Trac #34645: fix more W605 in rings

after #34639

URL: https://trac.sagemath.org/34645
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

src/sage/rings/complex_arb.pyx

@@ -2984,7 +2984,7 @@ cdef class ComplexBall(RingElement):
         return res
 
     def rising_factorial(self, n):
-        """
+        r"""
         Return the ``n``-th rising factorial of this ball.
 
         The `n`-th rising factorial of `x` is equal to `x (x+1) \cdots (x+n-1)`.
@@ -3704,7 +3704,7 @@ cdef class ComplexBall(RingElement):
         return res
 
     def polylog(self, s):
-        """
+        r"""
         Return the polylogarithm `\operatorname{Li}_s(\mathrm{self})`.
 
         EXAMPLES::

src/sage/rings/complex_double.pyx

@@ -1637,7 +1637,7 @@ cdef class ComplexDoubleElement(FieldElement):
         return self.real().is_NaN() or self.imag().is_NaN()
 
     cpdef _pow_(self, other):
-        """
+        r"""
         The complex number ``self`` raised to the power ``other``.
 
         This is computed using complex logarithms and exponentials

src/sage/rings/complex_mpc.pyx

@@ -137,15 +137,15 @@ cdef inline mpfr_rnd_t rnd_im(mpc_rnd_t rnd):
 sign = '[+-]'
 digit_ten = '[0123456789]'
 exponent_ten = '[e@]' + sign + '?[0123456789]+'
-number_ten = 'inf(?:inity)?|@inf@|nan(?:\([0-9A-Z_]*\))?|@nan@(?:\([0-9A-Z_]*\))?'\
-    '|(?:' + digit_ten + '*\.' + digit_ten + '+|' + digit_ten + '+\.?)(?:' + exponent_ten + ')?'
-imaginary_ten = 'i(?:\s*\*\s*(?:' + number_ten + '))?|(?:' + number_ten + ')\s*\*\s*i'
-complex_ten = '(?P<im_first>(?P<im_first_im_sign>' + sign + ')?\s*(?P<im_first_im_abs>' + imaginary_ten + ')' \
-    '(\s*(?P<im_first_re_sign>' + sign + ')\s*(?P<im_first_re_abs>' + number_ten + '))?)' \
+number_ten = r'inf(?:inity)?|@inf@|nan(?:\([0-9A-Z_]*\))?|@nan@(?:\([0-9A-Z_]*\))?'\
+    '|(?:' + digit_ten + r'*\.' + digit_ten + '+|' + digit_ten + r'+\.?)(?:' + exponent_ten + ')?'
+imaginary_ten = r'i(?:\s*\*\s*(?:' + number_ten + '))?|(?:' + number_ten + r')\s*\*\s*i'
+complex_ten = '(?P<im_first>(?P<im_first_im_sign>' + sign + r')?\s*(?P<im_first_im_abs>' + imaginary_ten + r')' \
+    r'(\s*(?P<im_first_re_sign>' + sign + r')\s*(?P<im_first_re_abs>' + number_ten + '))?)' \
     '|' \
-    '(?P<re_first>(?P<re_first_re_sign>' + sign + ')?\s*(?P<re_first_re_abs>' + number_ten + ')' \
-    '(\s*(?P<re_first_im_sign>' + sign + ')\s*(?P<re_first_im_abs>' + imaginary_ten + '))?)'
-re_complex_ten = re.compile('^\s*(?:' + complex_ten + ')\s*$', re.I)
+    '(?P<re_first>(?P<re_first_re_sign>' + sign + r')?\s*(?P<re_first_re_abs>' + number_ten + r')' \
+    r'(\s*(?P<re_first_im_sign>' + sign + r')\s*(?P<re_first_im_abs>' + imaginary_ten + '))?)'
+re_complex_ten = re.compile(r'^\s*(?:' + complex_ten + r')\s*$', re.I)
 
 cpdef inline split_complex_string(string, int base=10):
     """
@@ -185,17 +185,17 @@ cpdef inline split_complex_string(string, int base=10):
 
         # Warning: number, imaginary, and complex should be enclosed in parentheses
         # when used as regexp because of alternatives '|'
-        number = '@nan@(?:\([0-9A-Z_]*\))?|@inf@|(?:' + digit + '*\.' + digit + '+|' + digit + '+\.?)(?:' + exponent + ')?'
+        number = r'@nan@(?:\([0-9A-Z_]*\))?|@inf@|(?:' + digit + r'*\.' + digit + '+|' + digit + r'+\.?)(?:' + exponent + ')?'
         if base <= 10:
-            number = 'nan(?:\([0-9A-Z_]*\))?|inf(?:inity)?|' + number
-        imaginary = 'i(?:\s*\*\s*(?:' + number + '))?|(?:' + number + ')\s*\*\s*i'
-        complex = '(?P<im_first>(?P<im_first_im_sign>' + sign + ')?\s*(?P<im_first_im_abs>' + imaginary + ')' \
-            '(\s*(?P<im_first_re_sign>' + sign + ')\s*(?P<im_first_re_abs>' + number + '))?)' \
+            number = r'nan(?:\([0-9A-Z_]*\))?|inf(?:inity)?|' + number
+        imaginary = r'i(?:\s*\*\s*(?:' + number + '))?|(?:' + number + r')\s*\*\s*i'
+        complex = '(?P<im_first>(?P<im_first_im_sign>' + sign + r')?\s*(?P<im_first_im_abs>' + imaginary + r')' \
+            r'(\s*(?P<im_first_re_sign>' + sign + r')\s*(?P<im_first_re_abs>' + number + '))?)' \
             '|' \
-            '(?P<re_first>(?P<re_first_re_sign>' + sign + ')?\s*(?P<re_first_re_abs>' + number + ')' \
-            '(\s*(?P<re_first_im_sign>' + sign + ')\s*(?P<re_first_im_abs>' + imaginary + '))?)'
+            '(?P<re_first>(?P<re_first_re_sign>' + sign + r')?\s*(?P<re_first_re_abs>' + number + r')' \
+            r'(\s*(?P<re_first_im_sign>' + sign + r')\s*(?P<re_first_im_abs>' + imaginary + '))?)'
 
-        z = re.match('^\s*(?:' + complex + ')\s*$', string, re.I)
+        z = re.match(r'^\s*(?:' + complex + r')\s*$', string, re.I)
 
     x, y = None, None
     if z is not None:
@@ -207,18 +207,18 @@ cpdef inline split_complex_string(string, int base=10):
             return None
 
         if  z.group(prefix + '_re_abs') is not None:
-            x = z.expand('\g<' + prefix + '_re_abs>')
+            x = z.expand(r'\g<' + prefix + '_re_abs>')
             if z.group(prefix + '_re_sign') is not None:
-                x = z.expand('\g<' + prefix + '_re_sign>') + x
+                x = z.expand(r'\g<' + prefix + '_re_sign>') + x
 
         if z.group(prefix + '_im_abs') is not None:
-            y = re.search('(?P<im_part>' + number + ')', z.expand('\g<' + prefix + '_im_abs>'), re.I)
+            y = re.search('(?P<im_part>' + number + ')', z.expand(r'\g<' + prefix + '_im_abs>'), re.I)
             if y is None:
                 y = '1'
             else:
-                y = y.expand('\g<im_part>')
+                y = y.expand(r'\g<im_part>')
             if z.group(prefix + '_im_sign') is not None:
-                y = z.expand('\g<' + prefix + '_im_sign>') + y
+                y = z.expand(r'\g<' + prefix + '_im_sign>') + y
 
     return x, y
 
@@ -1701,7 +1701,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
         return z
 
     def cosh(self):
-        """
+        r"""
         Return the hyperbolic cosine of this complex number:
 
         .. MATH::
@@ -1721,7 +1721,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
         return z
 
     def sinh(self):
-        """
+        r"""
         Return the hyperbolic sine of this complex number:
 
         .. MATH::
@@ -2063,7 +2063,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
         return z
 
     def exp(self):
-        """
+        r"""
         Return the exponential of this complex number:
 
         .. MATH::

src/sage/rings/complex_mpfr.pyx

@@ -2549,7 +2549,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
 
     # Other special functions
     def agm(self, right, algorithm="optimal"):
-        """
+        r"""
         Return the Arithmetic-Geometric Mean (AGM) of ``self`` and ``right``.
 
         INPUT:

src/sage/rings/integer.pyx

@@ -1257,7 +1257,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
         return self.str(2)
 
     def bits(self):
-        """
+        r"""
         Return the bits in self as a list, least significant first. The
         result satisfies the identity
 
@@ -2434,7 +2434,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
                                                            integer_ring.ZZ(n).ordinal_str()))
 
     cpdef size_t _exact_log_log2_iter(self,Integer m):
-        """
+        r"""
         This is only for internal use only.  You should expect it to crash
         and burn for negative or other malformed input.  In particular, if
         the base `2 \leq m < 4` the log2 approximation of m is 1 and certain
@@ -3463,7 +3463,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
         return q, r
 
     def powermod(self, exp, mod):
-        """
+        r"""
         Compute self\*\*exp modulo mod.
 
         EXAMPLES::
@@ -6714,8 +6714,9 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
             raise ArithmeticError("inverse does not exist")
 
     def inverse_mod(self, n):
-        """
-        Returns the inverse of self modulo `n`, if this inverse exists.
+        r"""
+        Return the inverse of self modulo `n`, if this inverse exists.
+
         Otherwise, raises a ``ZeroDivisionError`` exception.
 
         INPUT:

src/sage/rings/real_arb.pyx

@@ -238,7 +238,7 @@ from sage.structure.unique_representation import UniqueRepresentation
 from sage.cpython.string cimport char_to_str, str_to_bytes
 
 cdef void mpfi_to_arb(arb_t target, const mpfi_t source, const long precision):
-    """
+    r"""
     Convert an MPFI interval to an Arb ball.
 
     INPUT:
@@ -282,7 +282,7 @@ cdef void mpfi_to_arb(arb_t target, const mpfi_t source, const long precision):
     mpfr_clear(right)
 
 cdef int arb_to_mpfi(mpfi_t target, arb_t source, const long precision) except -1:
-    """
+    r"""
     Convert an Arb ball to an MPFI interval.
 
     INPUT:
@@ -798,7 +798,7 @@ class RealBallField(UniqueRepresentation, sage.rings.abc.RealBallField):
     # Ball functions of non-ball arguments
 
     def sinpi(self, x):
-        """
+        r"""
         Return a ball enclosing `\sin(\pi x)`.
 
         This works even if ``x`` itself is not a ball, and may be faster or
@@ -844,7 +844,7 @@ class RealBallField(UniqueRepresentation, sage.rings.abc.RealBallField):
         return res
 
     def cospi(self, x):
-        """
+        r"""
         Return a ball enclosing `\cos(\pi x)`.
 
         This works even if ``x`` itself is not a ball, and may be faster or
@@ -2986,7 +2986,7 @@ cdef class RealBall(RingElement):
         return res
 
     def sqrt1pm1(self):
-        """
+        r"""
         Return `\sqrt{1+\mathrm{self}}-1`, computed accurately when ``self`` is
         close to zero.
 
@@ -3728,7 +3728,7 @@ cdef class RealBall(RingElement):
         return res
 
     def gamma(self, a=None):
-        """
+        r"""
         Image of this ball by the (upper incomplete) Euler Gamma function
 
         For `a` real, return the upper incomplete Gamma function
@@ -3770,7 +3770,7 @@ cdef class RealBall(RingElement):
     gamma_inc = gamma
 
     def gamma_inc_lower(self, a):
-        """
+        r"""
         Image of this ball by the lower incomplete Euler Gamma function
 
         For `a` real, return the lower incomplete Gamma function
@@ -3828,7 +3828,7 @@ cdef class RealBall(RingElement):
         return res
 
     def rising_factorial(self, n):
-        """
+        r"""
         Return the ``n``-th rising factorial of this ball.
 
         The `n`-th rising factorial of `x` is equal to `x (x+1) \cdots (x+n-1)`.
@@ -3934,7 +3934,7 @@ cdef class RealBall(RingElement):
         return res
 
     def polylog(self, s):
-        """
+        r"""
         Return the polylogarithm `\operatorname{Li}_s(\mathrm{self})`.
 
         EXAMPLES::