Description of fast matrix multiplication algorithm: ⟨14×16×21:2823⟩

Algorithm type

6 X^{6} Y^{8} Z^{4} + 6 X^{6} Y^{6} Z^{4} + 15 X^{4} Y^{8} Z^{4} + 2 X^{8} Y^{4} Z^{2} + 54 X^{6} Y^{4} Z^{4} + 15 X^{4} Y^{6} Z^{4} + 10 X^{2} Y^{8} Z^{4} + X Y^{12} Z + 2 X^{8} Y^{3} Z^{2} + 12 X^{3} Y^{8} Z^{2} + 12 X^{2} Y^{8} Z^{3} + 18 X^{8} Y^{2} Z^{2} + 12 X^{6} Y^{4} Z^{2} + 135 X^{4} Y^{4} Z^{4} + 56 X^{2} Y^{8} Z^{2} + 10 X^{2} Y^{6} Z^{4} + 12 X^{6} Y^{3} Z^{2} + 24 X^{3} Y^{6} Z^{2} + 6 X^{2} Y^{8} Z + 16 X^{2} Y^{7} Z^{2} + 12 X^{2} Y^{6} Z^{3} + 5 X^{2} Y^{5} Z^{4} + 19 X Y^{8} Z^{2} + 108 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 68 X^{2} Y^{6} Z^{2} + 7 X^{2} Y^{5} Z^{3} + 60 X^{2} Y^{4} Z^{4} + 6 X Y^{8} Z + 4 X^{4} Y^{4} Z + 12 X^{4} Y^{3} Z^{2} + 12 X^{3} Y^{4} Z^{2} + 2 X^{2} Y^{6} Z + 37 X^{2} Y^{5} Z^{2} + 8 X^{2} Y^{4} Z^{3} + X^{2} Y^{3} Z^{4} + 7 X Y^{7} Z + 31 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 8 X^{4} Y^{3} Z + 108 X^{4} Y^{2} Z^{2} + 24 X^{3} Y^{4} Z + 80 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 3 X Y^{6} Z + 2 X Y^{5} Z^{2} + 15 X Y^{4} Z^{3} + 4 X Y^{3} Z^{4} + 4 X^{4} Y^{2} Z + 48 X^{3} Y^{3} Z + 108 X^{3} Y^{2} Z^{2} + 43 X^{2} Y^{4} Z + 14 X^{2} Y^{3} Z^{2} + 7 X Y^{5} Z + 65 X Y^{4} Z^{2} + 13 X Y^{3} Z^{3} + 36 X^{4} Y Z + 24 X^{3} Y^{2} Z + 61 X^{2} Y^{3} Z + 363 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 57 X Y^{4} Z + 20 X Y^{3} Z^{2} + 2 X Y Z^{4} + 216 X^{3} Y Z + 24 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 57 X Y^{3} Z + 108 X Y^{2} Z^{2} + 222 X^{2} Y Z + 20 X Y^{2} Z + 27 X Y Z^{2} + 192 X Y Z

Algorithm definition

The algorithm ⟨14×16×21:2823⟩ is serendipitous tensor product (⟨2×4×7:45⟩ - 8) ⊗ ⟨7×4×3:63⟩ +4⟨7×4×6:123⟩.

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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