Description of fast matrix multiplication algorithm: ⟨8×15×24:1824⟩

Algorithm type

3 X Y^{15} Z + 10 X^{4} Y^{8} Z^{4} + 3 X^{2} Y^{12} Z^{2} + 50 X^{4} Y^{6} Z^{4} + 10 X^{2} Y^{10} Z^{2} + 2 X^{2} Y^{8} Z^{4} + 18 X Y^{12} Z + 15 X^{2} Y^{9} Z^{2} + 2 X Y^{10} Z^{2} + 3 X^{6} Y^{4} Z^{2} + 62 X^{4} Y^{4} Z^{4} + 61 X^{2} Y^{8} Z^{2} + 10 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{4} Z^{6} + X Y^{10} Z + 15 X^{6} Y^{3} Z^{2} + 10 X^{4} Y^{3} Z^{4} + 10 X^{2} Y^{3} Z^{6} + 24 X Y^{9} Z + 12 X Y^{8} Z^{2} + 18 X^{6} Y^{2} Z^{2} + X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 103 X^{2} Y^{6} Z^{2} + 23 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 6 X Y^{8} Z + 5 X^{4} Y^{3} Z^{2} + 3 X^{3} Y^{5} Z + 2 X^{2} Y^{5} Z^{2} + 55 X^{2} Y^{3} Z^{4} + 16 X Y^{6} Z^{2} + 2 X Y^{5} Z^{3} + 6 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{4} Z + X^{2} Y^{5} Z + 101 X^{2} Y^{4} Z^{2} + 66 X^{2} Y^{2} Z^{4} + 32 X Y^{6} Z + 11 X Y^{5} Z^{2} + 12 X Y^{4} Z^{3} + 24 X^{3} Y^{3} Z + 6 X^{2} Y^{4} Z + 31 X^{2} Y^{3} Z^{2} + 3 X Y^{5} Z + 82 X Y^{4} Z^{2} + 16 X Y^{3} Z^{3} + 24 X^{3} Y^{2} Z + 8 X^{2} Y^{3} Z + 164 X^{2} Y^{2} Z^{2} + 26 X Y^{4} Z + 88 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 39 X^{3} Y Z + 8 X^{2} Y^{2} Z + 26 X^{2} Y Z^{2} + 63 X Y^{3} Z + 114 X Y^{2} Z^{2} + 26 X Y Z^{3} + 13 X^{2} Y Z + 37 X Y^{2} Z + 143 X Y Z^{2} + 39 X Y Z

Algorithm definition

The algorithm ⟨8×15×24:1824⟩ is the (Kronecker) tensor product of ⟨2×5×6:48⟩ with ⟨4×3×4:38⟩.

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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