Description of fast matrix multiplication algorithm: ⟨8×25×32:3764⟩

Algorithm type

2 X^{2} Y^{12} Z^{3} + 336 X^{4} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z^{2} + X^{2} Y^{8} Z^{5} + 10 X Y^{12} Z^{2} + 2 X^{2} Y^{9} Z^{3} + 10 X Y^{12} Z + 2 X Y^{11} Z^{2} + 4 X^{2} Y^{8} Z^{3} + X^{2} Y^{6} Z^{5} + 2 X^{2} Y^{5} Z^{6} + 8 X^{6} Y^{4} Z^{2} + 480 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{6} Z^{4} + 5 X Y^{8} Z^{3} + 4 X^{2} Y^{6} Z^{3} + 8 X^{2} Y^{5} Z^{4} + 21 X Y^{8} Z^{2} + X Y^{7} Z^{3} + 56 X^{4} Y^{4} Z^{2} + 2 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{5} Z^{3} + 90 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{3} Z^{5} + 152 X Y^{8} Z + 8 X Y^{7} Z^{2} + 6 X^{2} Y^{5} Z^{2} + 13 X^{2} Y^{4} Z^{3} + 4 X^{2} Y^{3} Z^{4} + X^{2} Y^{2} Z^{5} + 4 X Y^{7} Z + X Y^{6} Z^{2} + X Y^{5} Z^{3} + 8 X^{3} Y^{4} Z + 135 X^{2} Y^{4} Z^{2} + 23 X^{2} Y^{3} Z^{3} + 9 X^{2} Y^{2} Z^{4} + 4 X Y^{6} Z + 23 X Y^{5} Z^{2} + 5 X Y^{4} Z^{3} + 56 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 40 X^{2} Y^{2} Z^{3} + 12 X Y^{5} Z + 130 X Y^{4} Z^{2} + 5 X Y^{3} Z^{3} + 711 X^{2} Y^{2} Z^{2} + 150 X Y^{4} Z + 63 X Y^{3} Z^{2} + 9 X Y^{2} Z^{3} + 16 X^{3} Y Z + 46 X Y^{3} Z + 48 X Y^{2} Z^{2} + 7 X Y Z^{3} + 112 X^{2} Y Z + 312 X Y^{2} Z + 276 X Y Z^{2} + 303 X Y Z

Algorithm definition

The algorithm ⟨8×25×32:3764⟩ is serendipitous tensor product (⟨4×5×8:118⟩ - 22) ⊗ ⟨2×5×4:32⟩ +2⟨2×5×12:94⟩ +8⟨2×5×8:63⟩.

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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