Description of fast matrix multiplication algorithm: ⟨16×30×32:8533⟩

Algorithm type

3 X^{16} Y^{16} Z^{16} + 3 X^{14} Y^{14} Z^{16} + X^{8} Y^{24} Z^{8} + X^{8} Y^{22} Z^{8} + 5 X^{8} Y^{16} Z^{8} + X^{8} Y^{14} Z^{8} + 79 X^{8} Y^{8} Z^{8} + 6 X^{8} Y^{6} Z^{8} + 18 X^{7} Y^{7} Z^{8} + 6 X^{6} Y^{8} Z^{8} + 6 X^{6} Y^{6} Z^{8} + 26 X^{4} Y^{12} Z^{4} + 6 X^{4} Y^{11} Z^{4} + 4 X^{4} Y^{10} Z^{4} + 118 X^{4} Y^{8} Z^{4} + 6 X^{2} Y^{12} Z^{2} + 6 X^{4} Y^{7} Z^{4} + 4 X^{4} Y^{6} Z^{4} + 4 X^{2} Y^{8} Z^{4} + 6 X^{6} Y^{4} Z^{2} + 679 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 36 X^{4} Y^{3} Z^{4} + 36 X^{3} Y^{4} Z^{4} + 9 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 15 X^{4} Y^{2} Z^{4} + 36 X^{3} Y^{3} Z^{4} + 197 X^{2} Y^{6} Z^{2} + 37 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 24 X^{2} Y^{5} Z^{2} + 3 X^{4} Y^{2} Z^{2} + 753 X^{2} Y^{4} Z^{2} + 36 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 24 X^{2} Y^{3} Z^{2} + 24 X Y^{4} Z^{2} + 36 X^{3} Y^{2} Z + 2143 X^{2} Y^{2} Z^{2} + 12 X Y^{4} Z + 24 X Y^{2} Z^{3} + 54 X^{3} Y Z + 12 X^{2} Y^{2} Z + 90 X^{2} Y Z^{2} + 462 X Y^{3} Z + 222 X Y^{2} Z^{2} + 36 X Y Z^{3} + 18 X^{2} Y Z + 1350 X Y^{2} Z + 216 X Y Z^{2} + 1590 X Y Z

Algorithm definition

The algorithm ⟨16×30×32:8533⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×15×16:1219⟩.

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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