Description of fast matrix multiplication algorithm: ⟨8×21×28:2823⟩

Algorithm type

6 X^{4} Y^{8} Z^{6} + 15 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{6} Z^{6} + 11 X^{4} Y^{8} Z^{2} + 15 X^{4} Y^{6} Z^{4} + 54 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{4} Z^{8} + 8 X^{3} Y^{8} Z^{2} + 12 X^{2} Y^{8} Z^{3} + 2 X^{2} Y^{3} Z^{8} + 11 X^{4} Y^{6} Z^{2} + 135 X^{4} Y^{4} Z^{4} + X^{2} Y^{9} Z + 56 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{4} Z^{6} + 18 X^{2} Y^{2} Z^{8} + 4 X^{4} Y^{5} Z^{2} + 8 X^{3} Y^{6} Z^{2} + 17 X^{2} Y^{8} Z + 21 X^{2} Y^{7} Z^{2} + 24 X^{2} Y^{6} Z^{3} + 12 X^{2} Y^{3} Z^{6} + X Y^{9} Z + 3 X Y^{8} Z^{2} + 58 X^{4} Y^{4} Z^{2} + 8 X^{3} Y^{5} Z^{2} + X^{2} Y^{7} Z + 67 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 108 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + X Y^{7} Z^{2} + 2 X^{4} Y^{4} Z + 8 X^{3} Y^{4} Z^{2} + 29 X^{2} Y^{6} Z + 38 X^{2} Y^{5} Z^{2} + 12 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{3} Z^{4} + 11 X Y^{7} Z + 4 X Y^{4} Z^{4} + 2 X^{4} Y^{3} Z + 8 X^{3} Y^{4} Z + 11 X^{2} Y^{5} Z + 75 X^{2} Y^{4} Z^{2} + 108 X^{2} Y^{2} Z^{4} + 4 X Y^{6} Z + 4 X Y^{5} Z^{2} + 24 X Y^{4} Z^{3} + 8 X Y^{3} Z^{4} + 4 X^{4} Y Z^{2} + 7 X^{3} Y^{3} Z + 6 X^{3} Y^{2} Z^{2} + 51 X^{2} Y^{4} Z + 12 X^{2} Y^{3} Z^{2} + 108 X^{2} Y^{2} Z^{3} + 23 X Y^{5} Z + 45 X Y^{4} Z^{2} + 48 X Y^{3} Z^{3} + 4 X Y^{2} Z^{4} + 2 X^{4} Y Z + 9 X^{2} Y^{3} Z + 363 X^{2} Y^{2} Z^{2} + 74 X Y^{4} Z + 58 X Y^{3} Z^{2} + 24 X Y^{2} Z^{3} + 36 X Y Z^{4} + 3 X^{3} Y Z + 108 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 58 X Y^{3} Z + 24 X Y^{2} Z^{2} + 216 X Y Z^{3} + 7 X^{2} Y Z + 23 X Y^{2} Z + 223 X Y Z^{2} + 192 X Y Z

Algorithm definition

The algorithm ⟨8×21×28:2823⟩ is serendipitous tensor product (⟨2×7×4:45⟩ - 8) ⊗ ⟨4×3×7:63⟩ +4⟨4×6×7:123⟩.

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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