Description of fast matrix multiplication algorithm: ⟨4×15×32:1258⟩

Algorithm type

4 X^{2} Y^{15} Z^{2} + 4 X^{4} Y^{10} Z^{4} + 28 X Y^{15} Z + 16 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{12} Z^{2} + 4 X^{4} Y^{6} Z^{4} + 28 X^{2} Y^{10} Z^{2} + 24 X Y^{12} Z + 4 X^{2} Y^{9} Z^{2} + 44 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + X^{2} Y^{7} Z^{2} + 32 X Y^{9} Z + 79 X^{2} Y^{6} Z^{2} + 15 X^{2} Y^{5} Z^{2} + 4 X Y^{7} Z + 74 X^{2} Y^{4} Z^{2} + 28 X Y^{6} Z + 14 X^{2} Y^{3} Z^{2} + 91 X Y^{5} Z + 199 X^{2} Y^{2} Z^{2} + 81 X Y^{4} Z + 165 X Y^{3} Z + 79 X Y^{2} Z + 200 X Y Z

Algorithm definition

The algorithm ⟨4×15×32:1258⟩ is serendipitous tensor product (⟨2×5×8:63⟩ - 4) ⊗ ⟨2×3×4:20⟩ +2⟨2×6×4:39⟩.

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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