Description of fast matrix multiplication algorithm: ⟨22×24×32:9331⟩

Algorithm type

3 X^{16} Y^{16} Z^{16} + 4 X^{14} Y^{16} Z^{14} + 2 X^{8} Y^{24} Z^{8} + 2 X^{8} Y^{16} Z^{16} + 4 X^{8} Y^{16} Z^{8} + 2 X^{8} Y^{8} Z^{14} + 82 X^{8} Y^{8} Z^{8} + 8 X^{8} Y^{8} Z^{6} + 24 X^{7} Y^{8} Z^{7} + 8 X^{6} Y^{8} Z^{8} + 8 X^{6} Y^{8} Z^{6} + 36 X^{4} Y^{12} Z^{4} + 36 X^{4} Y^{8} Z^{8} + 72 X^{4} Y^{8} Z^{4} + 36 X^{4} Y^{4} Z^{8} + 6 X^{2} Y^{2} Z^{12} + 12 X^{4} Y^{4} Z^{7} + 8 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{4} Z^{8} + 6 X^{6} Y^{2} Z^{4} + 720 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{2} Z^{8} + 48 X^{4} Y^{4} Z^{3} + 48 X^{3} Y^{4} Z^{4} + 18 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 48 X^{3} Y^{4} Z^{3} + 228 X^{2} Y^{6} Z^{2} + 262 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 6 X^{4} Y^{2} Z^{2} + 502 X^{2} Y^{4} Z^{2} + 292 X^{2} Y^{2} Z^{4} + 36 X Y Z^{6} + 48 X^{2} Y^{2} Z^{3} + 24 X Y^{2} Z^{4} + 36 X^{3} Y Z^{2} + 2186 X^{2} Y^{2} Z^{2} + 24 X Y^{3} Z^{2} + 12 X Y Z^{4} + 108 X^{3} Y Z + 144 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 504 X Y^{3} Z + 708 X Y^{2} Z^{2} + 108 X Y Z^{3} + 36 X^{2} Y Z + 1284 X Y^{2} Z + 456 X Y Z^{2} + 1020 X Y Z

Algorithm definition

The algorithm ⟨22×24×32:9331⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨11×12×16:1333⟩.

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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