Description of fast matrix multiplication algorithm: ⟨4×28×28:1974⟩

Algorithm type

X^{2} Y^{28} Z^{2} + X Y^{28} Z + X^{2} Y^{20} Z^{2} + 7 X Y^{21} Z + 4 X^{2} Y^{18} Z^{2} + X Y^{20} Z + 12 X^{4} Y^{12} Z^{4} + 2 X Y^{18} Z + 8 X^{2} Y^{15} Z^{2} + 24 X^{4} Y^{10} Z^{4} + 14 X^{2} Y^{14} Z^{2} + X Y^{16} Z + 34 X Y^{15} Z + 24 X^{4} Y^{8} Z^{4} + 30 X^{2} Y^{12} Z^{2} + 14 X Y^{14} Z + X^{2} Y^{11} Z^{2} + 18 X^{4} Y^{6} Z^{4} + 128 X^{2} Y^{10} Z^{2} + 20 X Y^{12} Z + 6 X^{2} Y^{9} Z^{2} + 2 X Y^{11} Z + 54 X^{4} Y^{4} Z^{4} + 69 X^{2} Y^{8} Z^{2} + 124 X Y^{10} Z + 4 X^{2} Y^{7} Z^{2} + 18 X Y^{9} Z + 6 X^{4} Y^{2} Z^{4} + 116 X^{2} Y^{6} Z^{2} + 48 X Y^{8} Z + 44 X^{2} Y^{5} Z^{2} + 36 X Y^{7} Z + 142 X^{2} Y^{4} Z^{2} + 98 X Y^{6} Z + 32 X^{2} Y^{3} Z^{2} + 168 X Y^{5} Z + 170 X^{2} Y^{2} Z^{2} + 100 X Y^{4} Z + 10 X^{2} Y Z^{2} + 114 X Y^{3} Z + 148 X Y^{2} Z + 120 X Y Z

Algorithm definition

The algorithm ⟨4×28×28:1974⟩ is serendipitous tensor product (⟨2×7×7:76⟩ - 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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