Polyhedron.integral_points(): OverflowError: value too large to convert to int #21993
Description
I noticed the following bug in Sage:
sage: %timeit (Polyhedron(vertices=((0, 0), (1789345,37121))) + 1/1000*polytopes.hypercube(2)).integral_points()
...
/Users/mkoeppe/s/sage/sage-rebasing/yet/another/local/lib/python2.7/site-packages/sage/geometry/polyhedron/base.pyc in integral_points(self, threshold)
4357 box_points<threshold:
4358 from sage.geometry.integral_points import rectangular_box_points
-> 4359 return rectangular_box_points(box_min, box_max, self)
4360
4361 # for more complicate polytopes, triangulate & use smith normal form
/Users/mkoeppe/s/sage/sage-rebasing/src/sage/geometry/integral_points.pyx in sage.geometry.integral_points.rectangular_box_points (build/cythonized/sage/geometry/integral_points.c:6809)()
552 v = vector(ZZ, d)
553 if not return_saturated:
--> 554 for p in loop_over_rectangular_box_points(box_min, box_max, inequalities, d, count_only):
555 # v = vector(ZZ, orig_perm.action(p)) # too slow
556 for i in range(0,d):
/Users/mkoeppe/s/sage/sage-rebasing/src/sage/geometry/integral_points.pyx in sage.geometry.integral_points.loop_over_rectangular_box_points (build/cythonized/sage/geometry/integral_points.c:7772)()
601 while True:
602 sig_check()
--> 603 inequalities.prepare_inner_loop(p)
604 i_min = box_min[0]
605 i_max = box_max[0]
/Users/mkoeppe/s/sage/sage-rebasing/src/sage/geometry/integral_points.pyx in sage.geometry.integral_points.InequalityCollection.prepare_inner_loop (build/cythonized/sage/geometry/integral_points.c:14134)()
1256 """
1257 for ineq in self.ineqs_int:
-> 1258 (<Inequality_int>ineq).prepare_inner_loop(p)
1259 for ineq in self.ineqs_generic:
1260 (<Inequality_generic>ineq).prepare_inner_loop(p)
/Users/mkoeppe/s/sage/sage-rebasing/src/sage/geometry/integral_points.pyx in sage.geometry.integral_points.Inequality_int.prepare_inner_loop (build/cythonized/sage/geometry/integral_points.c:10574)()
938 cdef int j
939 if self.dim>1:
--> 940 self.cache = self.cache_next + self.coeff_next*p[1]
941 else:
942 self.cache = self.cache_next
OverflowError: value too large to convert to int
(Note that this example would not get far with the code in Sage anyway because the code tries to use the rectangle bounding box method for all non-integral polytopes.)
CC: @novoselt @tscrim @vbraun @videlec @sagetrac-tmonteil @jplab
Component: geometry
Keywords: thursdaysbdx
Author: Matthias Koeppe
Branch/Commit: 76cd1ea
Reviewer: Sébastien Labbé
Issue created by migration from https://trac.sagemath.org/ticket/21993