Description of fast matrix multiplication algorithm: ⟨16×22×24:4732⟩

Algorithm type

6 X^{8} Y^{10} Z^{8} + 30 X^{8} Y^{8} Z^{8} + 2 X^{12} Y^{6} Z^{4} + X^{8} Y^{6} Z^{8} + 4 X^{4} Y^{10} Z^{8} + 5 X^{4} Y^{6} Z^{12} + 7 X^{12} Y^{4} Z^{4} + 7 X^{8} Y^{4} Z^{8} + 19 X^{4} Y^{12} Z^{4} + 7 X^{4} Y^{8} Z^{8} + 12 X^{4} Y^{4} Z^{12} + X^{8} Y^{6} Z^{4} + 55 X^{4} Y^{10} Z^{4} + 7 X^{4} Y^{6} Z^{8} + 4 X^{8} Y^{4} Z^{4} + 65 X^{4} Y^{8} Z^{4} + 14 X^{4} Y^{4} Z^{8} + 6 X^{2} Y^{12} Z^{2} + 7 X^{2} Y^{10} Z^{4} + 6 X^{6} Y^{6} Z^{2} + 47 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z^{2} + 2 X^{2} Y^{8} Z^{4} + 5 X^{2} Y^{6} Z^{6} + 36 X^{4} Y^{5} Z^{4} + 5 X^{6} Y^{4} Z^{2} + 2 X^{4} Y^{6} Z^{2} + 207 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{4} + 8 X^{2} Y^{4} Z^{6} + 12 X^{6} Y^{3} Z^{2} + 6 X^{4} Y^{3} Z^{4} + 24 X^{2} Y^{5} Z^{4} + 30 X^{2} Y^{3} Z^{6} + 43 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 42 X^{4} Y^{2} Z^{4} + 234 X^{2} Y^{6} Z^{2} + 56 X^{2} Y^{4} Z^{4} + 74 X^{2} Y^{2} Z^{6} + 6 X^{4} Y^{3} Z^{2} + 330 X^{2} Y^{5} Z^{2} + 42 X^{2} Y^{3} Z^{4} + 24 X^{4} Y^{2} Z^{2} + 490 X^{2} Y^{4} Z^{2} + 88 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 42 X Y^{5} Z^{2} + 36 X^{3} Y^{3} Z + 282 X^{2} Y^{3} Z^{2} + 36 X Y^{5} Z + 12 X Y^{4} Z^{2} + 30 X Y^{3} Z^{3} + 30 X^{3} Y^{2} Z + 12 X^{2} Y^{3} Z + 212 X^{2} Y^{2} Z^{2} + 24 X Y^{4} Z + 72 X Y^{3} Z^{2} + 48 X Y^{2} Z^{3} + 6 X^{3} Y Z + 12 X^{2} Y^{2} Z + 720 X Y^{3} Z + 84 X Y^{2} Z^{2} + 12 X Y Z^{3} + 600 X Y^{2} Z + 24 X Y Z^{2} + 300 X Y Z

Algorithm definition

The algorithm ⟨16×22×24:4732⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×12:676⟩.

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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