Z + 264 X^{3} Y Z + 24 X^{2} Y^{2} Z + 60 X Y^{3} Z + 132 X Y^{2} Z^{2} + 264 X^{2} Y Z + 20 X Y^{2} Z + 220 X Y Z

Algorithm definition

The algorithm ⟨14×16×21:2835⟩ is the (Kronecker) tensor product of ⟨2×4×7:45⟩ with ⟨7×4×3:63⟩.

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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