Description of fast matrix multiplication algorithm: ⟨4×24×24:1454⟩

Algorithm type

X^{2} Y^{22} Z^{2} + X Y^{22} Z + X^{2} Y^{16} Z^{2} + X Y^{18} Z + X Y^{16} Z + 2 X Y^{15} Z + 18 X^{4} Y^{8} Z^{4} + 7 X^{2} Y^{12} Z^{2} + 3 X Y^{14} Z + 2 X^{2} Y^{12} Z + 6 X^{4} Y^{8} Z^{2} + 7 X^{2} Y^{10} Z^{2} + 16 X Y^{12} Z + X^{2} Y^{9} Z^{2} + X Y^{11} Z + 78 X^{4} Y^{4} Z^{4} + 61 X^{2} Y^{8} Z^{2} + 15 X Y^{10} Z + 8 X^{2} Y^{8} Z + 4 X^{2} Y^{7} Z^{2} + 16 X Y^{9} Z + 80 X^{2} Y^{6} Z^{2} + 44 X Y^{8} Z + 4 X^{2} Y^{5} Z^{2} + 158 X^{2} Y^{4} Z^{2} + 80 X Y^{6} Z + 10 X^{2} Y^{4} Z + 16 X Y^{5} Z + 232 X^{2} Y^{2} Z^{2} + 108 X Y^{4} Z + 126 X Y^{3} Z + 176 X Y^{2} Z + 170 X Y Z

Algorithm definition

The algorithm ⟨4×24×24:1454⟩ is serendipitous tensor product (⟨2×6×6:56⟩ - 4) ⊗ ⟨2×4×4:26⟩ +2⟨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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