Account for random output in some tests

Author: antonio-rojas

src/sage/arith/misc.py

@@ -2691,9 +2691,14 @@ def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds):
 
     Any object which has a factor method can be factored like this::
 
-        sage: K.<i> = QuadraticField(-1)                                                # needs sage.rings.number_field
-        sage: factor(122 - 454*i)                                                       # needs sage.rings.number_field
-        (-i - 2)^3 * (-i - 1)^3 * (3*i + 2) * (i + 4)
+        sage: # needs sage.rings.number_field
+        sage: K.<i> = QuadraticField(-1)
+        sage: f = factor(122 - 454*i); f                                                # random
+        (i) * (i - 1)^3 * (i + 2)^3 * (3*i + 2) * (i + 4)
+        sage: len(f)
+        4
+        sage: product(p[0]^p[1] for p in f) * f.unit()
+        -454*i + 122
 
     To access the data in a factorization::
 
@@ -2775,8 +2780,10 @@ def radical(n, *args, **kwds):
         ...
         ArithmeticError: radical of 0 is not defined
         sage: K.<i> = QuadraticField(-1)                                                # needs sage.rings.number_field
-        sage: radical(K(2))                                                             # needs sage.rings.number_field
-        -i - 1
+        sage: r = radical(K(2)); r                                                      # random, needs sage.rings.number_field
+        i - 1
+        sage: r.norm()                                                                  # needs sage.rings.number_field
+        2
 
     Tests with numpy and gmpy2 numbers::
 
@@ -3031,7 +3038,7 @@ def is_squarefree(n):
         sage: is_squarefree(O(2))
         False
         sage: O(2).factor()
-        (-I) * (-I - 1)^2
+        (...) * (...)^2
 
     This method fails on domains which are not Unique Factorization Domains::
 

src/sage/rings/number_field/number_field_ideal.py

@@ -2069,7 +2069,7 @@ def ramification_index(self):
             sage: K.<a> = NumberField(x^2 + 2); K
             Number Field in a with defining polynomial x^2 + 2
             sage: f = K.factor(2); f
-            (Fractional ideal (a))^2
+            (Fractional ideal (...a))^2
             sage: f[0][0].ramification_index()
             2
             sage: K.ideal(13).ramification_index()