Description of fast matrix multiplication algorithm: ⟨14×24×32:6064⟩

Algorithm type

64 X^{8} Y^{8} Z^{8} + 64 X^{4} Y^{12} Z^{4} + 24 X^{4} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z^{2} + 600 X^{4} Y^{4} Z^{4} + 32 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{6} Z^{4} + 24 X Y^{9} Z + 12 X Y^{6} Z^{4} + 36 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{4} Z^{2} + 488 X^{2} Y^{6} Z^{2} + 128 X^{2} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{6} + 8 X Y^{6} Z^{3} + 24 X^{2} Y^{6} Z + 24 X Y^{6} Z^{2} + 24 X Y^{4} Z^{4} + 12 X^{4} Y^{2} Z^{2} + 340 X^{2} Y^{4} Z^{2} + 124 X^{2} Y^{2} Z^{4} + 160 X Y^{6} Z + 32 X Y^{4} Z^{3} + 12 X Y^{3} Z^{4} + 36 X^{3} Y^{3} Z + 36 X Y^{3} Z^{3} + 72 X Y^{2} Z^{4} + 12 X^{2} Y^{3} Z + 1196 X^{2} Y^{2} Z^{2} + 136 X Y^{4} Z + 28 X Y^{3} Z^{2} + 88 X Y^{2} Z^{3} + 48 X Y Z^{4} + 36 X^{3} Y Z + 24 X^{2} Y^{2} Z + 512 X Y^{3} Z + 88 X Y^{2} Z^{2} + 60 X Y Z^{3} + 12 X^{2} Y Z + 532 X Y^{2} Z + 92 X Y Z^{2} + 748 X Y Z

Algorithm definition

The algorithm ⟨14×24×32:6064⟩ is serendipitous tensor product (⟨2×3×4:20⟩ - 8) ⊗ ⟨7×8×8:306⟩ +4⟨7×8×16:598⟩.

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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