Description of fast matrix multiplication algorithm: ⟨16×30×32:8295⟩

Algorithm type

48 X^{8} Y^{16} Z^{8} + 24 X^{4} Y^{24} Z^{4} + 2 X^{8} Y^{8} Z^{12} + 24 X^{2} Y^{24} Z^{2} + 24 X^{8} Y^{8} Z^{10} + 24 X^{12} Y^{8} Z^{4} + 13 X^{8} Y^{8} Z^{8} + 48 X^{4} Y^{16} Z^{4} + 6 X^{12} Y^{4} Z^{6} + 3 X^{8} Y^{8} Z^{6} + 4 X^{4} Y^{12} Z^{6} + 6 X^{12} Y^{4} Z^{4} + 3 X^{8} Y^{8} Z^{4} + 2 X^{4} Y^{12} Z^{4} + 42 X^{4} Y^{8} Z^{8} + 32 X^{4} Y^{4} Z^{12} + 11 X^{8} Y^{4} Z^{6} + 62 X^{4} Y^{8} Z^{6} + 14 X^{4} Y^{4} Z^{10} + 9 X^{2} Y^{12} Z^{4} + 7 X^{8} Y^{4} Z^{4} + 24 X^{6} Y^{8} Z^{2} + 320 X^{4} Y^{8} Z^{4} + 31 X^{4} Y^{4} Z^{8} + 147 X^{2} Y^{12} Z^{2} + X^{2} Y^{8} Z^{6} + 12 X^{2} Y^{2} Z^{12} + 20 X^{6} Y^{4} Z^{4} + 20 X^{6} Y^{2} Z^{6} + 2 X^{4} Y^{8} Z^{2} + 51 X^{4} Y^{4} Z^{6} + 58 X^{2} Y^{8} Z^{4} + 10 X^{2} Y^{6} Z^{6} + 18 X^{2} Y^{4} Z^{8} + 4 X^{2} Y^{2} Z^{10} + 144 X Y^{12} Z + 144 X^{4} Y^{4} Z^{5} + 148 X^{6} Y^{4} Z^{2} + 2 X^{6} Y^{2} Z^{4} + 205 X^{4} Y^{4} Z^{4} + 24 X^{4} Y^{2} Z^{6} + 304 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 42 X^{2} Y^{4} Z^{6} + 4 X^{2} Y^{2} Z^{8} + 36 X^{6} Y^{2} Z^{3} + 18 X^{4} Y^{4} Z^{3} + 24 X^{2} Y^{6} Z^{3} + 86 X^{6} Y^{2} Z^{2} + 33 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 61 X^{2} Y^{6} Z^{2} + 289 X^{2} Y^{4} Z^{4} + 229 X^{2} Y^{2} Z^{6} + 66 X^{4} Y^{2} Z^{3} + 372 X^{2} Y^{4} Z^{3} + 84 X^{2} Y^{2} Z^{5} + 54 X Y^{6} Z^{2} + 51 X^{4} Y^{2} Z^{2} + 144 X^{3} Y^{4} Z + 212 X^{2} Y^{4} Z^{2} + 241 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 6 X Y^{4} Z^{3} + 72 X Y Z^{6} + 120 X^{3} Y^{2} Z^{2} + 120 X^{3} Y Z^{3} + 12 X^{2} Y^{4} Z + 234 X^{2} Y^{2} Z^{3} + 348 X Y^{4} Z^{2} + 60 X Y^{3} Z^{3} + 108 X Y^{2} Z^{4} + 24 X Y Z^{5} + 24 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 770 X^{2} Y^{2} Z^{2} + 144 X^{2} Y Z^{3} + 96 X Y^{4} Z + 6 X Y^{3} Z^{2} + 252 X Y^{2} Z^{3} + 24 X Y Z^{4} + 300 X^{3} Y Z + 90 X^{2} Y^{2} Z + 18 X^{2} Y Z^{2} + 294 X Y^{3} Z + 222 X Y^{2} Z^{2} + 222 X Y Z^{3} + 54 X^{2} Y Z + 120 X Y^{2} Z + 330 X Y Z^{2} + 48 X Y Z

Algorithm definition

The algorithm ⟨16×30×32:8295⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×15×16:1185⟩.

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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