Fix crash when specify invalid base for RR and RIF construction

Author: user202729

src/sage/rings/convert/mpfi.pyx

@@ -72,13 +72,42 @@ cdef int mpfi_set_sage(mpfi_ptr re, mpfi_ptr im, x, field, int base) except -1:
       imaginary component is 0.
 
     - in all other cases: raise an exception.
+
+    TESTS::
+
+        sage: RIF('0xabc')
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '0xabc' to real interval
+        sage: RIF("0x123.e1", base=0)  # rel tol 1e-12
+        291.87890625000000?
+        sage: RIF("0x123.@1", base=0)  # rel tol 1e-12
+        4656
+        sage: RIF("1Xx", base=36)  # rel tol 1e-12
+        2517
+        sage: RIF("-1Xx@-10", base=62)  # rel tol 1e-12
+        -7.088054920481391?e-15
+        sage: RIF("1", base=1)
+        Traceback (most recent call last):
+        ...
+        ValueError: base (=1) must be 0 or between 2 and 62
+        sage: RIF("1", base=-1)
+        Traceback (most recent call last):
+        ...
+        ValueError: base (=-1) must be 0 or between 2 and 62
+        sage: RIF("1", base=63)
+        Traceback (most recent call last):
+        ...
+        ValueError: base (=63) must be 0 or between 2 and 62
     """
     cdef RealIntervalFieldElement ri
     cdef ComplexIntervalFieldElement zi
     cdef ComplexNumber zn
     cdef ComplexDoubleElement zd
     cdef bytes s
 
+    if base != 0 and (base < 2 or base > 62):
+        raise ValueError(f"base (={base}) must be 0 or between 2 and 62")
     if im is not NULL and isinstance(x, tuple):
         # For complex numbers, interpret tuples as real/imag parts
         if len(x) != 2:

src/sage/rings/real_mpfr.pyx

@@ -1437,6 +1437,33 @@ cdef class RealNumber(sage.structure.element.RingElement):
 
             sage: RealNumber('1_3.1e-32_45')
             1.31000000000000e-3244
+
+        Test conversion from base different from `10`::
+
+            sage: RR('0xabc')
+            Traceback (most recent call last):
+            ...
+            TypeError: unable to convert '0xabc' to a real number
+            sage: RR("0x123.e1", base=0)  # rel tol 1e-12
+            291.878906250000
+            sage: RR("0x123.@1", base=0)  # rel tol 1e-12
+            4656.00000000000
+            sage: RR("1Xx", base=36)  # rel tol 1e-12
+            2517.00000000000
+            sage: RR("-1Xx@-10", base=62)  # rel tol 1e-12
+            -7.08805492048139e-15
+            sage: RR("1", base=1)
+            Traceback (most recent call last):
+            ...
+            ValueError: base (=1) must be 0 or between 2 and 62
+            sage: RR("1", base=-1)
+            Traceback (most recent call last):
+            ...
+            ValueError: base (=-1) must be 0 or between 2 and 62
+            sage: RR("1", base=63)
+            Traceback (most recent call last):
+            ...
+            ValueError: base (=63) must be 0 or between 2 and 62
         """
         if x is not None:
             self._set(x, base)
@@ -1485,6 +1512,8 @@ cdef class RealNumber(sage.structure.element.RingElement):
         # Real Numbers are supposed to be immutable.
         cdef RealField_class parent
         parent = self._parent
+        if base != 0 and (base < 2 or base > 62):
+            raise ValueError(f"base (={base}) must be 0 or between 2 and 62")
         if isinstance(x, RealNumber):
             if isinstance(x, RealLiteral):
                 s = (<RealLiteral>x).literal