deterministic choice of variable names

src/sage/rings/polynomial/skew_polynomial_ring.py

@@ -59,6 +59,8 @@
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.polynomial.skew_polynomial_element import SkewPolynomialBaseringInjection
 
+WORKING_CENTER_MAX_TRIES = 1000
+
 
 # Helper functions
 
@@ -1322,21 +1324,22 @@ def __init__(self, base_ring, twist_map, name, sparse, category=None):
             sage: S.center() is Z
             True
         """
-        import random, string
         SkewPolynomialRing.__init__(self, base_ring, twist_map, name, sparse, category)
         self._order = twist_map.order()
         (self._constants, self._embed_constants) = twist_map.fixed_field()
 
         # Configure and create center
         self._center = { }
         self._center_variable_name = 'z'
-        while self._center_variable_name is not None:
+        for i in range(WORKING_CENTER_MAX_TRIES):
             try:
                 self._working_center = self.center()
                 self._center_variable_name = None
+                break
             except ValueError:
-                self._center_variable_name = ''.join(random.choice(string.ascii_lowercase) for i in range(10))
-                pass
+                self._center_variable_name = "z%s_" % i
+        if self._center_variable_name is not None:
+            raise NotImplementedError("unable to create the center")
 
 
     def center(self, name=None, names=None, default=False):