Description of fast matrix multiplication algorithm: ⟨15×16×28:3843⟩

Algorithm type

36 X^{4} Y^{9} Z^{4} + 6 X^{4} Y^{6} Z^{6} + 12 X^{2} Y^{12} Z^{2} + 12 X^{4} Y^{9} Z^{2} + 6 X^{4} Y^{3} Z^{8} + 4 X^{2} Y^{12} Z + 144 X^{4} Y^{6} Z^{4} + 15 X^{4} Y^{4} Z^{6} + 15 X^{4} Y^{2} Z^{8} + 12 X^{2} Y^{6} Z^{6} + 16 X Y^{12} Z + 6 X^{4} Y^{3} Z^{6} + 6 X^{4} Y Z^{8} + 120 X^{2} Y^{9} Z^{2} + 2 X^{2} Y^{8} Z^{3} + 30 X^{4} Y^{6} Z^{2} + 135 X^{4} Y^{4} Z^{4} + 21 X^{4} Y^{2} Z^{6} + 24 X^{2} Y^{9} Z + 18 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{6} Z^{4} + 30 X^{2} Y^{4} Z^{6} + 4 X Y^{8} Z^{3} + 12 X^{6} Y^{3} Z^{2} + 60 X^{4} Y^{3} Z^{4} + 6 X^{4} Y Z^{6} + 12 X^{2} Y^{6} Z^{3} + 96 X Y^{9} Z + 8 X Y^{8} Z^{2} + 30 X^{6} Y^{2} Z^{2} + 114 X^{4} Y^{2} Z^{4} + 360 X^{2} Y^{6} Z^{2} + 62 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 20 X Y^{8} Z + 24 X Y^{6} Z^{3} + 12 X^{6} Y Z^{2} + 24 X^{4} Y^{3} Z^{2} + 24 X^{4} Y Z^{4} + 24 X^{2} Y^{6} Z + 14 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{3} Z^{4} + 48 X Y^{6} Z^{2} + 30 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 266 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 36 X^{2} Y^{2} Z^{4} + 216 X Y^{6} Z + 24 X Y^{4} Z^{3} + 12 X^{4} Y Z^{2} + 24 X^{3} Y^{3} Z + 4 X^{2} Y^{4} Z + 210 X^{2} Y^{3} Z^{2} + 22 X^{2} Y^{2} Z^{3} + 10 X^{2} Y Z^{4} + 48 X Y^{4} Z^{2} + 24 X^{3} Y^{2} Z + 44 X^{2} Y^{3} Z + 333 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 138 X Y^{4} Z + 20 X Y^{2} Z^{3} + 20 X^{3} Y Z + 24 X^{2} Y^{2} Z + 94 X^{2} Y Z^{2} + 188 X Y^{3} Z + 40 X Y^{2} Z^{2} + 20 X^{2} Y Z + 208 X Y^{2} Z + 90 X Y Z

Algorithm definition

The algorithm ⟨15×16×28:3843⟩ is the (Kronecker) tensor product of ⟨3×4×7:63⟩ with ⟨5×4×4:61⟩.

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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