Description of fast matrix multiplication algorithm: ⟨10×16×32:3058⟩

Algorithm type

X^{2} Y^{10} Z^{2} + 252 X^{4} Y^{4} Z^{4} + X^{2} Y^{8} Z^{2} + X Y^{10} Z + 7 X^{2} Y^{7} Z^{2} + X Y^{9} Z + 6 X^{6} Y^{2} Z^{2} + 87 X^{2} Y^{6} Z^{2} + X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 2 X Y^{8} Z + 16 X^{2} Y^{5} Z^{2} + 2 X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{3} Z^{4} + 9 X Y^{7} Z + X Y^{6} Z^{2} + 42 X^{4} Y^{2} Z^{2} + 417 X^{2} Y^{4} Z^{2} + 122 X^{2} Y^{2} Z^{4} + 33 X Y^{6} Z + 4 X Y^{5} Z^{2} + 2 X Y^{4} Z^{3} + 2 X^{3} Y^{3} Z + 15 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 4 X Y^{5} Z + 4 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 8 X^{3} Y^{2} Z + 14 X^{2} Y^{3} Z + 563 X^{2} Y^{2} Z^{2} + 134 X Y^{4} Z + 58 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 10 X^{3} Y Z + 56 X^{2} Y^{2} Z + 61 X Y^{3} Z + 163 X Y^{2} Z^{2} + 28 X Y Z^{3} + 70 X^{2} Y Z + 320 X Y^{2} Z + 230 X Y Z^{2} + 263 X Y Z

Algorithm definition

The algorithm ⟨10×16×32:3058⟩ is serendipitous tensor product (⟨5×4×8:118⟩ - 22) ⊗ ⟨2×4×4:26⟩ +2⟨2×4×12:77⟩ +8⟨2×4×8:51⟩.

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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