# Welcome to islpy’s documentation!¶

islpy is a Python wrapper around Sven Verdoolaege’s isl, a library for manipulating sets and relations of integer points bounded by linear constraints.

Supported operations on sets include

• intersection, union, set difference,
• emptiness check,
• convex hull,
• (integer) affine hull,
• integer projection,
• computing the lexicographic minimum using parametric integer programming,
• coalescing, and
• parametric vertex enumeration.

It also includes an ILP solver based on generalized basis reduction, transitive closures on maps (which may encode infinite graphs), dependence analysis and bounds on piecewise step-polynomials.

Now you obviously want to watch the library do something (at least mildly) cool? Well, sit back and watch:

import islpy as isl

space = isl.Space.create_from_names(isl.DEFAULT_CONTEXT, set=["x", "y"])

bset = (isl.BasicSet.universe(space)
print("set 1 %s:" % bset)

bset2 = isl.BasicSet("{[x, y] : x >= 0 and x < 5 and y >= 0 and y < x+4 }")
print("set 2: %s" % bset2)

bsets_in_union = []
bset.union(bset2).convex_hull().foreach_basic_set(bsets_in_union.append)
print(bsets_in_union)
union, = bsets_in_union
print("union: %s" % union)


This prints the following:

set 1: { [x, y] : x >= 1 and x <= 5 and y >= 1 and y <= 5 }
set 2: { [x, y] : x >= 0 and x <= 4 and y >= 0 and y <= 3 + x }
union: { [x, y] : x >= 0 and y >= 0 and x <= 5 and y <= 3 + 2x and y >= -4 + x and y <= 15 - 2x and 3y <= 13 + 2x }


With some hacky plotting code (not shown), you can actually see what this example just did. We gave it the two polyhedra on the left, asked it to compute the union, and computed the convex hull:

See example/demo.py to see the full example, including the less-than-perfect plotting code. :)

Note that far better plotting of isl(py) sets is available by installing Tobias Grosser’s islplot package.

## Overview¶

This manual will not try to teach you much about the isl itself, it simply lists, in a reference fashion, all the entrypoints available in islpy. To get information on how to use the isl, see the real isl manual. The manual for the barvinok package is also quite helpful to get an idea.