gh-35924: some pep8 fixes in functions/
    
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fixes some pycodestyle warnings in `functions`

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URL: #35924
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/functions/error.py

@@ -297,6 +297,7 @@ def _derivative_(self, x, diff_param=None):
         """
         return 2*exp(-x**2)/sqrt(pi)
 
+
 erf = Function_erf()
 
 
@@ -375,8 +376,10 @@ def _derivative_(self, x, diff_param=None):
         """
         return 2*exp(x**2)/sqrt(pi)
 
+
 erfi = Function_erfi()
 
+
 class Function_erfc(BuiltinFunction):
     r"""
     The complementary error function.
@@ -477,6 +480,7 @@ def _derivative_(self, x, diff_param=None):
         """
         return -2*exp(-x**2)/sqrt(pi)
 
+
 erfc = Function_erfc()
 
 
@@ -564,11 +568,14 @@ def _derivative_(self, x, diff_param=None):
         """
         return sqrt(pi)*exp(erfinv(x)**2)/2
 
+
 erfinv = Function_erfinv()
 
+
 from sage.misc.persist import register_unpickle_override
 register_unpickle_override('sage.functions.other', 'Function_erf', Function_erf)
 
+
 ############################
 # Fresnel integrals        #
 ############################
@@ -632,11 +639,11 @@ def _eval_(self, x):
                 return x
             if x.is_infinity():
                 if x.is_positive_infinity():
-                    return Rational((1,2))
+                    return Rational((1, 2))
                 elif x.imag_part().is_positive_infinity():
-                    return -I*Rational((1,2))
+                    return -I*Rational((1, 2))
                 elif x.imag_part().is_negative_infinity():
-                    return I*Rational((1,2))
+                    return I*Rational((1, 2))
         elif x < 0:
             return -fresnel_sin(-x)
         elif not x:
@@ -668,8 +675,10 @@ def _derivative_(self, x, diff_param=None):
         from sage.functions.trig import sin
         return sin(pi*x**2/2)
 
+
 fresnel_sin = Function_Fresnel_sin()
 
+
 class Function_Fresnel_cos(BuiltinFunction):
     def __init__(self):
         r"""
@@ -730,11 +739,11 @@ def _eval_(self, x):
                 return x
             if x.is_infinity():
                 if x.is_positive_infinity():
-                    return Rational((1,2))
+                    return Rational((1, 2))
                 elif x.imag_part().is_positive_infinity():
-                    return I*Rational((1,2))
+                    return I*Rational((1, 2))
                 elif x.imag_part().is_negative_infinity():
-                    return -I*Rational((1,2))
+                    return -I*Rational((1, 2))
         elif x < 0:
             return -fresnel_cos(-x)
         elif not x:
@@ -766,4 +775,5 @@ def _derivative_(self, x, diff_param=None):
         from sage.functions.trig import cos
         return cos(pi*x**2/2)
 
+
 fresnel_cos = Function_Fresnel_cos()

src/sage/functions/exp_integral.py

@@ -36,15 +36,15 @@
 
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2011 Benjamin Jones <[email protected]>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 
 from sage.symbolic.function import BuiltinFunction
@@ -182,7 +182,7 @@ def _eval_(self, n, z):
         # special case: z == 0 and n > 1
         if isinstance(z, Expression):
             if z.is_trivial_zero():
-                z_zero = True # for later
+                z_zero = True  # for later
                 if n > 1:
                     return 1/(n-1)
         else:
@@ -205,7 +205,7 @@ def _eval_(self, n, z):
                 else:
                     return exp(-z)/z
 
-        return None # leaves the expression unevaluated
+        return None  # leaves the expression unevaluated
 
     def _evalf_(self, n, z, parent=None, algorithm=None):
         """
@@ -217,7 +217,6 @@ def _evalf_(self, n, z, parent=None, algorithm=None):
             0.000281624451981418 - 0.179324535039359*I
             sage: exp_integral_e(1, RealField(100)(1))
             0.21938393439552027367716377546
-
         """
         import mpmath
         return mpmath_utils.call(mpmath.expint, n, z, parent=parent)
@@ -249,12 +248,11 @@ def _derivative_(self, n, z, diff_param=None):
             sage: f = exp_integral_e(2,sqrt(x))
             sage: f.diff(x)
             -1/2*exp_integral_e(1, sqrt(x))/sqrt(x)
-
         """
         if n in ZZ and n > 0:
-            return -1*exp_integral_e(n-1,z)
-        else:
-            raise NotImplementedError("The derivative of this function is only implemented for n = 1, 2, 3, ...")
+            return -1*exp_integral_e(n-1, z)
+        raise NotImplementedError("The derivative of this function is only implemented for n = 1, 2, 3, ...")
+
 
 exp_integral_e = Function_exp_integral_e()
 
@@ -367,6 +365,7 @@ def _derivative_(self, z, diff_param=None):
         """
         return -exp(-z)/z
 
+
 exp_integral_e1 = Function_exp_integral_e1()
 
 
@@ -501,8 +500,10 @@ def _derivative_(self, z, diff_param=None):
         """
         return 1/log(z)
 
+
 li = log_integral = Function_log_integral()
 
+
 class Function_log_integral_offset(BuiltinFunction):
     r"""
     The offset logarithmic integral, or Eulerian logarithmic integral,
@@ -642,7 +643,7 @@ def __init__(self):
                                  latex_name=r'\operatorname{log\_integral\_offset}',
                                  conversions=dict(sympy='Li'))
 
-    def _eval_(self,z):
+    def _eval_(self, z):
         """
         EXAMPLES::
 
@@ -694,8 +695,10 @@ def _derivative_(self, z, diff_param=None):
         """
         return 1/log(z)
 
+
 Li = log_integral_offset = Function_log_integral_offset()
 
+
 class Function_sin_integral(BuiltinFunction):
     r"""
     The trigonometric integral `\operatorname{Si}(z)` defined by
@@ -886,6 +889,7 @@ def _derivative_(self, z, diff_param=None):
         """
         return sin(z)/z
 
+
 Si = sin_integral = Function_sin_integral()
 
 
@@ -1026,6 +1030,7 @@ def _derivative_(self, z, diff_param=None):
         """
         return cos(z)/z
 
+
 Ci = cos_integral = Function_cos_integral()
 
 
@@ -1178,6 +1183,7 @@ def _derivative_(self, z, diff_param=None):
         """
         return sinh(z)/z
 
+
 Shi = sinh_integral = Function_sinh_integral()
 
 
@@ -1306,6 +1312,7 @@ def _derivative_(self, z, diff_param=None):
         """
         return cosh(z)/z
 
+
 Chi = cosh_integral = Function_cosh_integral()
 
 
@@ -1420,6 +1427,7 @@ def _derivative_(self, x, diff_param=None):
         """
         return exp(x)/x
 
+
 Ei = exp_integral_ei = Function_exp_integral()
 
 

src/sage/functions/jacobi.py

@@ -515,6 +515,7 @@ def _print_latex_(self, x, m):
                                                                       latex(x),
                                                                       latex(m))
 
+
 jacobi_nd = Jacobi('nd')
 jacobi_ns = Jacobi('ns')
 jacobi_nc = Jacobi('nc')
@@ -905,6 +906,7 @@ def _print_latex_(self, x, m):
                                                                          latex(x),
                                                                          latex(m))
 
+
 inverse_jacobi_nd = InverseJacobi('nd')
 inverse_jacobi_ns = InverseJacobi('ns')
 inverse_jacobi_nc = InverseJacobi('nc')
@@ -1050,6 +1052,7 @@ def inverse_jacobi(kind, x, m, **kwargs):
         raise ValueError("kind must be one of 'nd', 'ns', 'nc', 'dn', "
                          "'ds', 'dc', 'sn', 'sd', 'sc', 'cn', 'cd', 'cs'.")
 
+
 class JacobiAmplitude(BuiltinFunction):
     r"""
     The Jacobi amplitude function