Description of fast matrix multiplication algorithm: ⟨16×28×32:8036⟩

Algorithm type

3 X^{16} Y^{16} Z^{16} + X^{16} Y^{12} Z^{16} + 2 X^{12} Y^{12} Z^{16} + 2 X^{8} Y^{20} Z^{8} + 4 X^{8} Y^{16} Z^{8} + 2 X^{8} Y^{12} Z^{8} + 74 X^{8} Y^{8} Z^{8} + 2 X^{4} Y^{12} Z^{8} + 12 X^{8} Y^{6} Z^{8} + 2 X^{8} Y^{4} Z^{8} + 24 X^{6} Y^{6} Z^{8} + 18 X^{4} Y^{12} Z^{4} + 24 X^{4} Y^{10} Z^{4} + 72 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{6} Z^{4} + 630 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{6} Z^{4} + 36 X^{4} Y^{3} Z^{4} + 24 X^{4} Y^{2} Z^{4} + 72 X^{3} Y^{3} Z^{4} + 216 X^{2} Y^{6} Z^{2} + 72 X^{2} Y^{5} Z^{2} + 432 X^{2} Y^{4} Z^{2} + 72 X^{2} Y^{3} Z^{2} + 2160 X^{2} Y^{2} Z^{2} + 72 X Y^{3} Z^{2} + 72 X^{2} Y Z^{2} + 648 X Y^{3} Z + 864 X Y^{2} Z + 2376 X Y Z

Algorithm definition

The algorithm ⟨16×28×32:8036⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×14×16:1148⟩.

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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