**Curves&Braids** is a C++ programme with the following options:

- Draw curves in the n-punctured disk.

- Apply a set of braids to a curve.

- Obtain the minimal braid that turns a curve into a round one.

The algorithm to compute the minimal standardizer of a curve
is explained in my article "On the minimal positive standardizer of a parabolic subgroup of an Artin-Tits group". The output is a postscript file (.ps) with the drawings and results. You can download the code(.cpp) in the following link:

**How to enter the input?**
__Entering the interesections of the curve with the real axis__: Starting by an arcs in the
upper-half plane, run along the curve and note theintersections with the real axis in the next way:
0 if the intersection is before the first puncture, N if it is after the last puncture and I if
the intersection is between the punctures I and I+1. After that, write the number of punctures.

__Reduced Dynnikov coordinates__: Let us consider the following triangulation of the n-punctured disk:

Dynnikov coordinates are represented by

where each x represent the number of times that the curve intersects the corresponding line e.

**Dynnikov reduced coordinates**
are represented by

where

and

and

The programme also computes Dynnikov coordinates from the first input.

__Enter a braid__: To enter a braid just write separately the subscripts of the generators.

**Example**
If we select entering the curve arc by arc and write 0 1 2 3 in a 5-punctured disk, it will be obtained:

If we apply to this curve the braid 2 and then the braid 1 1, the output will be: