Description of fast matrix multiplication algorithm: ⟨16×18×22:3647⟩

Algorithm type

3 X^{8} Y^{8} Z^{12} + 4 X^{8} Y^{8} Z^{10} + 19 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{6} + X^{8} Y^{6} Z^{8} + 7 X^{4} Y^{12} Z^{6} + 7 X^{12} Y^{4} Z^{4} + X^{8} Y^{6} Z^{6} + 8 X^{8} Y^{4} Z^{8} + 12 X^{4} Y^{12} Z^{4} + 11 X^{4} Y^{4} Z^{12} + X^{2} Y^{16} Z^{2} + X^{12} Y^{4} Z^{2} + 12 X^{8} Y^{4} Z^{6} + X^{4} Y^{10} Z^{4} + 8 X^{4} Y^{8} Z^{6} + 5 X^{4} Y^{4} Z^{10} + 4 X^{8} Y^{4} Z^{4} + 32 X^{4} Y^{8} Z^{4} + 14 X^{4} Y^{4} Z^{8} + 13 X^{2} Y^{12} Z^{2} + 2 X^{4} Y^{8} Z^{2} + 19 X^{4} Y^{6} Z^{4} + 38 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{10} Z^{2} + 19 X^{2} Y^{6} Z^{6} + 24 X^{4} Y^{4} Z^{5} + 12 X^{6} Y^{4} Z^{2} + 8 X^{4} Y^{6} Z^{2} + 175 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{6} Z^{4} + 15 X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{4} Z^{3} + 6 X^{4} Y^{3} Z^{4} + 42 X^{2} Y^{6} Z^{3} + 63 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{3} Z^{3} + 95 X^{4} Y^{2} Z^{4} + 89 X^{2} Y^{6} Z^{2} + 20 X^{2} Y^{4} Z^{4} + 109 X^{2} Y^{2} Z^{6} + 6 X Y^{8} Z + 6 X^{6} Y^{2} Z + 72 X^{4} Y^{2} Z^{3} + 6 X^{2} Y^{5} Z^{2} + 48 X^{2} Y^{4} Z^{3} + 30 X^{2} Y^{2} Z^{5} + 34 X^{4} Y^{2} Z^{2} + 197 X^{2} Y^{4} Z^{2} + 107 X^{2} Y^{2} Z^{4} + 78 X Y^{6} Z + 12 X^{2} Y^{4} Z + 114 X^{2} Y^{3} Z^{2} + 120 X^{2} Y^{2} Z^{3} + 24 X Y^{5} Z + 114 X Y^{3} Z^{3} + 72 X^{3} Y^{2} Z + 48 X^{2} Y^{3} Z + 371 X^{2} Y^{2} Z^{2} + 12 X Y^{3} Z^{2} + 90 X Y^{2} Z^{3} + 126 X^{3} Y Z + 12 X^{2} Y^{2} Z + 282 X^{2} Y Z^{2} + 102 X Y^{3} Z + 120 X Y^{2} Z^{2} + 258 X Y Z^{3} + 60 X^{2} Y Z + 30 X Y^{2} Z + 138 X Y Z^{2} + 30 X Y Z

Algorithm definition

The algorithm ⟨16×18×22:3647⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×9×11:521⟩.

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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