SfStrongTriDec

SfStrongTriDec is short for square-free strong triangular decomposition (SFSTD). We propose an algorithm for SFSTD of zero-dimensional polynomial systems in our paper.

Code

All code is in "SFSTD.mpl".

• The procedure "PolylistToNormal" is used for computing strong triangular decomposition (STD) of zero-dimensional polynomial systems.
• The procedure "PolylistToSfNormal" is used for computing SFSTD of zero-dimensional polynomial systems.

Dependency

Maple 2021

Using

read ".../SFSTD.mpl";
PolylistToNormal(sys, vars);
PolylistToSfNormal(sys, vars);

Examples

• Testing examples in "cm.mpl" are from ¹.
• Testing examples in "wangzero.mpl" are from ².
• Testing examples in "xia2006.mpl" are from ³.
• Testing examples in "database1.mpl" and "database2.mpl" are from ⁴.

Total 151 testing examples are also in "allbench.wls".

Experimental Results

We present our experimental results in the sheet "allbench.csv". The column "Algorithm 3" and the column "mp-rc" record the time for triangular decomposition (followed by the numbers of components in parenthesis) by Algorithm 3 and the method mp-rc, respectively. All tests were conducted on 16-Core Intel Core i7-12900KF@3.20GHz with 128GB of memory and Windows 11.

Footnotes

1. https://doi.org/10.1007/978-3-662-43799-5_4 ↩

2. https://doi.org/10.1016/S0378-4754(96)00008-0 ↩

3. https://doi.org/10.1016/j.camwa.2006.06.003 ↩

4. http://homepages.math.uic.edu/~jan/demo.html ↩