Description of fast matrix multiplication algorithm: ⟨6×25×28:2525⟩

Algorithm type

16 X^{4} Y^{12} Z^{4} + 16 X^{2} Y^{16} Z^{2} + 16 X Y^{16} Z + 192 X^{4} Y^{8} Z^{4} + 48 X^{2} Y^{12} Z^{2} + 48 X^{2} Y^{8} Z^{4} + 32 X Y^{12} Z + X^{2} Y^{5} Z^{6} + 16 X^{6} Y^{4} Z^{2} + 304 X^{2} Y^{8} Z^{2} + 35 X^{2} Y^{4} Z^{6} + 3 X^{2} Y^{5} Z^{4} + 48 X Y^{8} Z^{2} + 16 X^{4} Y^{4} Z^{2} + 99 X^{2} Y^{4} Z^{4} + 20 X^{2} Y^{2} Z^{6} + 112 X Y^{8} Z + 2 X^{2} Y^{3} Z^{4} + X^{2} Y Z^{6} + 9 X Y^{5} Z^{3} + 16 X^{3} Y^{4} Z + 16 X^{2} Y^{4} Z^{2} + 5 X^{2} Y^{2} Z^{4} + 45 X Y^{4} Z^{3} + 16 X^{2} Y^{4} Z + 32 X^{2} Y^{3} Z^{2} + X^{2} Y Z^{4} + 3 X Y^{5} Z + 96 X Y^{4} Z^{2} + 15 X Y^{3} Z^{3} + 390 X^{2} Y^{2} Z^{2} + 53 X Y^{4} Z + 10 X Y^{2} Z^{3} + 4 X Y Z^{4} + 32 X^{3} Y Z + 65 X Y^{3} Z + 96 X Y^{2} Z^{2} + 101 X Y Z^{3} + 32 X^{2} Y Z + 230 X Y^{2} Z + 192 X Y Z^{2} + 41 X Y Z

Algorithm definition

The algorithm ⟨6×25×28:2525⟩ is serendipitous tensor product (⟨3×5×7:79⟩ - 5) ⊗ ⟨2×5×4:32⟩ +⟨2×5×20:157⟩.

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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