Better error handling of the polyhedron constructor for non-embedded NumberField and floats.

[jplab]

These error messages are not really informative of what the problem really is:

sage: K = NumberField(x^2-2,'s')
sage: s = K.0
sage: L = NumberField(x^3-2,'t')
sage: t = L.0
sage: P = Polyhedron(vertices = [[0,s],[t,0]])
Traceback (most recent call last):
...
AttributeError: 'Objects_with_category' object has no attribute 'is_exact'

similar problem with floats:

sage: f = float(1.1)
sage: f
1.1
sage: Polyhedron(vertices=[[f]])
Traceback (most recent call last):
...
AttributeError: type object 'float' has no attribute 'is_exact'

The constructor could try to detect the problem and return an informative message.

Once this is fixed, ticket #22552 is a follow-up ticket that should be fixed easily from the present resolution.

Depends on #23345

CC: @mo271 @mkoeppe @videlec @novoselt @sagetrac-tmonteil @tscrim

Component: geometry

Keywords: polyhedron, base ring

Author: Jean-Philippe Labbé, Vincent Delecroix, Marcelo Forets

Branch/Commit: af03de8

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/22605

[jplab]

Description changed:

--- 
+++ 
@@ -21,34 +21,10 @@
 sage: f
 1.1
 sage: Polyhedron(vertices=[[f]])
----------------------------------------------------------------------------
-AttributeError                            Traceback (most recent call last)
-<ipython-input-55-aea1b8b1f057> in <module>()
-----> 1 Polyhedron(vertices=[[f]])
-
-/Users/jplab/sage/sage2/src/sage/misc/lazy_import.pyx in sage.misc.lazy_import.LazyImport.__call__ (/Users/jplab/sage/sage2/src/build/cythonized/sage/misc/lazy_import.c:4007)()
-    387             True
-    388         """
---> 389         return self._get_object()(*args, **kwds)
-    390 
-    391     def __repr__(self):
-
-/Users/jplab/sage/sage2/local/lib/python2.7/site-packages/sage/geometry/polyhedron/constructor.pyc in Polyhedron(vertices, rays, lines, ieqs, eqns, ambient_dim, base_ring, minimize, verbose, backend)
-    490     # Specific backends can override the base_ring
-    491     from sage.geometry.polyhedron.parent import Polyhedra
---> 492     parent = Polyhedra(base_ring, ambient_dim, backend=backend)
-    493     base_ring = parent.base_ring()
-    494 
-
-/Users/jplab/sage/sage2/local/lib/python2.7/site-packages/sage/geometry/polyhedron/parent.pyc in Polyhedra(base_ring, ambient_dim, backend)
-     89         elif base_ring is RDF:
-     90             backend = 'cdd'
----> 91         elif base_ring.is_exact():
-     92             backend = 'field'
-     93         else:
-
+Traceback (most recent call last):
+...
 AttributeError: type object 'float' has no attribute 'is_exact'
 
 ```
 
-
+The constructor could try to detect the problem and return an informative message.

[videlec]

comment:3

Indeed. Do we want to convert float -> RDF these two are fully compatible?

[jplab]

comment:4

If this:

sage: RDF.has_coerce_map_from(float)
True

is all we need, I guess so... It would do a similar trick as for RR with 53 bits of precision...

[videlec]

comment:5

It is not: coercion has nothing to do with embedding

sage: Zmod(5).has_coerce_map_from(ZZ)
True
sage: RealField(5).has_coerce_map_from(RealField(256))
True

[jplab]

comment:6

So how to check for the embedding? Simply wrap?

[jplab]

Branch: u/jipilab/22605

[jplab]

Commit: 8678e17

[jplab]

comment:8

I added a way to catch the float and set the base ring to RDF. Now, I'm wondering how we could handle the algebraic numbers in an efficient way. Indeed, it seems that they are automatically converted while they might not need it.

---

New commits:

8678e17

Made support for floats

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1235ae4	Merge branch 'u/jipilab/22605' of git://trac.sagemath.org/sage into 22605
47d9425	Added handling of not embedded NumberFields and tests

[sagetrac-git]

Changed commit from 8678e17 to 47d9425