Description of fast matrix multiplication algorithm: ⟨16×30×30:7980⟩

Algorithm type

3 X^{8} Y^{12} Z^{8} + 12 X^{16} Y^{4} Z^{4} + 69 X^{8} Y^{8} Z^{8} + 12 X^{4} Y^{4} Z^{16} + 45 X^{4} Y^{12} Z^{4} + 24 X^{4} Y^{8} Z^{8} + 150 X^{4} Y^{8} Z^{4} + 12 X^{4} Y^{4} Z^{8} + 78 X^{2} Y^{12} Z^{2} + 24 X^{8} Y^{4} Z^{2} + 24 X^{4} Y^{6} Z^{4} + 48 X^{2} Y^{8} Z^{4} + 24 X^{2} Y^{4} Z^{8} + 96 X^{8} Y^{2} Z^{2} + 597 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 96 X^{2} Y^{2} Z^{8} + 348 X^{2} Y^{6} Z^{2} + 216 X^{2} Y^{4} Z^{4} + 1014 X^{2} Y^{4} Z^{2} + 96 X^{2} Y^{2} Z^{4} + 468 X Y^{6} Z + 144 X^{4} Y^{2} Z + 36 X^{2} Y^{3} Z^{2} + 288 X Y^{4} Z^{2} + 144 X Y^{2} Z^{4} + 144 X^{4} Y Z + 1188 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 144 X Y Z^{4} + 468 X Y^{3} Z + 432 X Y^{2} Z^{2} + 684 X Y^{2} Z + 144 X Y Z^{2} + 540 X Y Z

Algorithm definition

The algorithm ⟨16×30×30:7980⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×15×15:1140⟩.

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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