Fix test and a typo

Author: user202729

src/sage/arith/misc.py

@@ -2560,7 +2560,7 @@ def trial_division(n, bound=None):
         return ZZ(n).trial_division(bound)
 
 
-def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds):
+def factor(n, proof=None, int_=False, algorithm=None, verbose=0, **kwds):
     """
     Return the factorization of ``n``.  The result depends on the
     type of ``n``.
@@ -2734,6 +2734,11 @@ def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds):
 
         sage: len(factor(2^2203-1,proof=false))
         1
+
+    Test ``limit``::
+
+        sage: factor(2990, limit=10)
+        2 * 5 * 299
     """
     try:
         m = n.factor

src/sage/misc/sageinspect.py

@@ -1448,7 +1448,7 @@ def sage_getargspec(obj):
                     annotations={})
         sage: sage_getargspec(factor)
         FullArgSpec(args=['n', 'proof', 'int_', 'algorithm', 'verbose'],
-                    varargs=None, varkw='kwds', defaults=(None, False, 'pari', 0),
+                    varargs=None, varkw='kwds', defaults=(None, False, None, 0),
                     kwonlyargs=[], kwonlydefaults=None, annotations={})
 
     In the case of a class or a class instance, the :class:`FullArgSpec` of the
@@ -1808,7 +1808,7 @@ def sage_signature(obj):
         sage: sage_signature(identity_matrix)                                          # needs sage.modules
         <Signature (ring, n=0, sparse=False)>
         sage: sage_signature(factor)
-        <Signature (n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds)>
+        <Signature (n, proof=None, int_=False, algorithm=None, verbose=0, **kwds)>
 
     In the case of a class or a class instance, the :class:`Signature` of the
     ``__new__``, ``__init__`` or ``__call__`` method is returned::
@@ -2671,8 +2671,8 @@ def __internal_tests():
 
     A cython function with default arguments (one of which is a string)::
 
-        sage: sage_getdef(sage.rings.integer.Integer.factor, obj_name='factor')
-        "factor(algorithm='pari', proof=None, limit=None, int_=False, verbose=0)"
+        sage: sage_getdef(sage.rings.integer.Integer.binomial, obj_name='binomial')
+        "binomial(m, algorithm='gmp')"
 
     This used to be problematic, but was fixed in :issue:`10094`::
 

src/sage/rings/integer.pyx

@@ -3877,7 +3877,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
             return x
 
     def factor(self, algorithm=None, proof=None, limit=None, int_=False,
-               verbose=0, flint_bits=None):
+               verbose=0, *, flint_bits=None):
         """
         Return the prime factorization of this integer as a
         formal Factorization object.
@@ -4016,7 +4016,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
 
         if limit is not None:
             if algorithm is not None:
-                raise ValueError('trial division will always be used when when limit is provided')
+                raise ValueError('trial division will always be used when limit is provided')
             from sage.rings.factorint import factor_trial_division
             return factor_trial_division(self, limit)