Description of fast matrix multiplication algorithm: ⟨8×21×28:2835⟩

Algorithm type

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

Algorithm definition

The algorithm ⟨8×21×28:2835⟩ is the (Kronecker) tensor product of ⟨2×7×4:45⟩ with ⟨4×3×7:63⟩.

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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