Volume of a Voronoi cell is wrong #37086
Description
Steps To Reproduce
sage: from sage.modules.free_module_integer import IntegerLattice
sage: l = [7, 0, -1, -2, -1, -2, 7, -2, 0, 0, -2, 0, 7, -2, 0, -1, -2, -1, 7, 0 , -1, -1, 0, -2, 7]
sage: M = matrix(5, 5, l)
sage: c = IntegerLattice(M).voronoi_cell()
sage: M
[ 7 0 -1 -2 -1]
[-2 7 -2 0 0]
[-2 0 7 -2 0]
[-1 -2 -1 7 0]
[-1 -1 0 -2 7]
sage: c
A 5-dimensional polyhedron in QQ^5 defined as the convex hull of 598 vertices
Expected Behavior
The volume of c should be equal to the determinant of M:
sage: c.volume()
12858
sage: M.det()
12858
Actual Behavior
sage: c.volume()
138219104/10715
sage: n(_)
12899.5897340177
Additional Information
This was first reported here:
https://ask.sagemath.org/question/74836/is-there-a-problem-in-voronoi-cell-computation/
Environment
- **OS**: Ubuntu 22.04.1 LTS
- SageMath version 10.2, Release Date: 2023-12-03
- Using Python 3.10.12. Type "help()" for help.Checklist
- I have searched the existing issues for a bug report that matches the one I want to file, without success.
- I have read the documentation and troubleshoot guide