Description of fast matrix multiplication algorithm: ⟨10×12×20:1502⟩

Algorithm type

104 X^{4} Y^{8} Z^{4} + 24 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 24 X Y^{12} Z + 32 X^{6} Y^{4} Z^{2} + 16 X^{4} Y^{4} Z^{4} + 121 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{4} Z^{6} + X^{2} Y^{7} Z^{2} + 8 X Y^{8} Z^{2} + 48 X^{4} Y^{4} Z^{2} + 64 X^{2} Y^{4} Z^{4} + 23 X Y^{8} Z + 4 X^{2} Y^{5} Z^{2} + 32 X^{3} Y^{4} Z + 42 X^{2} Y^{4} Z^{2} + 4 X Y^{6} Z + 16 X Y^{4} Z^{3} + 48 X^{2} Y^{4} Z + 5 X^{2} Y^{3} Z^{2} + 11 X Y^{5} Z + 64 X Y^{4} Z^{2} + 221 X^{2} Y^{2} Z^{2} + 30 X Y^{4} Z + 64 X^{3} Y Z + 32 X^{2} Y Z^{2} + 62 X Y^{3} Z + 16 X Y^{2} Z^{2} + 32 X Y Z^{3} + 96 X^{2} Y Z + 52 X Y^{2} Z + 128 X Y Z^{2} + 54 X Y Z

Algorithm definition

The algorithm ⟨10×12×20:1502⟩ is serendipitous tensor product (⟨5×3×4:47⟩ - 4) ⊗ ⟨2×4×5:32⟩ +2⟨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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