Description of fast matrix multiplication algorithm: ⟨16×24×28:6125⟩

Algorithm type

2 X^{16} Y^{16} Z^{16} + 2 X^{16} Y^{12} Z^{12} + X^{8} Y^{24} Z^{8} + 2 X^{8} Y^{20} Z^{8} + X^{8} Y^{20} Z^{4} + 54 X^{8} Y^{8} Z^{8} + 24 X^{8} Y^{6} Z^{6} + 2 X^{8} Y^{4} Z^{8} + 24 X^{4} Y^{12} Z^{4} + 24 X^{4} Y^{10} Z^{4} + X^{8} Y^{4} Z^{4} + 12 X^{4} Y^{10} Z^{2} + 18 X^{4} Y^{8} Z^{4} + 486 X^{4} Y^{4} Z^{4} + 72 X^{4} Y^{3} Z^{3} + 24 X^{4} Y^{2} Z^{4} + 180 X^{2} Y^{6} Z^{2} + 72 X^{2} Y^{5} Z^{2} + 12 X^{4} Y^{2} Z^{2} + 36 X^{2} Y^{5} Z + 216 X^{2} Y^{4} Z^{2} + 1728 X^{2} Y^{2} Z^{2} + 72 X^{2} Y Z^{2} + 432 X Y^{3} Z + 36 X^{2} Y Z + 648 X Y^{2} Z + 1944 X Y Z

Algorithm definition

The algorithm ⟨16×24×28:6125⟩ is the (Kronecker) tensor product of ⟨4×4×4:49⟩ with ⟨4×6×7:125⟩.

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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