I have a program in which I start with a triangulation of an n-dimensional simplex - for now, the triangulation is defined using a list of monomials and a list of coefficients. I also have a (long) list of signs distributions on the vertices of that triangulation. For each signs distribution, I want to compute the Betti numbers of the associated patchworked hypersurface.

In other words, it looks something like this :

Code: Select all

```
my $my_monomials = ...;
my @my_coeffs = ...;
my $h1 = new Hypersurface<Min>(MONOMIALS=>$my_monomials, COEFFICIENTS=>@my_coeffs);
my @Betti_num_array=();
# I get my signs distributions from a file
open(INPUT, "<", "$ARGV[0]/$ARGV[1]");
while(<INPUT>){
push(@Betti_num_array,$h1->PATCHWORK(SIGNS=>$_)->BETTI_NUMBERS_Z2);
}
```

For example, I understand that polymake uses production rules to compute new properties, and I thought there might be some intermediate property that would depend only on the triangulation (and not on the signs) that I could compute once beforehand to save some time, or maybe some more low-level optimization trick.

Note that I am not complaining, I am already very impressed with polymake's performance.

Best regards and thanks in advance,

Charles Arnal