Description of fast matrix multiplication algorithm: ⟨4×24×25:1503⟩

Algorithm type

X^{3} Y^{21} Z^{2} + 16 X^{4} Y^{16} Z^{4} + 5 X^{2} Y^{21} Z + 2 X^{4} Y^{17} Z^{2} + X^{3} Y^{18} Z^{2} + X^{2} Y^{20} Z + X Y^{21} Z + X^{2} Y^{17} Z^{2} + X^{2} Y^{17} Z + 32 X^{2} Y^{16} Z^{2} + X Y^{18} Z + 2 X^{2} Y^{16} Z + 2 X Y^{17} Z + 16 X Y^{16} Z + X^{3} Y^{12} Z^{2} + 88 X^{4} Y^{8} Z^{4} + 3 X^{2} Y^{13} Z + 64 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{12} Z + 2 X Y^{13} Z + 4 X^{3} Y^{9} Z^{2} + 65 X Y^{12} Z + 3 X^{3} Y^{8} Z^{2} + X^{2} Y^{9} Z^{2} + 3 X^{2} Y^{9} Z + 123 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{8} Z + 2 X Y^{9} Z + 32 X Y^{8} Z + 6 X^{2} Y^{5} Z + 176 X^{2} Y^{4} Z^{2} + 7 X^{2} Y^{4} Z + 176 X^{2} Y^{2} Z^{2} + 180 X Y^{4} Z + 128 X Y^{3} Z + 64 X Y^{2} Z + 288 X Y Z

Algorithm definition

The algorithm ⟨4×24×25:1503⟩ is serendipitous tensor product (⟨2×6×5:47⟩ - 2) ⊗ ⟨2×4×5:32⟩ +⟨2×8×5:63⟩.

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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