Description of fast matrix multiplication algorithm: ⟨18×20×30:6090⟩

Algorithm type

3 X^{12} Y^{8} Z^{4} + 51 X^{8} Y^{8} Z^{8} + 6 X^{4} Y^{16} Z^{4} + 3 X^{4} Y^{8} Z^{12} + 15 X^{12} Y^{4} Z^{4} + 6 X^{8} Y^{8} Z^{4} + 3 X^{4} Y^{12} Z^{4} + 6 X^{4} Y^{8} Z^{8} + 15 X^{4} Y^{4} Z^{12} + 6 X^{2} Y^{4} Z^{12} + 3 X^{8} Y^{4} Z^{4} + 39 X^{4} Y^{8} Z^{4} + 105 X^{4} Y^{4} Z^{8} + 30 X^{2} Y^{2} Z^{12} + 6 X^{6} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z^{4} + 12 X^{2} Y^{4} Z^{8} + 24 X^{6} Y^{4} Z^{2} + 30 X^{6} Y^{2} Z^{4} + 441 X^{4} Y^{4} Z^{4} + 48 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{6} Z^{4} + 24 X^{2} Y^{4} Z^{6} + 6 X^{2} Y^{2} Z^{8} + 120 X^{6} Y^{2} Z^{2} + 48 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 24 X^{2} Y^{6} Z^{2} + 126 X^{2} Y^{4} Z^{4} + 120 X^{2} Y^{2} Z^{6} + 36 X Y^{2} Z^{6} + 24 X^{4} Y^{2} Z^{2} + 312 X^{2} Y^{4} Z^{2} + 678 X^{2} Y^{2} Z^{4} + 180 X Y Z^{6} + 36 X^{3} Y^{2} Z^{2} + 72 X Y^{4} Z^{2} + 72 X Y^{2} Z^{4} + 36 X^{3} Y^{2} Z + 180 X^{3} Y Z^{2} + 852 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 36 X Y^{3} Z^{2} + 36 X Y^{2} Z^{3} + 36 X Y Z^{4} + 180 X^{3} Y Z + 72 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 36 X Y^{3} Z + 540 X Y^{2} Z^{2} + 180 X Y Z^{3} + 36 X^{2} Y Z + 468 X Y^{2} Z + 288 X Y Z^{2} + 252 X Y Z

Algorithm definition

The algorithm ⟨18×20×30:6090⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×10×15:870⟩.

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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