Trac #34574: Uniformize headline: functions

URL: https://trac.sagemath.org/34574
Reported by: klee
Ticket author(s): Kwankyu Lee
Reviewer(s): Matthias Koeppe

Author: Release Manager

src/sage/functions/airy.py

@@ -1,5 +1,5 @@
 r"""
-Airy Functions
+Airy functions
 
 This module implements Airy functions and their generalized derivatives. It
 supports symbolic functionality through Maxima and numeric evaluation through

src/sage/functions/bessel.py

@@ -1,5 +1,5 @@
 r"""
-Bessel Functions
+Bessel functions
 
 This module provides symbolic Bessel and Hankel functions, and their
 spherical versions. These functions use the `mpmath library`_ for numerical

src/sage/functions/error.py

@@ -1,5 +1,5 @@
 r"""
-Error Functions
+Error functions
 
 This module provides symbolic error functions. These functions use the
 `mpmath library` for numerical evaluation and Maxima, Pynac for

src/sage/functions/exp_integral.py

@@ -1,5 +1,5 @@
 r"""
-Exponential Integrals
+Exponential integrals
 
 AUTHORS:
 

src/sage/functions/generalized.py

@@ -1,5 +1,5 @@
 r"""
-Generalized Functions
+Generalized functions
 
 Sage implements several generalized functions (also known as
 distributions) such as Dirac delta, Heaviside step functions. These

src/sage/functions/hyperbolic.py

@@ -1,5 +1,5 @@
 r"""
-Hyperbolic Functions
+Hyperbolic functions
 
 The full set of hyperbolic and inverse hyperbolic functions is
 available:

src/sage/functions/hypergeometric.py

@@ -1,5 +1,5 @@
 r"""
-Hypergeometric Functions
+Hypergeometric functions
 
 This module implements manipulation of infinite hypergeometric series
 represented in standard parametric form (as `\,_pF_q` functions).

src/sage/functions/jacobi.py

@@ -1,5 +1,5 @@
 r"""
-Jacobi Elliptic Functions
+Jacobi elliptic functions
 
 This module implements the 12 Jacobi elliptic functions, along with their
 inverses and the Jacobi amplitude function.

src/sage/functions/log.py

@@ -1,5 +1,5 @@
 """
-Logarithmic Functions
+Logarithmic functions
 
 AUTHORS:
 

src/sage/functions/min_max.py

@@ -1,5 +1,5 @@
 r"""
-Symbolic Minimum and Maximum
+Symbolic minimum and maximum
 
 Sage provides a symbolic maximum and minimum due to the fact that the Python
 builtin max and min are not able to deal with variables as users might expect.

src/sage/functions/orthogonal_polys.py

@@ -1,5 +1,5 @@
 r"""
-Orthogonal Polynomials
+Orthogonal polynomials
 
 Chebyshev polynomials
 ---------------------

src/sage/functions/piecewise.py

@@ -1,6 +1,6 @@
 # -*- coding: utf-8 -*-
 r"""
-Piecewise-defined Functions
+Piecewise functions
 
 This module implement piecewise functions in a single variable. See
 :mod:`sage.sets.real_set` for more information about how to construct

src/sage/functions/prime_pi.pyx

@@ -1,5 +1,13 @@
 r"""
-Counting Primes
+Counting primes
+
+EXAMPLES::
+
+    sage: z = sage.functions.prime_pi.PrimePi()
+    sage: loads(dumps(z))
+    prime_pi
+    sage: loads(dumps(z)) == z
+    True
 
 AUTHORS:
 
@@ -12,14 +20,6 @@ AUTHORS:
 - Dima Pasechnik (2021): removed buggy cython code, replaced it with
   calls to primecount/primecountpy spkg
 
-
-EXAMPLES::
-
-    sage: z = sage.functions.prime_pi.PrimePi()
-    sage: loads(dumps(z))
-    prime_pi
-    sage: loads(dumps(z)) == z
-    True
 """
 
 # ****************************************************************************

src/sage/functions/special.py

@@ -1,20 +1,5 @@
 r"""
-Miscellaneous Special Functions
-
-AUTHORS:
-
-- David Joyner (2006-13-06): initial version
-
-- David Joyner (2006-30-10): bug fixes to pari wrappers of Bessel
-  functions, hypergeometric_U
-
-- William Stein (2008-02): Impose some sanity checks.
-
-- David Joyner (2008-04-23): addition of elliptic integrals
-
-- Eviatar Bach (2013): making elliptic integrals symbolic
-
-- Eric Gourgoulhon (2022): add Condon-Shortley phase to spherical harmonics
+Miscellaneous special functions
 
 This module provides easy access to many of Maxima and PARI's
 special functions.
@@ -104,6 +89,11 @@
 
   and the complete ones are obtained by taking `\phi =\pi/2`.
 
+.. WARNING::
+
+    SciPy's versions are poorly documented and seem less accurate than the
+    Maxima and PARI versions. Typically they are limited by hardware floats
+    precision.
 
 REFERENCES:
 
@@ -118,16 +108,20 @@
 
 AUTHORS:
 
-- David Joyner and William Stein
+- David Joyner (2006-13-06): initial version
 
-Added 16-02-2008 (wdj): optional calls to scipy and replace all
-'#random' by '...' (both at the request of William Stein)
+- David Joyner (2006-30-10): bug fixes to pari wrappers of Bessel
+  functions, hypergeometric_U
 
-.. warning::
+- William Stein (2008-02): Impose some sanity checks.
 
-    SciPy's versions are poorly documented and seem less
-    accurate than the Maxima and PARI versions; typically they are limited
-    by hardware floats precision.
+- David Joyner (2008-02-16): optional calls to scipy and replace all ``#random`` by ``...``
+
+- David Joyner (2008-04-23): addition of elliptic integrals
+
+- Eviatar Bach (2013): making elliptic integrals symbolic
+
+- Eric Gourgoulhon (2022): add Condon-Shortley phase to spherical harmonics
 """
 
 # ****************************************************************************

src/sage/functions/spike_function.py

@@ -1,5 +1,5 @@
 r"""
-Spike Functions
+Spike functions
 
 AUTHORS:
 

src/sage/functions/transcendental.py

@@ -1,5 +1,5 @@
 """
-Number-Theoretic Functions
+Number-theoretic functions
 """
 # ****************************************************************************
 #       Copyright (C) 2005 William Stein <[email protected]>

src/sage/functions/trig.py

@@ -1,5 +1,5 @@
 r"""
-Trigonometric Functions
+Trigonometric functions
 """
 from sage.symbolic.function import GinacFunction
 import math