Description of fast matrix multiplication algorithm: ⟨10×24×32:4407⟩

Algorithm type

X^{2} Y^{12} Z^{2} + X^{2} Y^{10} Z^{2} + X Y^{12} Z + 3 X^{2} Y^{7} Z^{4} + 420 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{6} Z^{4} + X^{2} Y^{4} Z^{6} + 2 X Y^{10} Z + 6 X^{2} Y^{6} Z^{3} + 2 X^{2} Y^{5} Z^{4} + 3 X Y^{9} Z + 3 X Y^{8} Z^{2} + 143 X^{2} Y^{6} Z^{2} + 7 X^{2} Y^{5} Z^{3} + 15 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 4 X Y^{8} Z + 8 X Y^{7} Z^{2} + 2 X^{2} Y^{5} Z^{2} + 11 X^{2} Y^{4} Z^{3} + 9 X^{2} Y^{3} Z^{4} + X^{2} Y^{2} Z^{5} + 4 X Y^{7} Z + 23 X Y^{6} Z^{2} + 90 X^{4} Y^{2} Z^{2} + 709 X^{2} Y^{4} Z^{2} + 15 X^{2} Y^{3} Z^{3} + 126 X^{2} Y^{2} Z^{4} + 51 X Y^{6} Z + 12 X Y^{5} Z^{2} + 4 X Y^{4} Z^{3} + 10 X^{2} Y^{3} Z^{2} + 11 X^{2} Y^{2} Z^{3} + 9 X Y^{5} Z + 27 X Y^{4} Z^{2} + 5 X Y^{3} Z^{3} + 30 X^{2} Y^{3} Z + 841 X^{2} Y^{2} Z^{2} + 207 X Y^{4} Z + 79 X Y^{3} Z^{2} + 120 X^{2} Y^{2} Z + 80 X Y^{3} Z + 216 X Y^{2} Z^{2} + 17 X Y Z^{3} + 150 X^{2} Y Z + 407 X Y^{2} Z + 250 X Y Z^{2} + 262 X Y Z

Algorithm definition

The algorithm ⟨10×24×32:4407⟩ is serendipitous tensor product (⟨5×6×8:170⟩ - 27) ⊗ ⟨2×4×4:26⟩ +⟨2×4×12:77⟩ +12⟨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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