Description of fast matrix multiplication algorithm: ⟨12×16×22:2499⟩

Algorithm type

12 X^{8} Y^{8} Z^{8} + X^{8} Y^{8} Z^{6} + X^{8} Y^{6} Z^{8} + 4 X^{8} Y^{6} Z^{6} + 13 X^{4} Y^{8} Z^{4} + 13 X^{4} Y^{4} Z^{8} + X^{4} Y^{8} Z^{2} + 3 X^{4} Y^{6} Z^{4} + 3 X^{4} Y^{4} Z^{6} + X^{4} Y^{2} Z^{8} + X^{4} Y^{6} Z^{2} + 165 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 6 X^{4} Y^{4} Z^{3} + 6 X^{4} Y^{3} Z^{4} + 9 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{4} Z^{2} + 24 X^{4} Y^{3} Z^{3} + 6 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 9 X^{4} Y^{2} Z^{2} + 156 X^{2} Y^{4} Z^{2} + 150 X^{2} Y^{2} Z^{4} + 6 X^{2} Y^{4} Z + 18 X^{2} Y^{3} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 6 X^{2} Y^{3} Z + 573 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 54 X^{3} Y Z + 18 X^{2} Y^{2} Z + 36 X Y^{3} Z + 36 X Y^{2} Z^{2} + 72 X Y Z^{3} + 54 X^{2} Y Z + 468 X Y^{2} Z + 432 X Y Z^{2} + 90 X Y Z

Algorithm definition

The algorithm ⟨12×16×22:2499⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×8×11:357⟩.

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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