Merge #32416

src/sage/geometry/convex_set.py

@@ -859,11 +859,14 @@ def _test_contains(self, tester=None, **options):
                 ext_space = self.ambient_vector_space(AA)
                 ext_space_point = ext_space(space_point)
                 tester.assertEqual(contains_space_point, self.contains(ext_space_point))
-            from sage.symbolic.ring import SR
-            symbolic_space = self.ambient_vector_space(SR)
-            symbolic_space_point = symbolic_space(space_point)
-            # Only test that it can accept SR vectors without error.
-            self.contains(symbolic_space_point)
+            try:
+                from sage.symbolic.ring import SR
+                symbolic_space = self.ambient_vector_space(SR)
+                symbolic_space_point = symbolic_space(space_point)
+                # Only test that it can accept SR vectors without error.
+                self.contains(symbolic_space_point)
+            except ImportError:
+                pass
             # Test that elements returned by some_elements are contained.
             try:
                 points = self.some_elements()

src/sage/geometry/polyhedron/base.py

@@ -1824,7 +1824,7 @@ def Hrepresentation_str(self, separator='\n', latex=False, style='>=', align=Non
 
             sage: c = polytopes.cube()
             sage: c.Hrepresentation_str(separator=', ', style='positive')
-            '1 >= x0, 1 >= x1, 1 >= x2, x0 + 1 >= 0, x2 + 1 >= 0, x1 + 1 >= 0'
+            '1 >= x0, 1 >= x1, 1 >= x2, 1 + x0 >= 0, 1 + x2 >= 0, 1 + x1 >= 0'
         """
         pretty_hs = [h.repr_pretty(split=True, latex=latex, style=style, **kwds) for h in self.Hrepresentation()]
         shift = any(pretty_h[2].startswith('-') for pretty_h in pretty_hs)

src/sage/geometry/polyhedron/constructor.py

@@ -649,7 +649,10 @@ def Polyhedron(vertices=None, rays=None, lines=None,
         if base_ring not in Rings():
             raise ValueError('invalid base ring')
 
-        from sage.symbolic.ring import SR
+        try:
+            from sage.symbolic.ring import SR
+        except ImportError:
+            SR = None
         if base_ring is not SR and not base_ring.is_exact():
             # TODO: remove this hack?
             if base_ring is RR:

src/sage/geometry/polyhedron/parent.py

@@ -145,7 +145,10 @@ def Polyhedra(ambient_space_or_base_ring=None, ambient_dim=None, backend=None, *
         else:
             raise ValueError("no default backend for computations with {}".format(base_ring))
 
-    from sage.symbolic.ring import SR
+    try:
+        from sage.symbolic.ring import SR
+    except ImportError:
+        SR = None
     if backend == 'ppl' and base_ring is QQ:
         return Polyhedra_QQ_ppl(base_ring, ambient_dim, backend)
     elif backend == 'ppl' and base_ring is ZZ:

src/sage/geometry/polyhedron/plot.py

@@ -11,14 +11,15 @@
 #                  https://www.gnu.org/licenses/
 ########################################################################
 
+from math import pi
+
 from sage.rings.all import RDF
 from sage.structure.sage_object import SageObject
 from sage.modules.free_module_element import vector
 from sage.matrix.constructor import matrix, identity_matrix
 from sage.matrix.special import diagonal_matrix
 from sage.misc.functional import norm
 from sage.misc.latex import LatexExpr
-from sage.symbolic.constants import pi
 from sage.structure.sequence import Sequence
 
 from sage.plot.all import Graphics, point2d, line2d, arrow, polygon2d

src/sage/geometry/polyhedron/representation.py

@@ -712,7 +712,7 @@ def _latex_(self):
             ....:     print(latex(h))
             x_{0} + x_{1} - x_{2} = 1
             x_{0} \geq 0
-            2 \, x_{0} + x_{1} \geq -1
+            2x_{0} + x_{1} \geq -1
         """
         return self.repr_pretty(latex=True)
 
@@ -1690,15 +1690,16 @@ def repr_pretty(coefficients, type, prefix='x', indices=None,
         sage: print(repr_pretty((1, -1, -1, 1), PolyhedronRepresentation.EQUATION))
         -x0 - x1 + x2 == -1
     """
-    from sage.misc.latex import latex as latex_function
-    from sage.modules.free_module_element import vector
-    from sage.symbolic.ring import SR
+    from sage.misc.repr import repr_lincomb
 
-    coeffs = vector(coefficients)
+    coeffs = list(coefficients)
     if indices is None:
         indices = range(len(coeffs)-1)
-    vars = vector([1] + list(SR(prefix + '{}'.format(i)) for i in indices))
-    f = latex_function if latex else repr
+    vars = [1]
+    if latex:
+        vars += ['x_{{{}}}'.format(i) for i in indices]
+    else:
+        vars += ['x{}'.format(i) for i in indices]
     if type == PolyhedronRepresentation.EQUATION:
         rel = '=' if latex else '=='
     elif type == PolyhedronRepresentation.INEQUALITY:
@@ -1710,18 +1711,20 @@ def repr_pretty(coefficients, type, prefix='x', indices=None,
         raise NotImplementedError(
             'no pretty printing available: wrong type {}'.format(type))
 
+    rvars = range(len(vars))
+
     if style == 'positive':
-        pos_part = vector([max(c, 0) for c in coeffs])
-        neg_part = pos_part - coeffs
-        assert coeffs == pos_part - neg_part
-        left_part = f(pos_part*vars)
-        right_part = f(neg_part*vars)
+        pos_part = [max(c, 0) for c in coeffs]
+        neg_part = [pos_part[i] - coeffs[i] for i in rvars]
+        assert all(coeffs[i] == pos_part[i] - neg_part[i] for i in rvars)
+        left_part = repr_lincomb([[vars[i], pos_part[i]] for i in rvars], is_latex=latex, strip_one=True)
+        right_part = repr_lincomb([[vars[i], neg_part[i]] for i in rvars], is_latex=latex, strip_one=True)
     elif style == '>=':
-        left_part = f(coeffs[1:]*vars[1:])
-        right_part = f(-coeffs[0])
+        left_part = repr_lincomb([[vars[i], coeffs[i]] for i in rvars[1:]], is_latex=latex)
+        right_part = repr_lincomb([[vars[0], -coeffs[0]]], is_latex=latex, strip_one=True)
     elif style == '<=':
-        left_part = f(-coeffs[1:]*vars[1:])
-        right_part = f(coeffs[0])
+        left_part = repr_lincomb([[vars[i], -coeffs[i]] for i in rvars[1:]], is_latex=latex)
+        right_part = repr_lincomb([[vars[0], coeffs[0]]], is_latex=latex, strip_one=True)
     else:
         raise NotImplementedError('no pretty printing available: wrong style {}'.format(style))