Spelling correction: covert => convert

Replaced some asserts in non-test code with exceptions (#5090)

.ci/README.rst

@@ -0,0 +1,10 @@
+This folder currently holds ``durations.json`` and ``blacklisted.json`` which are used in our pytest configuration.
+``durations.json`` allows the two options ``--quickcheck`` and ``--veryquickcheck`` to be passed to ``pytest``.
+Currently, the list of slow tests is updated intermittently by running::
+
+  $ ./.ci/generate_durations_log.sh
+  $ ./.ci/parse_durations_log.py
+  $ git commit -am "pytest: Updated .ci/durations.json"
+
+make sure you have a C compiler, a Fortran compiler, numpy, scipy, cython, matplotlib & sage installed (the latter can
+be tricky, in which case just make sure that no sage tests are removed in the git diff).

.ci/generate_durations_log.sh

@@ -1,4 +1,4 @@
-#!/bin/bash
+#!/bin/bash -e
 ABS_REPO_PATH=$(unset CDPATH && cd "$(dirname "$0")/.." && echo $PWD)
 cat <<EOF >${ABS_REPO_PATH}/.ci/blacklisted.json
 {
@@ -10,4 +10,4 @@ cat <<EOF >${ABS_REPO_PATH}/.ci/blacklisted.json
     ]
 }
 EOF
-python3 -m pytest -ra --durations 0 --verbose | tee $ABS_REPO_PATH/.ci/durations.log
+${PYTHON:-python} -m pytest -ra --durations 0 --verbose | tee $ABS_REPO_PATH/.ci/durations.log

.github/FUNDING.yml

@@ -0,0 +1,3 @@
+# These are supported funding model platforms
+
+custom: ['https://numfocus.salsalabs.org/donate-to-sympy/index.html']

.gitignore

@@ -7,9 +7,12 @@
 # track a file that is ignored for some reason, you have to use
 # "git add -f". See "git help gitignore" for more information.
 
+# Virtualenv
+/.venv/
 
 # Regular Python bytecode file
 *.pyc
+__pycache__/
 
 # Optimized Python bytecode file
 *.pyo
@@ -17,6 +20,12 @@
 # Vim's swap files
 *.sw[op]
 
+# VSCode settings file
+.vscode/
+
+# PyCharm settings file
+/.idea/
+
 # Generated files from Jython
 *$py.class
 

.mailmap

@@ -355,6 +355,7 @@ Peter Enenkel <peter.enenkel+git@gmail.com> <peter.enenkel+github@gmail.com>
 Jithin D. George <jithindgeorge93@gmail.com>
 Lev Chelyadinov <leva181777@gmail.com>
 Sourav Ghosh <souravghosh2197@gmail.com>
+Ethan Ward <etkewa@gmail.com> etkewa@gmail.com <qsRf9sGKy9rV>
 Ethan Ward <etkewa@gmail.com>
 Ethan Ward <etkewa@gmail.com> <ethanward@email.arizona.edu>
 Nilabja Bhattacharya <nilabja10201992@gmail.com>
@@ -412,3 +413,8 @@ Supreet Agrawal <supreet11agrawal@gmail.com> stm <supreet11agrawal@gmail.com>
 Bavish Kulur <bavishkulur@gmail.com> bavish2201 <bavishkulur@gmail.com>
 Divyanshu Thakur <divyanshu@iiitmanipur.ac.in> Divyanshu <divyanshu@iiitmanipur.ac.in>
 Shubham Kumar Jha <skjha832@gmail.com> ShubhamKJha <skjha832@gmail.com>
+Frédéric Chapoton <fchapoton2@gmail.com> fchapoton <fchapoton2@gmail.com>
+Salmista-94 <alejandrogroso@hotmail.com> alejandrogroso@hotmail.com <Salmista-94>
+Jack <ivanenko@ucu.edu.ua> LilJohny <ivanenko@ucu.edu.ua>
+Nabanita Dash <dashnabanita@gmail.com> Nabanita Dash <31562743+Naba7@users.noreply.github.com>
+Rajiv Ranjan Singh <rajivperfect007@gmail.com> Rajiv Ranjan Singh <42106787+iamrajiv@users.noreply.github.com>

.travis.yml

@@ -8,14 +8,13 @@ env:
   matrix:
   - SPLIT="1/2" TEST_SYMPY="true"
   - SPLIT="2/2" TEST_SYMPY="true"
-  - TEST_DOCTESTS="true" FASTCACHE="false" TEST_SETUP="true"
+  - TEST_DOCTESTS="true" FASTCACHE="false" TEST_SETUP="true" TEST_EXAMPLES="true"
   global:
     - secure: "YIEZal9EBTL+fg2YmoZoS8Bvt3eAVUOZjb38CtqpzR2CCSXWoUk35KG23m2NknlY1iKfYJyt7XWBszT/VKOQEbWQq7PIakV4vIByrWacgBxy1x3WC+rZoW7TX+JJiL+y942qIYbMoNMMB8xFpE5RDLSjSecMpFhJJXoafVTvju8="
 dist: trusty
 
 python:
   - 2.7
-  - 3.4
   - 3.5
 
 matrix:
@@ -32,7 +31,7 @@ matrix:
       dist: xenial
       sudo: true
       env:
-        - TEST_DOCTESTS="true" FASTCACHE="false" TEST_SETUP="true"
+        - TEST_DOCTESTS="true" FASTCACHE="false" TEST_SETUP="true" TEST_EXAMPLES="true"
     - python: 3.7
       dist: xenial
       sudo: true
@@ -45,11 +44,26 @@ matrix:
         - SPLIT="2/2" TEST_SYMPY="true"
 
     - stage: test
-      python: 2.7
+      python: 3.8-dev
+      dist: xenial
+      sudo: true
+      env:
+        - TEST_DOCTESTS="true" FASTCACHE="false" TEST_SETUP="true" TEST_EXAMPLES="true"
+    - python: 3.8-dev
+      dist: xenial
+      sudo: true
+      env:
+        - SPLIT="1/2" TEST_SYMPY="true"
+    - python: 3.8-dev
+      dist: xenial
+      sudo: true
+      env:
+        - SPLIT="2/2" TEST_SYMPY="true"
+    - python: 2.7
       env:
         - TEST_ASCII="true"
         # space separated list of optional dependencies(conda packages) to install and test
-        - TEST_OPT_DEPENDENCY="numpy scipy gmpy2 matplotlib>=2.2 theano llvmlite autowrap cython wurlitzer python-symengine=0.3.* tensorflow numexpr ipython antlr-python-runtime>=4.7,<4.8 antlr>=4.7,<4.8 cloudpickle python=2.7"
+        - TEST_OPT_DEPENDENCY="numpy scipy gmpy2 matplotlib>=2.2 theano llvmlite autowrap cython wurlitzer python-symengine=0.3.* tensorflow numexpr ipython antlr-python-runtime>=4.7,<4.8 antlr>=4.7,<4.8 cloudpickle python=2.7 pyglet pycosat python-clang"
       addons:
         apt:
           packages:
@@ -64,7 +78,7 @@ matrix:
       # and we aren't actually using the Travis Python anyway.
       env:
         - TEST_ASCII="true"
-        - TEST_OPT_DEPENDENCY="numpy scipy gmpy2 matplotlib theano llvmlite autowrap cython wurlitzer python-symengine=0.3.* tensorflow numexpr ipython antlr-python-runtime>=4.7,<4.8 antlr>=4.7,<4.8 cloudpickle"
+        - TEST_OPT_DEPENDENCY="numpy scipy gmpy2 matplotlib theano llvmlite autowrap cython wurlitzer python-symengine=0.3.* tensorflow numexpr ipython antlr-python-runtime>=4.7,<4.8 antlr>=4.7,<4.8 cloudpickle pyglet pycosat lfortran python-clang"
         - TEST_SAGE="true"
       addons:
         apt:
@@ -152,7 +166,7 @@ matrix:
     # duplicated here and in that section below.
     - python: "pypy"
       env:
-        - TEST_DOCTESTS="true"
+        - TEST_DOCTESTS="true" TEST_EXAMPLES="true"
         - FASTCACHE="false"
       addons:
         apt:
@@ -230,6 +244,9 @@ before_install:
       pip install coverage;
       coverage debug sys;
     fi
+  - if [ "$TRAVIS_PYTHON_VERSION" == "3.8-dev" ]; then
+        pip uninstall -y Cython;
+    fi
   - |
     if [[ -n "${TEST_OPT_DEPENDENCY}" ]]; then
     # We do this conditionally because it saves us some downloading if the
@@ -267,7 +284,7 @@ before_install:
         pip list | grep "numpy" && pip uninstall -y numpy;
     fi
   - if [[ "${TEST_SPHINX}" == "true" ]]; then
-      pip install "sphinx" "docutils" doctr matplotlib;
+      pip install "sphinx" "docutils" doctr matplotlib sphinx-math-dollar;
     fi
 
 install:
@@ -282,6 +299,9 @@ install:
   - pip install mpmath
   # -We:invalid makes invalid escape sequences error in Python 3.6. See
   # -#12028.
+  # SyntaxWarning flag for catching errors in Python3.8
+  # Issue -  #16973. -We:invalid can be dropped from 3.8 onwards, but
+  # it needs to be there for earlier versions.
   - |
     if [[ "${TEST_SETUP}" == "true" ]]; then
       # The install cycle below is to test installation on systems without
@@ -291,7 +311,7 @@ install:
       ~/.venv-no-setuptools/bin/pip uninstall -y setuptools;
       ~/.venv-no-setuptools/bin/python -We:invalid setup.py -q install;
     fi
-    python -We:invalid -m compileall -f -q sympy/;
+    python -We:invalid -We::SyntaxWarning -m compileall -f -q sympy/;
     python -We:invalid setup.py -q install;
     pip list --format=columns;
 

AUTHORS

@@ -4,7 +4,7 @@ those who explicitly didn't want to be mentioned. People with a * next
 to their names are not found in the metadata of the git history. This
 file is generated automatically by running `./bin/authors_update.py`.
 
-There are a total of 798 authors.
+There are a total of 822 authors.
 
 Ondřej Čertík <ondrej@certik.cz>
 Fabian Pedregosa <fabian@fseoane.net>
@@ -785,7 +785,7 @@ Daniel Ingram <ingramds@appstate.edu>
 Jogi Miglani <jmig5776@gmail.com>
 Takumasa Nakamura <n.takumasa@gmail.com>
 Ritu Raj Singh <RituRajSingh878@gmail.com>
-Rajiv Ranjan Singh <42106787+iamrajiv@users.noreply.github.com>
+Rajiv Ranjan Singh <rajivperfect007@gmail.com>
 Vera Lozhkina <veralozhkina@gmail.com>
 adhoc-king <46354827+adhoc-king@users.noreply.github.com>
 Mikel Rouco <mikel.mrm@gmail.com>
@@ -804,3 +804,27 @@ Alpesh Jamgade <alpeshjamgade21@gmail.com>
 Shubham Abhang <shubhamabhang77@gmail.com>
 Vishesh Mangla <manglavishesh64@gmail.com>
 Nicko van Someren <nicko@nicko.org>
+dandiez <47832466+dandiez@users.noreply.github.com>
+Frédéric Chapoton <fchapoton2@gmail.com>
+jhanwar <f2015463@pilani.bits-pilani.ac.in>
+Noumbissi valere Gille Geovan <noumbissivalere@gmail.com>
+Salmista-94 <alejandrogroso@hotmail.com>
+Shivani Kohli <shivanikohli.09@gmail.com>
+Parker Berry <parker.berry@marquette.edu>
+Pragyan Mehrotra <pragyan18168@iiitd.ac.in>
+Nabanita Dash <dashnabanita@gmail.com>
+Gaetano Guerriero <x.guerriero@tin.it>
+Ankit Pandey <pandeyan@grinnell.edu>
+Ritesh Kumar <ritesh99rakesh@gmail.com>
+kkkkx <709563092@qq.com>
+wate123 <junlin0604@gmail.com>
+Corwinpro <corwinat@gmail.com>
+Anway De <anway1756@gmail.com>
+znxftw <vishnu2101@gmail.com>
+Jack <ivanenko@ucu.edu.ua>
+OrestisVaggelis <orestis22000@gmail.com>
+Nikhil Maan <nikhilmaan22@gmail.com>
+Abhinav Anand <abhinav.anand2807@gmail.com>
+sqs <googol.sqs@gmail.com>
+Juan Barbosa <js.barbosa10@uniandes.edu.co>
+Prionti Nasir <pdn3628@rit.edu>

bin/authors_update.py

@@ -20,7 +20,7 @@ if sys.version_info < (3, 6):
 
 from subprocess import run, PIPE
 from distutils.version import LooseVersion
-from collections import defaultdict, OrderedDict
+from collections import OrderedDict
 
 def red(text):
     return "\033[31m%s\033[0m" % text
@@ -47,8 +47,6 @@ git_ver = run(['git', '--version'], stdout=PIPE, encoding='utf-8').stdout[12:]
 if LooseVersion(git_ver) < LooseVersion(minimal):
     print(yellow("Please use a git version >= %s" % minimal))
 
-from sympy.utilities.misc import filldedent
-
 def author_name(line):
     assert line.count("<") == line.count(">") == 1
     assert line.endswith(">")

bin/coverage_doctest.py

@@ -30,6 +30,9 @@ except ImportError:
     # It's html.parser in Python 3
     from html.parser import HTMLParser
 
+from sympy.utilities.misc import filldedent
+
+
 # Load color templates, used from sympy/utilities/runtests.py
 color_templates = (
     ("Black", "0;30"),
@@ -310,14 +313,21 @@ def process_function(name, c_name, b_obj, mod_path, f_sk, f_md, f_mdt, f_idt,
     if name.startswith('_'):
         f_sk.append(full_name)
     else:
-        if not obj.__doc__:
-            add_md = True
-        elif not '>>>' in obj.__doc__:
-            add_mdt = True
-        elif _is_indirect(name, obj.__doc__):
-            add_idt = True
-        else:
+        doc = obj.__doc__
+        if type(doc) is str:
+            if not doc:
+                add_md = True
+            elif not '>>>' in doc:
+                add_mdt = True
+            elif _is_indirect(name, doc):
+                add_idt = True
+            else:
+                f_doctest = True
+        elif doc is None:
+            # this was a function defined in the docstring
             f_doctest = True
+        else:
+            assert None, type(doc)
 
         function = True
 
@@ -370,15 +380,23 @@ def process_class(c_name, obj, c_sk, c_md, c_mdt, c_idt, c_has_doctest,
 
     c = True
     full_name = "LINE %d: %s" % (line_no, c_name)
-    if not obj.__doc__:
-        c_md.append(full_name)
-    elif not '>>>' in obj.__doc__:
-        c_mdt.append(full_name)
-    elif _is_indirect(c_name, obj.__doc__):
-        c_idt.append(full_name)
-    else:
+    doc = obj.__doc__
+    if type(doc) is str:
+        if not doc:
+            c_md.append(full_name)
+        elif not '>>>' in doc:
+            c_mdt.append(full_name)
+        elif _is_indirect(c_name, doc):
+            c_idt.append(full_name)
+        else:
+            c_dt = True
+            c_has_doctest.append(full_name)
+    elif doc is None:
+        # this was a class defined in the docstring
         c_dt = True
         c_has_doctest.append(full_name)
+    else:
+        assert None, type(doc)
 
     in_sphinx = False
     if sphinx:
@@ -435,7 +453,7 @@ def coverage(module_path, verbose=False, no_color=False, sphinx=True):
         if member in skip_members:
             continue
 
-        # Identify if the member (class/def) a part of this module
+        # Identify if the member (class/def) is a part of this module
         obj = getattr(m, member)
         obj_mod = inspect.getmodule(obj)
 
@@ -534,6 +552,10 @@ def coverage(module_path, verbose=False, no_color=False, sphinx=True):
 
 
 def go(sympy_top, file, verbose=False, no_color=False, exact=True, sphinx=True):
+
+    # file names containing any string in skip_paths will be skipped,
+    skip_paths = []
+
     if os.path.isdir(file):
         doctests, total_sphinx, num_functions = 0, 0, 0
         for F in os.listdir(file):
@@ -584,10 +606,11 @@ if __name__ == "__main__":
     args = parser.parse_args()
 
     if args.sphinx and not os.path.exists(os.path.join(sympy_top, 'doc', '_build', 'html')):
-        print("""
-Cannot check Sphinx coverage without a documentation build. To build the
-docs, run "cd doc; make html".  To skip checking Sphinx coverage, pass --no-sphinx.
-""")
+        print(filldedent("""
+            Cannot check Sphinx coverage without a documentation build.
+            To build the docs, run "cd doc; make html".  To skip
+            checking Sphinx coverage, pass --no-sphinx.
+            """))
         sys.exit(1)
 
     full_coverage = True

bin/coverage_report.py

@@ -27,7 +27,7 @@ from __future__ import print_function
 import os
 import re
 import sys
-from optparse import OptionParser
+from argparse import ArgumentParser
 
 minver = '3.4'
 try:
@@ -41,8 +41,6 @@ except ImportError:
         "https://launchpad.net/ubuntu/+source/python-coverage/" % minver)
     sys.exit(-1)
 
-REPORT_DIR = "covhtml"
-REFRESH = False
 
 omit_dir_patterns = ['.*tests', 'benchmark', 'examples',
                      'pyglet', 'test_external']
@@ -60,13 +58,13 @@ def generate_covered_files(top_dir):
                 yield os.path.join(dirpath, filename)
 
 
-def make_report(source_dir, report_dir, use_cache=False, slow=False):
+def make_report(
+    test_args, source_dir='sympy/', report_dir='covhtml', use_cache=False,
+    slow=False
+    ):
     # code adapted from /bin/test
-    bin_dir = os.path.abspath(os.path.dirname(__file__))  # bin/
-    sympy_top = os.path.split(bin_dir)[0]  # ../
-    sympy_dir = os.path.join(sympy_top, 'sympy')  # ../sympy/
-    if os.path.isdir(sympy_dir):
-        sys.path.insert(0, sympy_top)
+    from get_sympy import path_hack
+    sympy_top = path_hack()
     os.chdir(sympy_top)
 
     cov = coverage.coverage()
@@ -79,40 +77,43 @@ def make_report(source_dir, report_dir, use_cache=False, slow=False):
         cov.erase()
         cov.start()
         import sympy
-        sympy.test(source_dir, subprocess=False)
-        if slow:
-            sympy.test(source_dir, subprocess=False, slow=slow)
+        sympy.test(*test_args, subprocess=False, slow=slow)
         #sympy.doctest()  # coverage doesn't play well with doctests
         cov.stop()
-        cov.save()
+        try:
+            cov.save()
+        except PermissionError:
+            import warnings
+            warnings.warn(
+                "PermissionError has been raised while saving the " \
+                "coverage result.",
+                RuntimeWarning
+            )
 
     covered_files = list(generate_covered_files(source_dir))
-
-    if report_dir in os.listdir(os.curdir):
-        for f in os.listdir(report_dir):
-            if f.split('.')[-1] in ['html', 'css', 'js']:
-                os.remove(os.path.join(report_dir, f))
-
     cov.html_report(morfs=covered_files, directory=report_dir)
 
+parser = ArgumentParser()
+parser.add_argument(
+    '-c', '--use-cache', action='store_true', default=False,
+    help='Use cached data.')
+parser.add_argument(
+    '-d', '--report-dir', default='covhtml',
+    help='Directory to put the generated report in.')
+parser.add_argument(
+    "--slow", action="store_true", dest="slow", default=False,
+    help="Run slow functions also.")
+options, args = parser.parse_known_args()
+
 if __name__ == '__main__':
-    parser = OptionParser()
-    parser.add_option('-c', '--use-cache', action='store_true', default=False,
-                      help='Use cached data.')
-    parser.add_option('-d', '--report-dir', default='covhtml',
-                      help='Directory to put the generated report in.')
-    parser.add_option("--slow", action="store_true", dest="slow",
-                      default=False, help="Run slow functions also.")
-
-    options, args = parser.parse_args()
-
-    if args:
-        source_dir = args[0]
-    else:
-        source_dir = 'sympy/'
-
-    make_report(source_dir, **options.__dict__)
+    report_dir = options.report_dir
+    use_cache = options.use_cache
+    slow = options.slow
+    make_report(
+        args, report_dir=report_dir, use_cache=use_cache, slow=slow)
 
     print("The generated coverage report is in covhtml directory.")
-    print("Open %s in your web browser to view the report" % os.sep.join(
-        'sympy covhtml index.html'.split()))
+    print(
+        "Open %s in your web browser to view the report" %
+        os.sep.join([report_dir, 'index.html'])
+    )

bin/mailmap_update.py

@@ -1,5 +1,4 @@
 #!/usr/bin/env python
-# -*- coding: utf-8 -*-
 """
 A tool to help keep .mailmap up-to-date with the
 current git authors.
@@ -50,6 +49,11 @@ def author_name(line):
     assert line.endswith(">")
     return line.split("<", 1)[0].strip()
 
+def author_email(line):
+    assert line.count("<") == line.count(">") == 1
+    assert line.endswith(">")
+    return line.split("<", 1)[1][:-1].strip()
+
 sysexit = 0
 print(blue("checking git authors..."))
 
@@ -116,6 +120,41 @@ if multi:
         for e in sorted(dups[k]):
             print('\t%s' % e)
 
+bad_names = []
+bad_emails = []
+for i in git_people:
+    name = author_name(i)
+    email = author_email(i)
+    if '@' in name:
+        bad_names.append(i)
+    elif '@' not in email:
+        bad_emails.append(i)
+if bad_names:
+    print()
+    print(yellow(filldedent("""
+        The following people appear to have an email address
+        listed for their name. Entries should be added to
+        .mailmap so that names are formatted like
+        "Name <email address>".
+        """)))
+    for i in bad_names:
+        print("\t%s" % i)
+
+# TODO: Should we check for bad emails as well? Some people have empty email
+# addresses. The above check seems to catch people who get the name and email
+# backwards, so let's leave this alone for now.
+
+# if bad_emails:
+#     print()
+#     print(yellow(filldedent("""
+#         The following names do not appear to have valid
+#         emails. Entries should be added to .mailmap that
+#         use a proper email address. If there is no email
+#         address for a person, use "none@example.com".
+#         """)))
+#     for i in bad_emails:
+#         print("\t%s" % i)
+
 print()
 print(blue("checking .mailmap..."))
 

bin/test_external_imports.py

@@ -25,7 +25,7 @@ hard_dependencies = ['mpmath']
 # These libraries are optional, but are always imported at SymPy import time
 # when they are installed. External libraries should only be added to this
 # list if they are required for core SymPy functionality.
-hard_optional_dependencies = ['gmpy', 'gmpy2', 'fastcache']
+hard_optional_dependencies = ['gmpy', 'gmpy2', 'fastcache', 'pycosat']
 
 import sys
 import os

bin/test_travis.sh

@@ -58,7 +58,7 @@ else:
     coverage.process_startup()
 ''')
 EOF
-    export COVERAGE_PROCESS_START=$TRAVIS_BUILD_DIR/.coveragerc
+    export COVERAGE_PROCESS_START=$TRAVIS_BUILD_DIR/coveragerc_travis
 fi
 
 if [[ "${TEST_ASCII}" == "true" ]]; then
@@ -137,9 +137,8 @@ test_list = [
     # ipython
     '*ipython*',
 
-    # antlr
-    'sympy/parsing/tests/test_autolev',
-    'sympy/parsing/tests/test_latex',
+    # antlr, lfortran, clang
+    'sympy/parsing/',
 
     # matchpy
     '*rubi*',
@@ -151,6 +150,11 @@ test_list = [
 
     # cloudpickle
     'pickling',
+
+    # pycosat
+    'sympy/logic',
+    'sympy/assumptions',
+
 ]
 
 blacklist = [
@@ -180,15 +184,19 @@ doctest_list = [
     # ipython
     '*ipython*',
 
-    # antlr
-    'sympy/parsing/autolev',
-    'sympy/parsing/latex',
+    # antlr, lfortran, clang
+    'sympy/parsing/',
 
     # matchpy
     '*rubi*',
 
     # codegen
     'sympy/codegen/',
+
+    # pycosat
+    'sympy/logic',
+    'sympy/assumptions',
+
 ]
 
 if not (sympy.test(*test_list, blacklist=blacklist) and sympy.doctest(*doctest_list)):
@@ -242,3 +250,8 @@ fi
 if [[ "${TEST_COVERAGE}" == "true" ]]; then
     unset COVERAGE_PROCESS_START
 fi
+
+if [[ "${TEST_EXAMPLES}" == "true" ]]; then
+    # No need to change directory if executed after the rst doctest
+    examples/all.py -q
+fi

data/TeXmacs/bin/tm_sympy

@@ -11,7 +11,7 @@
 # heuristics to know where a multi-line expression is
 # broken. As a result you can't use more than one space
 # in a sequence. However you can and must indent your
-# expression using standard Pyhon rules.
+# expression using standard Python rules.
 #
 # You can retrieve the last output using '_' built-in
 # symbol. If the previous command did not generate

doc/README.rst

@@ -7,6 +7,7 @@ Debian/Ubuntu
 To make the html documentation, install the prerequisites::
 
     apt-get install python-sphinx texlive-latex-recommended dvipng librsvg2-bin imagemagick docbook2x graphviz
+    python -m pip install sphinx-math-dollar
 
 and do::
 
@@ -30,6 +31,7 @@ Fedora
 Fedora (and maybe other RPM based distributions), install the prerequisites::
 
     dnf install python3-sphinx librsvg2 ImageMagick docbook2X texlive-dvipng-bin texlive-scheme-medium librsvg2-tools
+    python -m pip install sphinx-math-dollar
 
 After that, run::
 
@@ -47,6 +49,30 @@ And view it at::
 
     _build/html/index.html
 
+Mac
+---
+
+- Install MacTex: http://www.tug.org/mactex/
+- Install homebrew: https://brew.sh/
+
+Install these packages with homebrew:
+
+```bash
+brew install imagemagick graphviz docbook librsvg
+```
+
+Install these packages with either pip or conda:
+
+```bash
+python -m pip install mpmath matplotlib sphinx sphinx-math-dollar
+```
+
+or
+
+```bash
+conda install -c conda-forge mpmpath matplotlib sphinx sphinx-math-dollar
+```
+
 Windows 10
 ----------
 

doc/src/_static/default.css_t

@@ -9,7 +9,7 @@
  *
  */
 
-@import url("basic.css");
+@import url("classic.css");
 @import url(https://fonts.googleapis.com/css?family=Open+Sans);
 
 /* -- page layout ----------------------------------------------------------- */

doc/src/conf.py

@@ -12,6 +12,9 @@
 # serve to show the default value.
 
 import sys
+import inspect
+import os
+import subprocess
 import sympy
 
 # If your extensions are in another directory, add it here.
@@ -22,7 +25,7 @@ sys.path = ['ext'] + sys.path
 
 # Add any Sphinx extension module names here, as strings. They can be extensions
 # coming with Sphinx (named 'sphinx.addons.*') or your custom ones.
-extensions = ['sphinx.ext.autodoc', 'sphinx.ext.viewcode',
+extensions = ['sphinx.ext.autodoc', 'sphinx.ext.linkcode', 'sphinx_math_dollar',
               'sphinx.ext.mathjax', 'numpydoc', 'sympylive',
               'sphinx.ext.graphviz', 'matplotlib.sphinxext.plot_directive']
 
@@ -204,5 +207,83 @@ texinfo_documents = [
 ]
 
 # Use svg for graphviz
-
 graphviz_output_format = 'svg'
+
+
+# Requried for linkcode extension.
+# Get commit hash from the external file.
+commit_hash_filepath = '../commit_hash.txt'
+commit_hash = None
+if os.path.isfile(commit_hash_filepath):
+    with open(commit_hash_filepath, 'r') as f:
+        commit_hash = f.readline()
+
+# Get commit hash from the external file.
+if not commit_hash:
+    try:
+        commit_hash = subprocess.check_output(['git', 'rev-parse', 'HEAD'])
+        commit_hash = commit_hash.decode('ascii')
+        commit_hash = commit_hash.rstrip()
+    except:
+        import warnings
+        warnings.warn(
+            "Failed to get the git commit hash as the command " \
+            "'git rev-parse HEAD' is not working. The commit hash will be " \
+            "assumed as the SymPy master, but the lines may be misleading " \
+            "or nonexistent as it is not the correct branch the doc is " \
+            "built with. Check your installation of 'git' if you want to " \
+            "resolve this warning.")
+        commit_hash = 'master'
+
+fork = 'sympy'
+blobpath = \
+    "https://github.com/{}/sympy/blob/{}/sympy/".format(fork, commit_hash)
+
+
+def linkcode_resolve(domain, info):
+    """Determine the URL corresponding to Python object."""
+    if domain != 'py':
+        return
+
+    modname = info['module']
+    fullname = info['fullname']
+
+    submod = sys.modules.get(modname)
+    if submod is None:
+        return
+
+    obj = submod
+    for part in fullname.split('.'):
+        try:
+            obj = getattr(obj, part)
+        except Exception:
+            return
+
+    # strip decorators, which would resolve to the source of the decorator
+    # possibly an upstream bug in getsourcefile, bpo-1764286
+    try:
+        unwrap = inspect.unwrap
+    except AttributeError:
+        pass
+    else:
+        obj = unwrap(obj)
+
+    try:
+        fn = inspect.getsourcefile(obj)
+    except Exception:
+        fn = None
+    if not fn:
+        return
+
+    try:
+        source, lineno = inspect.getsourcelines(obj)
+    except Exception:
+        lineno = None
+
+    if lineno:
+        linespec = "#L%d-L%d" % (lineno, lineno + len(source) - 1)
+    else:
+        linespec = ""
+
+    fn = os.path.relpath(fn, start=os.path.dirname(sympy.__file__))
+    return blobpath + fn + linespec

doc/src/guide.rst

@@ -127,7 +127,7 @@ For easier use, there is a syntactic sugar for expressions.
 For example, ``cos(x) + 1`` is equal to ``cos(x).__add__(1)`` is equal to
 ``Add(cos(x), Integer(1))``
 
-This works becauses Python allows you to override the behavior of built-in
+This works because Python allows you to override the behavior of built-in
 operations ``+, *, -, /`` etc., by defining methods with names ``__add__``,
 ``__mul__`` etc., so ``cos(x) + 1`` is evaluated as ``cos(x).__add__(1)``.
 

doc/src/install.rst

@@ -9,7 +9,7 @@ recommended method of installation is through Anaconda, which includes
 mpmath, as well as several other useful libraries.  Alternatively, some Linux
 distributions have SymPy packages available.
 
-SymPy officially supports Python 2.7, 3.4, 3.5, 3.6 and PyPy.
+SymPy officially supports Python 2.7, 3.5, 3.6, 3.7, and PyPy.
 
 Anaconda
 ========

doc/src/modules/algebras.rst

@@ -1,6 +1,6 @@
-===============
-Algebras Module
-===============
+========
+Algebras
+========
 
 Introduction
 ------------

doc/src/modules/assumptions/handlers/common.rst

@@ -0,0 +1,6 @@
+======
+Common
+======
+
+.. automodule:: sympy.assumptions.handlers.common
+   :members:

doc/src/modules/assumptions/handlers/index.rst

@@ -11,6 +11,8 @@ Contents
     :maxdepth: 3
 
     calculus.rst
+    common.rst
+    matrices.rst
     ntheory.rst
     order.rst
     sets.rst

doc/src/modules/assumptions/handlers/matrices.rst

@@ -0,0 +1,6 @@
+========
+Matrices
+========
+
+.. automodule:: sympy.assumptions.handlers.matrices
+   :members:

doc/src/modules/assumptions/index.rst

@@ -1,8 +1,8 @@
 .. _assumptions_module:
 
-==================
-Assumptions Module
-==================
+===========
+Assumptions
+===========
 
 .. automodule:: sympy.assumptions
 

doc/src/modules/calculus/index.rst

@@ -10,5 +10,10 @@ Calculus
 .. automodule:: sympy.calculus.singularities
     :members:
 
-.. automodule :: sympy.calculus.finite_diff
+.. _finite_diff:
+
+.. automodule:: sympy.calculus.finite_diff
+    :members:
+
+.. automodule:: sympy.calculus.util
     :members:

doc/src/modules/categories.rst

@@ -1,5 +1,6 @@
-Category Theory Module
-======================
+===============
+Category Theory
+===============
 
 Introduction
 ------------

doc/src/modules/codegen.rst

@@ -1,8 +1,8 @@
 .. _codegen_prose:
 
-================================================
-Structural Details of Code Generation with SymPy
-================================================
+===============
+Code Generation
+===============
 
 Several submodules in SymPy allow one to generate directly compilable and
 executable code in a variety of different programming languages from SymPy
@@ -164,8 +164,8 @@ An example of Mathematica code printer::
 
     >>> expr = summation(expr, (n, -1, 1))
     >>> mathematica_code(expr)
-    T*x[-T]*Sin[(T + t)/T]/(T + t) + T*x[T]*Sin[(-T + t)/T]/(-T + t) + T*x[0]*Sin[
-    t/T]/t
+    T*(x[-T]*Sin[(T + t)/T]/(T + t) + x[T]*Sin[(-T + t)/T]/(-T + t) + x[0]*Sin[t/T
+    ]/t)
 
 We can go through a common expression in different languages we support and see
 how it works::
@@ -548,6 +548,9 @@ Classes and functions for rewriting expressions (sympy.codegen.rewriting)
 .. automodule:: sympy.codegen.rewriting
    :members:
 
+.. automodule:: sympy.codegen.matrix_nodes
+   :members:
+
 Tools for simplifying expressions using approximations (sympy.codegen.approximations)
 -------------------------------------------------------------------------------------
 
@@ -612,3 +615,10 @@ Fortran utilities (sympy.codegen.futils)
 
 .. automodule:: sympy.codegen.futils
    :members:
+
+
+Array utilities (sympy.codegen.array_utils)
+-------------------------------------------
+
+.. automodule:: sympy.codegen.array_utils
+   :members:

doc/src/modules/combinatorics/index.rst

@@ -1,8 +1,8 @@
 .. _combinatiorics-docs:
 
-====================
-Combinatorics Module
-====================
+=============
+Combinatorics
+=============
 
 Contents
 ========
@@ -23,3 +23,4 @@ Contents
    testutil.rst
    tensor_can.rst
    fp_groups.rst
+   pc_groups.rst

doc/src/modules/combinatorics/pc_groups.rst

@@ -0,0 +1,307 @@
+Polycyclic Groups
+=================
+
+Introduction
+------------
+
+This module presents the functionality designed for computing with
+polycyclic groups(PcGroup for short). The name of the corresponding
+SymPy object is ``PolycyclicGroup``. The functions or classes described
+here are studied under **Computational Group Theory**.
+
+Overview of functionalities
+```````````````````````````
+
+* The construction of PolycyclicGroup from a given PermutationGroup.
+
+* Computation of polycyclic generating sequence(pcgs for short) and
+  polycyclic series(pc_series).
+
+* Computation of relative order for polycyclic series.
+
+* Implementation of class Collector which can be treated as a base for polycylic groups.
+
+* Implementation of polycyclic group presentation(pc_presentation for short).
+
+* Computation of exponent vector, depth and leading exponent for a given element
+  of a polycyclic group.
+
+For a description of fundamental algorithms of polycyclic groups, we
+often make use of *Handbook of Computational Group Theory*.
+
+
+The Construction of Polycyclic Groups
+-------------------------------------
+
+Given a Permutation Group, A Polycyclic Group is constructed by computing the
+corresponding polycylic generating sequence, polycyclic series and it's
+relative order.
+
+Attributes of PolycyclicGroup
+`````````````````````````````
+
+* ``pc_sequence`` : Polycyclic sequence is formed by collecting all the missing 
+  generators between the adjacent groups in the derived series of given
+  permutation group.
+
+* ``pc_series`` : Polycyclic series is formed by adding all the missing generators
+  of ``der[i+1]`` in ``der[i]``, where ``der`` represents derived series.
+
+* ``relative_order`` : A list, computed by the ratio of adjacent groups in pc_series.
+
+* ``collector`` : By default, it is None. Collector class provides the polycyclic presentation.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> G = SymmetricGroup(4)
+>>> PcGroup = G.polycyclic_group()
+>>> len(PcGroup.pcgs)
+4
+>>> pc_series = PcGroup.pc_series
+>>> pc_series[0]==G
+True
+>>> gen = pc_series[len(pc_series)-1].generators[0]
+>>> gen.is_identity
+True
+>>> PcGroup.relative_order
+[2, 3, 2, 2]
+
+
+The Construction of Collector
+-----------------------------
+
+Collector is one of the attributes of class PolycyclicGroup.
+
+Attributes of Collector
+```````````````````````
+
+Collector posses all the attributes of PolycyclicGroup, In addition there are
+few more attributes which are defined below:
+
+* ``free_group`` : free_group provides the mapping of polycyclic generating sequence with
+  the free group elements.
+
+* ``pc_presentation`` : Provides the presentation of polycyclic groups with the
+  help of power and conjugate relators.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> G = SymmetricGroup(3)
+>>> PcGroup = G.polycyclic_group()
+>>> Collector = PcGroup.collector
+>>> Collector.free_group
+<free group on the generators (x0, x1)>
+>>> Collector.pc_presentation
+{x0**2: (), x1**3: (), x0**-1*x1*x0: x1**2}
+
+
+Computation of Minimal Uncollected Subword
+``````````````````````````````````````````
+
+A word ``V`` defined on generators in the free_group of pc_group is a minimal
+uncollected subword of the word ``W`` if ``V`` is a subword of ``W`` and it has one of
+the following form:
+
+* `v = {x_{i+1}}^{a_j}x_i`
+* `v = {x_{i+1}}^{a_j}{x_i}^{-1}`
+* `v = {x_i}^{a_j}`
+
+`a_j \notin \{0, \ldots \mathrm{relative\_order}[j]-1\}`.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> from sympy.combinatorics.free_groups import free_group
+>>> G = SymmetricGroup(4)
+>>> PcGroup = G.polycyclic_group()
+>>> collector = PcGroup.collector
+>>> F, x1, x2 = free_group("x1, x2")
+>>> word = x2**2*x1**7
+>>> collector.minimal_uncollected_subword(word)
+((x2, 2),)
+
+
+Computation of Subword Index
+````````````````````````````
+
+For a given word and it's subword, subword_index computes the
+starting and ending index of the subword in the word.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> from sympy.combinatorics.free_groups import free_group
+>>> G = SymmetricGroup(4)
+>>> PcGroup = G.polycyclic_group()
+>>> collector = PcGroup.collector
+>>> F, x1, x2 = free_group("x1, x2")
+>>> word = x2**2*x1**7
+>>> w = x2**2*x1
+>>> collector.subword_index(word, w)
+(0, 3)
+>>> w = x1**7
+>>> collector.subword_index(word, w)
+(2, 9)
+
+
+Computation of Collected Word
+`````````````````````````````
+
+A word ``W`` is called collected, if ``W`` `= {x_{i_1}}^{a_1} \ldots {x_{i_r}}^{a_r}`
+with `i_1 < i_2< \ldots < i_r` and `a_j` is in `\{1 \ldots s_{j-1}\}`, where `s_j`
+represents the respective relative order.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> from sympy.combinatorics.perm_groups import PermutationGroup
+>>> from sympy.combinatorics.free_groups import free_group
+>>> G = SymmetricGroup(4)
+>>> PcGroup = G.polycyclic_group()
+>>> collector = PcGroup.collector
+>>> F, x0, x1, x2, x3 = free_group("x0, x1, x2, x3")
+>>> word = x3*x2*x1*x0
+>>> collected_word = collector.collected_word(word)
+>>> free_to_perm = {}
+>>> free_group = collector.free_group
+>>> for sym, gen in zip(free_group.symbols, collector.pcgs):
+...     free_to_perm[sym] = gen
+>>> G1 = PermutationGroup()
+>>> for w in word:
+...     sym = w[0]
+...     perm = free_to_perm[sym]
+...     G1 = PermutationGroup([perm] + G1.generators)
+>>> G2 = PermutationGroup()
+>>> for w in collected_word:
+...     sym = w[0]
+...     perm = free_to_perm[sym]
+...     G2 = PermutationGroup([perm] + G2.generators)
+>>> G1 == G2
+True
+
+
+Computation of Polycyclic Presentation
+--------------------------------------
+
+The computation of presentation starts from the bottom of the pcgs and polycyclic series.
+Storing all the previous generators from pcgs and then taking the last generator
+as the generator which acts as a conjugator and conjugates all the previous
+generators in the list.
+
+To get a clear picture, start with an example of SymmetricGroup(4). For S(4) there are 4
+generators in pcgs say `[x_0, x_1, x_2, x_3]` and the relative_order vector is [2, 3, 2, 2].
+Starting from bottom of this sequence the presentation is computed in order as below.
+
+using only `[x_3]` from ``pcgs`` and ``pc_series[4]`` compute:
+
+* `x_3^2`
+
+using only `[x_3]` from ``pcgs`` and ``pc_series[3]`` compute:
+
+* `x_2^2`
+* `x_2^{-1}x_3x_2`
+
+using `[x_3, x_2]` from ``pcgs`` and ``pc_series[2]`` compute:
+
+* `x_1^3`
+* `x_1^{-1}x_3x_1`
+* `x_1^{-1}x_2x_1`
+
+using `[x_3, x_2, x_1]` from ``pcgs`` and ``pc_series[1]`` compute:
+
+* `x_0^2`
+* `x_0^{-1}x_3x_0`
+* `x_0^{-1}x_2x_0`
+* `x_0^{-1}x_1x_0`
+
+
+One thing to note is same group can have different pcgs due to variying derived_series which,
+results in different polycyclic presentations.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> from sympy.combinatorics.permutations import Permutation
+>>> G = SymmetricGroup(4)
+>>> PcGroup = G.polycyclic_group()
+>>> collector = PcGroup.collector
+>>> pcgs = PcGroup.pcgs
+>>> len(pcgs)
+4
+>>> free_group = collector.free_group
+>>> pc_resentation = collector.pc_presentation
+>>> free_to_perm = {}
+>>> for s, g in zip(free_group.symbols, pcgs):
+...     free_to_perm[s] = g
+>>> for k, v in pc_resentation.items():
+...     k_array = k.array_form
+...     if v != ():
+...        v_array = v.array_form
+...     lhs = Permutation()
+...     for gen in k_array:
+...         s = gen[0]
+...         e = gen[1]
+...         lhs = lhs*free_to_perm[s]**e
+...     if v == ():
+...         assert lhs.is_identity
+...         continue
+...     rhs = Permutation()
+...     for gen in v_array:
+...         s = gen[0]
+...         e = gen[1]
+...         rhs = rhs*free_to_perm[s]**e
+...     assert lhs == rhs
+
+
+Computation of Exponent Vector
+------------------------------
+
+Any generator of the polycyclic group can be represented with the help of it's
+polycyclic generating sequence. Hence, the length of exponent vector is equal to
+the length of the pcgs.
+
+A given generator ``g`` of the polycyclic group, can be represented as
+`g = x_1^{e_1} \ldots x_n^{e_n}`, where `x_i` represents polycyclic generators 
+and ``n`` is the number of generators in the free_group equal to the length of pcgs.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> from sympy.combinatorics.permutations import Permutation
+>>> G = SymmetricGroup(4)
+>>> PcGroup = G.polycyclic_group()
+>>> collector = PcGroup.collector
+>>> pcgs = PcGroup.pcgs
+>>> collector.exponent_vector(G[0])
+[1, 0, 0, 0]
+>>> exp = collector.exponent_vector(G[1])
+>>> g = Permutation()
+>>> for i in range(len(exp)):
+...     g = g*pcgs[i]**exp[i] if exp[i] else g
+>>> assert g == G[1]
+
+
+Depth of Polycyclic generator
+`````````````````````````````
+
+Depth of a given polycyclic generator is defined as the index of the first
+non-zero entry in the exponent vector.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> G = SymmetricGroup(3)
+>>> PcGroup = G.polycyclic_group()
+>>> collector = PcGroup.collector
+>>> collector.depth(G[0])
+2
+>>> collector.depth(G[1])
+1
+
+
+Computation of Leading Exponent
+```````````````````````````````
+
+Leading exponent represents the exponent of polycyclic generator at the above depth.
+
+>>> from sympy.combinatorics.named_groups import SymmetricGroup
+>>> G = SymmetricGroup(3)
+>>> PcGroup = G.polycyclic_group()
+>>> collector = PcGroup.collector
+>>> collector.leading_exponent(G[1])
+1
+
+
+Bibliography
+------------
+
+.. [Ho05] Derek F. Holt,
+    Handbook of Computational Group Theory.
+    In the series 'Discrete Mathematics and its Applications',
+    `Chapman & Hall/CRC 2005, xvi + 514 p <https://www.crcpress.com/Handbook-of-Computational-Group-Theory/Holt-Eick-OBrien/p/book/9781584883722>`_.

doc/src/modules/concrete.rst

@@ -1,5 +1,6 @@
-Concrete Mathematics
-====================
+========
+Concrete
+========
 
 Hypergeometric terms
 --------------------

doc/src/modules/core.rst

@@ -1,5 +1,6 @@
-SymPy Core
-==========
+====
+Core
+====
 
 sympify
 -------

doc/src/modules/crypto.rst

@@ -1,5 +1,6 @@
-Basic Cryptography Module
-=========================
+============
+Cryptography
+============
 
 .. warning::
 
@@ -50,10 +51,18 @@ substitutions at different times in the message.
 
 .. autofunction:: decipher_shift
 
+.. autofunction:: encipher_rot13
+
+.. autofunction:: decipher_rot13
+
 .. autofunction:: encipher_affine
 
 .. autofunction:: decipher_affine
 
+.. autofunction:: encipher_atbash
+
+.. autofunction:: decipher_atbash
+
 .. autofunction:: encipher_substitution
 
 .. autofunction:: encipher_vigenere
@@ -133,3 +142,7 @@ substitutions at different times in the message.
 .. autofunction:: encipher_gm
 
 .. autofunction:: decipher_gm
+
+.. autofunction:: encipher_railfence
+
+.. autofunction:: decipher_railfence

doc/src/modules/diffgeom.rst

@@ -1,5 +1,6 @@
-Differential Geometry Module
-============================
+=====================
+Differential Geometry
+=====================
 
 .. module:: sympy.diffgeom
 

doc/src/modules/discrete.rst

@@ -1,5 +1,6 @@
-Discrete Module
-===============
+========
+Discrete
+========
 
 The ``discrete`` module in SymPy implements methods to compute discrete
 transforms and convolutions of finite sequences.

doc/src/modules/evalf.rst

@@ -1,6 +1,7 @@
 .. _evalf-label:
 
-Numerical evaluation
+====================
+Numerical Evaluation
 ====================
 
 Basics

doc/src/modules/functions/index.rst

@@ -1,7 +1,8 @@
 .. _functions:
 
-Functions Module
-****************
+=========
+Functions
+=========
 
 .. module:: sympy.functions
 

doc/src/modules/geometry/index.rst

@@ -1,6 +1,6 @@
-===============
-Geometry Module
-===============
+========
+Geometry
+========
 
 
 Introduction

doc/src/modules/holonomic/about.rst

@@ -36,7 +36,7 @@ Here `D` is the Differential Operator and `L` is called the annihilator
 of the function.
 
 A unique holonomic function can be defined from the annihilator and a set of
-initial conditons.
+initial conditions.
 For instance:
 
 .. math::

doc/src/modules/holonomic/convert.rst

@@ -1,7 +1,7 @@
 Converting other representations to holonomic
 =============================================
 
-.. module:: sympy.holonomic.holonomic
+.. currentmodule:: sympy.holonomic.holonomic
 
 Converting hypergeometric functions
 -----------------------------------

doc/src/modules/holonomic/index.rst

@@ -1,8 +1,8 @@
 .. _holonomic-docs:
 
-===================
-Holonomic Functions
-===================
+=========
+Holonomic
+=========
 
 .. automodule:: sympy.holonomic
 

doc/src/modules/holonomic/operations.rst

@@ -29,7 +29,7 @@ a holonomic functions.
     >>> p * q
     HolonomicFunction((2) + (-2)*Dx + (1)*Dx**2, x, 0, [0, 1])
 
-.. module:: sympy.holonomic.holonomic
+.. currentmodule:: sympy.holonomic.holonomic
 
 Integration and Differentiation
 -------------------------------

doc/src/modules/holonomic/represent.rst

@@ -1,7 +1,7 @@
 Representation of holonomic functions in SymPy
 ==============================================
 
-.. module:: sympy.holonomic.holonomic
+.. currentmodule:: sympy.holonomic.holonomic
 
 Class :class:`DifferentialOperator` is used to represent the annihilator
 but we create differential operators easily using the function

doc/src/modules/holonomic/uses.rst

@@ -1,4 +1,4 @@
-.. module:: sympy.holonomic.holonomic
+.. currentmodule:: sympy.holonomic.holonomic
 
 Uses and Current limitations
 ============================

doc/src/modules/index.rst

@@ -16,49 +16,49 @@ access any SymPy module, or use the list below:
 .. toctree::
    :maxdepth: 2
 
-   core.rst
-   combinatorics/index.rst
-   ntheory.rst
-   crypto.rst
-   concrete.rst
-   discrete.rst
-   evalf.rst
+   algebras.rst
+   assumptions/index.rst
+   calculus/index.rst
+   categories.rst
    codegen.rst
-   numeric-computation.rst
+   combinatorics/index.rst
+   concrete.rst
+   core.rst
+   crypto.rst
+   diffgeom.rst
+   solvers/diophantine.rst
+   discrete.rst
    functions/index.rst
    geometry/index.rst
    holonomic/index.rst
+   simplify/hyperexpand.rst
+   solvers/inequalities.rst
    integrals/integrals.rst
    liealgebras/index.rst
    logic.rst
    matrices/index.rst
+   ntheory.rst
+   numeric-computation.rst
+   evalf.rst
+   solvers/ode.rst
+   parsing.rst
+   solvers/pde.rst
+   physics/index.rst
+   plotting.rst
    polys/index.rst
    printing.rst
-   plotting.rst
-   assumptions/index.rst
-   rewriting.rst
    series/index.rst
    sets.rst
    simplify/simplify.rst
-   simplify/hyperexpand.rst
-   stats.rst
-   solvers/ode.rst
-   solvers/pde.rst
    solvers/solvers.rst
-   solvers/diophantine.rst
-   solvers/inequalities.rst
    solvers/solveset.rst
+   stats.rst
    tensor/index.rst
+   rewriting.rst
    utilities/index.rst
-   parsing.rst
-   calculus/index.rst
-   physics/index.rst
-   categories.rst
-   diffgeom.rst
    vector/index.rst
-   algebras.rst
 
-Contributions to docs
+Contributions to Docs
 ---------------------
 
 All contributions are welcome. If you'd like to improve something, look into

doc/src/modules/integrals/integrals.rst

@@ -1,5 +1,6 @@
-Symbolic Integrals
-==================
+=========
+Integrals
+=========
 
 .. module:: sympy.integrals
 

doc/src/modules/liealgebras/index.rst

@@ -1,6 +1,6 @@
-==================
-Lie Algebra Module
-==================
+===========
+Lie Algebra
+===========
 
 .. automodule:: sympy.liealgebras
 

doc/src/modules/logic.rst

@@ -1,5 +1,6 @@
-Logic Module
-============
+=====
+Logic
+=====
 
 .. module:: sympy.logic
 

doc/src/modules/matrices/expressions.rst

@@ -34,6 +34,10 @@ Matrix Expressions Core Reference
    :members:
 .. autoclass:: MatPow
    :members:
+.. autoclass:: HadamardProduct
+   :members:
+.. autoclass:: HadamardPower
+   :members:
 .. autoclass:: Inverse
    :members:
 .. autoclass:: Transpose

doc/src/modules/matrices/matrices.rst

@@ -325,6 +325,31 @@ but we can also apply functions to our matrix entries using ``applyfunc()``. Her
     [       ]
     [0  0  2]
 
+If you want to extract a common factor from a matrix you can do so by
+applying ``gcd`` to the data of the matrix:
+
+    >>> from sympy.abc import x, y
+    >>> from sympy import gcd
+    >>> m = Matrix([[x, y], [1, x*y]]).inv(); m
+    [  -x*y          y     ]
+    [----------  ----------]
+    [   2           2      ]
+    [- x *y + y  - x *y + y]
+    [                      ]
+    [    1          -x     ]
+    [----------  ----------]
+    [   2           2      ]
+    [- x *y + y  - x *y + y]
+    >>> gcd(tuple(_))
+        1
+    ----------
+       2
+    - x *y + y
+    >>> m/_
+    [-x*y  y ]
+    [        ]
+    [ 1    -x]
+
 One more useful matrix-wide entry application function is the substitution function. Let's declare a matrix with symbolic entries then substitute a value. Remember we can substitute anything - even another symbol!:
 
     >>> from sympy import Symbol

doc/src/modules/ntheory.rst

@@ -1,5 +1,6 @@
+=============
 Number Theory
-====================
+=============
 
 .. module:: sympy.ntheory.generate
 
@@ -49,6 +50,8 @@ Ntheory Functions Reference
 
 .. autofunction:: factorint
 
+.. autofunction:: factorrat
+
 .. autofunction:: primefactors
 
 .. autofunction:: divisors
@@ -85,6 +88,20 @@ Ntheory Functions Reference
 .. autoclass:: primeomega
     :members:
 
+.. autofunction:: mersenne_prime_exponent
+
+.. autofunction:: is_perfect
+
+.. autofunction:: is_mersenne_prime
+
+.. autofunction:: abundance
+
+.. autofunction:: is_abundant
+
+.. autofunction:: is_deficient
+
+.. autofunction:: is_amicable
+
 .. module:: sympy.ntheory.modular
 
 .. autofunction:: symmetric_residue
@@ -113,8 +130,18 @@ Ntheory Functions Reference
 
 .. module:: sympy.ntheory.primetest
 
+.. autofunction:: is_euler_pseudoprime
+
+.. autofunction:: is_square
+
 .. autofunction:: mr
 
+.. autofunction:: is_lucas_prp
+
+.. autofunction:: is_strong_lucas_prp
+
+.. autofunction:: is_extra_strong_lucas_prp
+
 .. autofunction:: isprime
 
 .. module:: sympy.ntheory.residue_ntheory
@@ -127,6 +154,8 @@ Ntheory Functions Reference
 
 .. autofunction:: sqrt_mod
 
+.. autofunction:: sqrt_mod_iter
+
 .. autofunction:: quadratic_residues
 
 .. autofunction:: nthroot_mod
@@ -150,3 +179,7 @@ Ntheory Functions Reference
 .. module:: sympy.ntheory.egyptian_fraction
 
 .. autofunction:: egyptian_fraction
+
+.. module:: sympy.ntheory.bbp_pi
+
+.. autofunction:: pi_hex_digits

doc/src/modules/parsing.rst

@@ -1,5 +1,6 @@
-Parsing input
-=============
+=======
+Parsing
+=======
 
 Parsing Functions Reference
 ---------------------------
@@ -90,6 +91,27 @@ change between releases, and become stricter, more relaxed, or some mix.
 
 .. autoclass:: sympy.parsing.latex.LaTeXParsingError
 
+
+SymPy Expression Reference
+--------------------------
+
+.. module:: sympy.parsing.sym_expr
+
+.. autoclass:: SymPyExpression
+  :members:
+
+`Fortran` Parsing Reference
+---------------------------------
+
+.. module:: sympy.parsing.fortran.fortran_parser
+
+.. autoclass:: ASR2PyVisitor
+  :members:
+
+.. autofunction:: call_visitor
+
+.. autofunction:: src_to_sympy
+
 Runtime Installation
 --------------------
 

doc/src/modules/physics/continuum_mechanics/beam_problems.rst

@@ -5,7 +5,7 @@ Solving Beam Bending Problems using Singularity Functions
 To make this document easier to read, enable pretty printing:
 
 .. plot::
-   :context:
+   :context: reset
    :format: doctest
    :include-source: True
 
@@ -175,7 +175,7 @@ final loading can be displayed:
        - 258⋅<x>   + 52⋅<x>   - 8⋅<x>  + 50⋅<x - 5>   + 8⋅<x - 5>  - 12⋅<x - 9>
 
 At this point, the beam is fully defined and the internal shear and bending
-moments are calculated like so:
+moments are calculated:
 
 .. plot::
    :context:
@@ -246,7 +246,7 @@ Example 2
 ---------
 
 There is a beam of length 30 meters. A moment of magnitude 120 Nm is
-applied in the clockwise direction at the end of the beam. A pointload
+applied in the clockwise direction at the end of the beam. A point load
 of magnitude 8 N is applied from the top of the beam at the starting
 point. There are two simple supports below the beam. One at the end
 and another one at a distance of 10 meters from the start. The
@@ -377,7 +377,7 @@ Example 4
 An overhanging beam of length 8 meters is pinned at 1 meter from starting point
 and supported by a roller 1 meter before the other end. It is subjected
 to a distributed constant load of 10 KN/m from the starting point till
-2 meters away from it. Two pointloads of 20KN and 8KN are applied at
+2 meters away from it. Two point loads of 20KN and 8KN are applied at
 5 meters and 7.5 meters away from the starting point respectively.
 
 ::
@@ -738,7 +738,7 @@ Example 9
 ---------
 
 There is a cantilever beam of length 4 meters. For first 2 meters
-its moment of inertia is ``1.5*I`` and ``I`` for the other end.
+its moment of inertia is ``1.5*I`` and ``I`` for the rest.
 A pointload of magnitude 20 N is applied from the top at its free end.
 
 ::
@@ -791,7 +791,7 @@ Example 10
 
 A combined beam, with constant flexural rigidity ``E*I``, is formed by joining
 a Beam of length ``2*l`` to the right of another Beam of length ``l``. The whole beam
-is fixed at both of its both end. A point load of magnitude ``P`` is also applied
+is fixed at both of its ends. A point load of magnitude ``P`` is also applied
 from the top at a distance of ``2*l`` from starting point.
 
 ::
@@ -866,7 +866,7 @@ from the top at a distance of ``2*l`` from starting point.
                         E⋅I                                               E⋅I                                                                             E⋅I
 
 Example 11
-==========
+----------
 
 Any type of load defined by a polynomial can be applied to the beam. This
 allows approximation of arbitrary load distributions. The following example

doc/src/modules/physics/index.rst

@@ -1,8 +1,8 @@
 .. _physics-docs:
 
-==============
-Physics Module
-==============
+=======
+Physics
+=======
 
 .. automodule:: sympy.physics
 

doc/src/modules/physics/mechanics/autolev_parser.rst

@@ -82,7 +82,7 @@ The parser can be used as follows::
     >>> sympy_code = parse_autolev(open('double_pendulum.al'), include_numeric=True)
 
     # The include_pydy flag is False by default. Setting it to True will
-    # enable PyDy simulation code to be outputed if applicable.
+    # enable PyDy simulation code to be outputted if applicable.
 
     >>> print(sympy_code)
     import sympy.physics.mechanics as me

doc/src/modules/physics/mechanics/masses.rst

@@ -223,40 +223,42 @@ The following example shows how to use the momenta functions in
 One begins by creating the requisite symbols to describe the system. Then
 the reference frame is created and the kinematics are done. ::
 
-  >> from sympy import symbols
-  >> from sympy.physics.mechanics import dynamicsymbols, ReferenceFrame
-  >> from sympy.physics.mechanics import RigidBody, Particle, Point, outer
-  >> from sympy.physics.mechanics import linear_momentum, angular_momentum
-  >> m, M, l1 = symbols('m M l1')
-  >> q1d = dynamicsymbols('q1d')
-  >> N = ReferenceFrame('N')
-  >> O = Point('O')
-  >> O.set_vel(N, 0 * N.x)
-  >> Ac = O.locatenew('Ac', l1 * N.x)
-  >> P = Ac.locatenew('P', l1 * N.x)
-  >> a = ReferenceFrame('a')
-  >> a.set_ang_vel(N, q1d * N.z)
-  >> Ac.v2pt_theory(O, N, a)
-  >> P.v2pt_theory(O, N, a)
+  >>> from sympy import symbols
+  >>> from sympy.physics.mechanics import dynamicsymbols, ReferenceFrame
+  >>> from sympy.physics.mechanics import RigidBody, Particle, Point, outer
+  >>> from sympy.physics.mechanics import linear_momentum, angular_momentum
+  >>> m, M, l1 = symbols('m M l1')
+  >>> q1d = dynamicsymbols('q1d')
+  >>> N = ReferenceFrame('N')
+  >>> O = Point('O')
+  >>> O.set_vel(N, 0 * N.x)
+  >>> Ac = O.locatenew('Ac', l1 * N.x)
+  >>> P = Ac.locatenew('P', l1 * N.x)
+  >>> a = ReferenceFrame('a')
+  >>> a.set_ang_vel(N, q1d * N.z)
+  >>> Ac.v2pt_theory(O, N, a)
+  l1*q1d*N.y
+  >>> P.v2pt_theory(O, N, a)
+  2*l1*q1d*N.y
 
 Finally, the bodies that make up the system are created. In this case the
 system consists of a particle Pa and a RigidBody A. ::
 
-  >> Pa = Particle('Pa', P, m)
-  >> I = outer(N.z, N.z)
-  >> A = RigidBody('A', Ac, a, M, (I, Ac))
+  >>> Pa = Particle('Pa', P, m)
+  >>> I = outer(N.z, N.z)
+  >>> A = RigidBody('A', Ac, a, M, (I, Ac))
 
 Then one can either choose to evaluate the momenta of individual components
 of the system or of the entire system itself. ::
 
-  >> linear_momentum(N,A)
+  >>> linear_momentum(N,A)
   M*l1*q1d*N.y
-  >> angular_momentum(O, N, Pa)
+  >>> angular_momentum(O, N, Pa)
   4*l1**2*m*q1d*N.z
-  >> linear_momentum(N, A, Pa)
+  >>> linear_momentum(N, A, Pa)
   (M*l1*q1d + 2*l1*m*q1d)*N.y
-  >> angular_momentum(O, N, A, Pa)
-  (4*l1**2*m*q1d + q1d)*N.z
+  >>> angular_momentum(O, N, A, Pa)
+  (M*l1**2*q1d + 4*l1**2*m*q1d + q1d)*N.z
 
 It should be noted that the user can determine either momenta in any frame
 in :mod:`mechanics` as the user is allowed to specify the reference frame when
@@ -325,33 +327,34 @@ The following example shows how to use the energy functions in
 As was discussed above in the momenta functions, one first creates the system
 by going through an identical procedure. ::
 
-  >> from sympy import symbols
-  >> from sympy.physics.mechanics import dynamicsymbols, ReferenceFrame, outer
-  >> from sympy.physics.mechanics import RigidBody, Particle, mechanics_printing
-  >> from symp.physics.mechanics import kinetic_energy, potential_energy, Point
-  >> mechanics_printing()
-  >> m, M, l1, g, h, H = symbols('m M l1 g h H')
-  >> omega = dynamicsymbols('omega')
-  >> N = ReferenceFrame('N')
-  >> O = Point('O')
-  >> O.set_vel(N, 0 * N.x)
-  >> Ac = O.locatenew('Ac', l1 * N.x)
-  >> P = Ac.locatenew('P', l1 * N.x)
-  >> a = ReferenceFrame('a')
-  >> a.set_ang_vel(N, omega * N.z)
-  >> Ac.v2pt_theory(O, N, a)
-  >> P.v2pt_theory(O, N, a)
-  >> Pa = Particle('Pa', P, m)
-  >> I = outer(N.z, N.z)
-  >> A = RigidBody('A', Ac, a, M, (I, Ac))
+  >>> from sympy import symbols
+  >>> from sympy.physics.mechanics import dynamicsymbols, ReferenceFrame, outer
+  >>> from sympy.physics.mechanics import RigidBody, Particle
+  >>> from sympy.physics.mechanics import kinetic_energy, potential_energy, Point
+  >>> m, M, l1, g, h, H = symbols('m M l1 g h H')
+  >>> omega = dynamicsymbols('omega')
+  >>> N = ReferenceFrame('N')
+  >>> O = Point('O')
+  >>> O.set_vel(N, 0 * N.x)
+  >>> Ac = O.locatenew('Ac', l1 * N.x)
+  >>> P = Ac.locatenew('P', l1 * N.x)
+  >>> a = ReferenceFrame('a')
+  >>> a.set_ang_vel(N, omega * N.z)
+  >>> Ac.v2pt_theory(O, N, a)
+  l1*omega*N.y
+  >>> P.v2pt_theory(O, N, a)
+  2*l1*omega*N.y
+  >>> Pa = Particle('Pa', P, m)
+  >>> I = outer(N.z, N.z)
+  >>> A = RigidBody('A', Ac, a, M, (I, Ac))
 
 The user can then determine the kinetic energy of any number of entities of the
 system: ::
 
-  >> kinetic_energy(N, Pa)
-  2*l1**2*m*q1d**2
-  >> kinetic_energy(N, Pa, A)
-  M*l1**2*q1d**2/2 + 2*l1**2*m*q1d**2 + q1d**2/2
+  >>> kinetic_energy(N, Pa)
+  2*l1**2*m*omega(t)**2
+  >>> kinetic_energy(N, Pa, A)
+  M*l1**2*omega(t)**2/2 + 2*l1**2*m*omega(t)**2 + omega(t)**2/2
 
 It should be noted that the user can determine either kinetic energy relative
 to any frame in :mod:`mechanics` as the user is allowed to specify the
@@ -363,14 +366,15 @@ every entity of the system using the :mod:`potential_energy` property. The
 potential energy of any number of entities comprising the system can then be
 determined: ::
 
-  >> Pa.potential_energy = m * g * h
-  >> A.potential_energy = M * g * H
-  >> potential_energy(A, Pa)
+  >>> Pa.potential_energy = m * g * h
+  >>> A.potential_energy = M * g * H
+  >>> potential_energy(A, Pa)
   H*M*g + g*h*m
 
 One can also determine the Lagrangian for this system: ::
 
-  >> Lagrangian(Pa, A)
-  -H*M*g + M*l1**2*q1d**2/2 - g*h*m + 2*l1**2*m*q1d**2 + q1d**2/2
+  >>> from sympy.physics.mechanics import Lagrangian
+  >>> Lagrangian(N, Pa, A)
+  -H*M*g + M*l1**2*omega(t)**2/2 - g*h*m + 2*l1**2*m*omega(t)**2 + omega(t)**2/2
 
 Please refer to the docstrings to learn more about each function.

doc/src/modules/physics/units/examples.rst

@@ -108,9 +108,9 @@ the outcoming result):
 
     >>> from sympy.physics.units import convert_to
     >>> convert_to(q, day)
-    71.5123904642338*pi*day
+    71.5112118495813*pi*day
     >>> convert_to(q, day).n()
-    224.662800523082*day
+    224.659097795948*day
 
 We could also have the solar mass and the day as units coming from the
 astrophysical system, but we wanted to show how to create a unit that one needs.

doc/src/modules/plotting.rst

@@ -1,5 +1,6 @@
-Plotting Module
-===============
+========
+Plotting
+========
 
 .. module:: sympy.plotting.plot
 
@@ -45,6 +46,12 @@ Plotting Function Reference
 
 .. autofunction:: sympy.plotting.plot_implicit.plot_implicit
 
+PlotGrid Class
+--------------
+
+.. autoclass:: sympy.plotting.plot.PlotGrid
+   :members:
+
 Series Classes
 --------------
 
@@ -81,8 +88,8 @@ Series Classes
 
 
 
-Pyglet Plotting Module
-======================
+Pyglet Plotting
+---------------
 
 .. module:: sympy.plotting.pygletplot
 

doc/src/modules/polys/index.rst

@@ -1,8 +1,8 @@
 .. _polys-docs:
 
-===============================
-Polynomials Manipulation Module
-===============================
+=======================
+Polynomial Manipulation
+=======================
 
 Computations with polynomials are at the core of computer algebra and
 having a fast and robust polynomials manipulation module is a key for

doc/src/modules/printing.rst

@@ -1,7 +1,8 @@
-Printing System
-===============
+========
+Printing
+========
 
-See the :ref:`tutorial-printing` section in Tutorial for introduction into
+See the :ref:`tutorial-printing` section in tutorial for introduction into
 printing.
 
 This guide documents the printing system in SymPy and how it works
@@ -13,8 +14,7 @@ Printer Class
 .. automodule:: sympy.printing.printer
 
 The main class responsible for printing is ``Printer`` (see also its
-`source code
-<https://github.com/sympy/sympy/blob/master/sympy/printing/printer.py>`_):
+`source code <https://github.com/sympy/sympy/blob/master/sympy/printing/printer.py>`_):
 
 .. autoclass:: Printer
     :members: doprint, _print, set_global_settings, order
@@ -185,10 +185,10 @@ An example where line wrapping is required:
 
     >>> expr = sqrt(1-x**2).series(x,n=20).removeO()
     >>> print(fcode(expr))
-          -715.0d0/65536.0d0*x**18 - 429.0d0/32768.0d0*x**16 - 33.0d0/
-         @ 2048.0d0*x**14 - 21.0d0/1024.0d0*x**12 - 7.0d0/256.0d0*x**10 -
-         @ 5.0d0/128.0d0*x**8 - 1.0d0/16.0d0*x**6 - 1.0d0/8.0d0*x**4 - 1.0d0
-         @ /2.0d0*x**2 + 1
+        -715.0d0/65536.0d0*x**18 - 429.0d0/32768.0d0*x**16 - 33.0d0/
+        @ 2048.0d0*x**14 - 21.0d0/1024.0d0*x**12 - 7.0d0/256.0d0*x**10 -
+        @ 5.0d0/128.0d0*x**8 - 1.0d0/16.0d0*x**6 - 1.0d0/8.0d0*x**4 - 1.0d0
+        @ /2.0d0*x**2 + 1
 
 In case of line wrapping, it is handy to include the assignment so that lines
 are wrapped properly when the assignment part is added.
@@ -301,6 +301,20 @@ Mathematica code printing
 
 .. autofunction:: sympy.printing.mathematica.mathematica_code
 
+Maple code printing
+-------------------
+
+.. module:: sympy.printing.maple
+
+.. autoclass:: sympy.printing.maple.MapleCodePrinter
+   :members:
+
+   .. autoattribute:: MapleCodePrinter.printmethod
+
+.. autofunction:: sympy.printing.maple.maple_code
+
+.. autofunction:: sympy.printing.maple.print_maple_code
+
 Javascript Code printing
 ------------------------
 

doc/src/modules/rewriting.rst

@@ -1,4 +1,5 @@
-Term rewriting
+==============
+Term Rewriting
 ==============
 
 Term rewriting is a very general class of functionalities which are used to
@@ -61,7 +62,7 @@ use ``rewrite()`` to do specific type of rewrite::
 Common Subexpression Detection and Collection
 ---------------------------------------------
 
-.. module:: sympy.simplify.cse_main
+.. currentmodule:: sympy.simplify.cse_main
 
 Before evaluating a large expression, it is often useful to identify common
 subexpressions, collect them and evaluate them at once. This is implemented

doc/src/modules/series/index.rst

@@ -1,8 +1,8 @@
 .. _series-docs:
 
-=============
-Series Module
-=============
+======
+Series
+======
 
 The series module implements series expansions as a function and many related
 functions.

doc/src/modules/sets.rst

@@ -1,5 +1,6 @@
+====
 Sets
-===========
+====
 
 .. automodule:: sympy.sets.sets
 
@@ -93,3 +94,27 @@ ComplexRegion
    :members:
 
 .. autofunction:: normalize_theta_set
+
+Iteration over sets
+^^^^^^^^^^^^^^^^^^^
+
+For set unions, `\{a, b\} \cup \{x, y\}` can be treated as
+`\{a, b, x, y\}` for iteration regardless of the distinctiveness of
+the elements, however, for set intersections, assuming that
+`\{a, b\} \cap \{x, y\}` is `\varnothing` or `\{a, b \}` would not
+always be valid, since some of `a`, `b`, `x` or `y` may or may not be
+the elements of the intersection.
+
+Iterating over the elements of a set involving intersection, complement,
+or symmetric difference yields (possibly duplicate) elements of the set
+provided that all elements are known to be the elements of the set.
+If any element cannot be determined to be a member of a set then the
+iteration gives ``TypeError``.
+This happens in the same cases where ``x in y`` would give an error.
+
+There are some reasons to implement like this, even if it breaks the
+consistency with how the python set iterator works.
+We keep in mind that sympy set comprehension like ``FiniteSet(*s)`` from
+a existing sympy sets could be a common usage.
+And this approach would make ``FiniteSet(*s)`` to be consistent with any
+symbolic set processing methods like ``FiniteSet(*simplify(s))``.

doc/src/modules/simplify/hyperexpand.rst

@@ -1,11 +1,12 @@
-Details on the Hypergeometric Function Expansion Module
-#######################################################
+========================
+Hypergeometric Expansion
+========================
 
 This page describes how the function :func:`hyperexpand` and related code
 work. For usage, see the documentation of the symplify module.
 
 Hypergeometric Function Expansion Algorithm
-*******************************************
+===========================================
 
 This section describes the algorithm used to expand hypergeometric functions.
 Most of it is based on the papers [Roach1996]_ and [Roach1997]_.

doc/src/modules/simplify/simplify.rst

@@ -1,5 +1,6 @@
+========
 Simplify
-********
+========
 
 .. currentmodule:: sympy.simplify.simplify
 
@@ -15,6 +16,10 @@ nthroot
 -------
 .. autofunction:: nthroot
 
+kroneckersimp
+-------------
+.. autofunction:: kroneckersimp
+
 besselsimp
 ----------
 .. autofunction:: besselsimp

doc/src/modules/solvers/ode.rst

@@ -64,6 +64,10 @@ the various ODE solving methods. For this reason, they are documented here.
 ^^^^^^^^^^^^^^^^^^^^^^^^^
 .. autofunction:: sympy.solvers.ode.ode_sol_simplicity
 
+:obj:`factorable`
+^^^^^^^^^^^^^^^^^^
+.. autofunction:: sympy.solvers.ode.ode_factorable
+
 :obj:`1st_exact`
 ^^^^^^^^^^^^^^^^
 .. autofunction:: sympy.solvers.ode.ode_1st_exact
@@ -84,6 +88,14 @@ the various ODE solving methods. For this reason, they are documented here.
 ^^^^^^^^^^^^^^^^^
 .. autofunction:: sympy.solvers.ode.ode_1st_linear
 
+:obj:`2nd_linear_airy`
+^^^^^^^^^^^^^^^^^^^^^^
+.. autofunction:: sympy.solvers.ode.ode_2nd_linear_airy
+
+:obj:`2nd_linear_bessel`
+^^^^^^^^^^^^^^^^^^^^^^^^
+.. autofunction:: sympy.solvers.ode.ode_2nd_linear_bessel
+
 :obj:`Bernoulli`
 ^^^^^^^^^^^^^^^^
 .. autofunction:: sympy.solvers.ode.ode_Bernoulli
@@ -112,6 +124,10 @@ the various ODE solving methods. For this reason, they are documented here.
 ^^^^^^^^^^^^^^^^^^^^
 .. autofunction:: sympy.solvers.ode.ode_nth_algebraic
 
+:obj:`nth_order_reducible`
+^^^^^^^^^^^^^^^^^^^^^^^^^^
+.. autofunction:: sympy.solvers.ode.ode_nth_order_reducible
+
 :obj:`separable`
 ^^^^^^^^^^^^^^^^
 .. autofunction:: sympy.solvers.ode.ode_separable

doc/src/modules/solvers/solveset.rst

@@ -524,7 +524,7 @@ How are symbolic parameters handled in solveset?
     >>> not_empty_in(FiniteSet(x/2).intersect(Interval(0, 1)), x)
     Interval(0, 2)
     >>> not_empty_in(FiniteSet(x, x**2).intersect(Interval(1, 2)), x)
-    Union(Interval(-sqrt(2), -1), Interval(1, 2))
+    Union(Interval(1, 2), Interval(-sqrt(2), -1))
 
 
 References

doc/src/modules/stats.rst

@@ -1,5 +1,6 @@
+=====
 Stats
-===========
+=====
 
 .. automodule:: sympy.stats
 
@@ -7,7 +8,7 @@ Random Variable Types
 ^^^^^^^^^^^^^^^^^^^^^
 
 Finite Types
----------------
+------------
 .. autofunction:: DiscreteUniform
 .. autofunction:: Die
 .. autofunction:: Bernoulli
@@ -18,7 +19,7 @@ Finite Types
 .. autofunction:: Rademacher
 
 Discrete Types
------------------
+--------------
 .. autofunction:: Geometric
 .. autofunction:: Poisson
 .. autofunction:: Logarithmic
@@ -27,7 +28,7 @@ Discrete Types
 .. autofunction:: Zeta
 
 Continuous Types
--------------------
+----------------
 
 .. autofunction:: Arcsin
 .. autofunction:: Benini
@@ -45,6 +46,8 @@ Continuous Types
 .. autofunction:: Frechet
 .. autofunction:: Gamma
 .. autofunction:: GammaInverse
+.. autofunction:: Gompertz
+.. autofunction:: Gumbel
 .. autofunction:: Kumaraswamy
 .. autofunction:: Laplace
 .. autofunction:: Logistic
@@ -57,6 +60,8 @@ Continuous Types
 .. autofunction:: RaisedCosine
 .. autofunction:: Rayleigh
 .. autofunction:: StudentT
+.. autofunction:: ShiftedGompertz
+.. autofunction:: Trapezoidal
 .. autofunction:: Triangular
 .. autofunction:: Uniform
 .. autofunction:: UniformSum
@@ -65,6 +70,22 @@ Continuous Types
 .. autofunction:: WignerSemicircle
 .. autofunction:: ContinuousRV
 
+Joint Types
+-----------
+.. autofunction:: JointRV
+.. autofunction:: GeneralizedMultivariateLogGamma
+.. autofunction:: GeneralizedMultivariateLogGammaOmega
+.. autofunction:: Multinomial
+.. autofunction:: MultivariateBeta
+.. autofunction:: MultivariateEwens
+.. autofunction:: MultivariateT
+.. autofunction:: NegativeMultinomial
+.. autofunction:: NormalGamma
+
+Stochastic Processes
+--------------------
+.. autofunction:: DiscreteMarkovChain
+
 Interface
 ^^^^^^^^^
 
@@ -73,6 +94,7 @@ Interface
 .. autofunction:: E
 .. autoclass:: Expectation
 .. autofunction:: density
+.. autofunction:: entropy
 .. autofunction:: given
 .. autofunction:: where
 .. autofunction:: variance

doc/src/modules/tensor/index.rst

@@ -1,8 +1,8 @@
 .. _tensor_module:
 
-=============
-Tensor Module
-=============
+======
+Tensor
+======
 
 .. automodule:: sympy.tensor
 

doc/src/modules/tensor/tensor.rst

@@ -5,25 +5,12 @@ Tensor
 
 .. module:: sympy.tensor.tensor
 
-.. autoclass:: _TensorManager
-   :members:
-
 .. autoclass:: TensorIndexType
    :members:
 
 .. autoclass:: TensorIndex
    :members:
 
-.. autofunction:: tensor_indices
-
-.. autoclass:: TensorSymmetry
-   :members:
-
-.. autofunction:: tensorsymmetry
-
-.. autoclass:: TensorType
-   :members:
-
 .. autoclass:: TensorHead
    :members:
 
@@ -38,8 +25,17 @@ Tensor
 
 .. autofunction:: canon_bp
 
-.. autofunction:: tensor_mul
-
 .. autofunction:: riemann_cyclic_replace
 
 .. autofunction:: riemann_cyclic
+
+.. autoclass:: TensorSymmetry
+   :members:
+
+.. autofunction:: tensorsymmetry
+
+.. autoclass:: TensorType
+   :members:
+
+.. autoclass:: _TensorManager
+   :members:

doc/src/modules/vector/index.rst

@@ -1,6 +1,6 @@
-=============
-Vector Module
-=============
+======
+Vector
+======
 
 The vector module provides tools for basic vector math
 and differential calculus with respect to 3D Cartesian coordinate

doc/src/special_topics/finite_diff_derivatives.rst

@@ -101,7 +101,7 @@ Coefficients of `c_i` evaluated at `x_i + 2*h`:
 	>>> m32 = P(x0+2*h, x0, c, n).diff(c[1])
 	>>> m33 = P(x0+2*h, x0, c, n).diff(c[2])
 
-Matrix of the coeffcients is 3x3 in this case:
+Matrix of the coefficients is 3x3 in this case:
 
 	>>> M = Matrix([[m11, m12, m13], [m21, m22, m23], [m31, m32, m33]])
 
@@ -143,7 +143,7 @@ at `x_i` and thus using points at `x_{i-1}`,  `x_{i}`,  and `x_{i+1}`. So here i
 	>>> m31 = P(x0+h, x0, c, n).diff(c[0])
 	>>> m32 = P(x0+h, x0, c, n).diff(c[1])
 	>>> m33 = P(x0+h, x0, c, n).diff(c[2])
-	>>> # matrix of the coeffcients is 3x3 in this case
+	>>> # matrix of the coefficients is 3x3 in this case
 	>>> M = Matrix([[m11, m12, m13], [m21, m22, m23], [m31, m32, m33]])
 
 Now that we have the matrix of coefficients we next form the right-hand-side and solve by inverting `M`:
@@ -219,7 +219,7 @@ degree polynomial P coefficients of `c_i` evaluated at `x_i, x_{i-1},` and `x_{i
     >>> m32 = P(xN-2*h, xN, c, n).diff(c[1])
     >>> m33 = P(xN-2*h, xN, c, n).diff(c[2])
 
-Next we construct the `3 \times 3` matrix of the coeffcients:
+Next we construct the `3 \times 3` matrix of the coefficients:
 
     >>> M = Matrix([[m11, m12, m13], [m21, m22, m23], [m31, m32, m33]])
     >>> # matrix of the function values...actually a vector of right hand sides
@@ -247,7 +247,8 @@ Also,  we note that output of formats appropriate to Fortran,  C,  etc. may be d
 given above.
 
 Next we show how to perform these and many other discritizations of derivatives,  but using a
-much more efficient approach originally due to Bengt Fornberg and now incorported into SymPy.
-
+much more efficient approach originally due to Bengt Fornberg and now incorporated into SymPy.
 
+:ref:`calculus-finite-differences`
 
+:ref:`Finite difference weights <finite_diff>`

doc/src/tutorial/calculus.rst

@@ -196,11 +196,11 @@ definite integrals.  Here is a sampling of some of the power of ``integrate``.
     ⎮ sin⎝x ⎠ dx
     ⌡
     >>> integ.doit()
-                    ⎛√2⋅x⎞
-    3⋅√2⋅√π⋅fresnels⎜────⎟⋅Γ(3/4)
-                    ⎝ √π ⎠
-    ─────────────────────────────
-               8⋅Γ(7/4)
+             ⎛√2⋅x⎞
+    3⋅√2⋅√π⋅S⎜────⎟⋅Γ(3/4)
+             ⎝ √π ⎠
+    ──────────────────────
+           8⋅Γ(7/4)
 
     >>> integ = Integral(x**y*exp(-x), (x, 0, oo))
     >>> integ
@@ -322,6 +322,8 @@ The ``O`` notation supports arbitrary limit points (other than 0):
     -5 + ──────── + ──────── + ──────── + ──────── + x + O⎝(x - 6) ; x → 6⎠
             2          6          24        120
 
+.. _calculus-finite-differences:
+
 Finite differences
 ==================
 

doc/src/tutorial/manipulation.rst

@@ -30,37 +30,38 @@ expression looks like internally by using ``srepr``
 The easiest way to tear this apart is to look at a diagram of the expression
 tree:
 
-.. This comes from dotprint(2**x + x*y, labelfunc=srepr)
+.. This comes from dotprint(x**2 + x*y, labelfunc=srepr)
 
 .. graphviz::
 
     digraph{
 
     # Graph style
+    "ordering"="out"
     "rankdir"="TD"
 
     #########
     # Nodes #
     #########
 
-    "Symbol(x)_(0, 0)" ["color"="black", "label"="Symbol('x')", "shape"="ellipse"];
-    "Integer(2)_(1, 1)" ["color"="black", "label"="Integer(2)", "shape"="ellipse"];
-    "Symbol(y)_(0, 1)" ["color"="black", "label"="Symbol('y')", "shape"="ellipse"];
-    "Symbol(x)_(1, 0)" ["color"="black", "label"="Symbol('x')", "shape"="ellipse"];
-    "Mul(Symbol(x), Symbol(y))_(0,)" ["color"="black", "label"="Mul", "shape"="ellipse"];
-    "Pow(Symbol(x), Integer(2))_(1,)" ["color"="black", "label"="Pow", "shape"="ellipse"];
-    "Add(Mul(Symbol(x), Symbol(y)), Pow(Symbol(x), Integer(2)))_()" ["color"="black", "label"="Add", "shape"="ellipse"];
+    "Add(Pow(Symbol('x'), Integer(2)), Mul(Symbol('x'), Symbol('y')))_()" ["color"="black", "label"="Add", "shape"="ellipse"];
+    "Pow(Symbol('x'), Integer(2))_(0,)" ["color"="black", "label"="Pow", "shape"="ellipse"];
+    "Symbol('x')_(0, 0)" ["color"="black", "label"="Symbol('x')", "shape"="ellipse"];
+    "Integer(2)_(0, 1)" ["color"="black", "label"="Integer(2)", "shape"="ellipse"];
+    "Mul(Symbol('x'), Symbol('y'))_(1,)" ["color"="black", "label"="Mul", "shape"="ellipse"];
+    "Symbol('x')_(1, 0)" ["color"="black", "label"="Symbol('x')", "shape"="ellipse"];
+    "Symbol('y')_(1, 1)" ["color"="black", "label"="Symbol('y')", "shape"="ellipse"];
 
     #########
     # Edges #
     #########
 
-    "Mul(Symbol(x), Symbol(y))_(0,)" -> "Symbol(x)_(0, 0)";
-    "Mul(Symbol(x), Symbol(y))_(0,)" -> "Symbol(y)_(0, 1)";
-    "Pow(Symbol(x), Integer(2))_(1,)" -> "Symbol(x)_(1, 0)";
-    "Pow(Symbol(x), Integer(2))_(1,)" -> "Integer(2)_(1, 1)";
-    "Add(Mul(Symbol(x), Symbol(y)), Pow(Symbol(x), Integer(2)))_()" -> "Mul(Symbol(x), Symbol(y))_(0,)";
-    "Add(Mul(Symbol(x), Symbol(y)), Pow(Symbol(x), Integer(2)))_()" -> "Pow(Symbol(x), Integer(2))_(1,)";
+    "Add(Pow(Symbol('x'), Integer(2)), Mul(Symbol('x'), Symbol('y')))_()" -> "Pow(Symbol('x'), Integer(2))_(0,)";
+    "Add(Pow(Symbol('x'), Integer(2)), Mul(Symbol('x'), Symbol('y')))_()" -> "Mul(Symbol('x'), Symbol('y'))_(1,)";
+    "Pow(Symbol('x'), Integer(2))_(0,)" -> "Symbol('x')_(0, 0)";
+    "Pow(Symbol('x'), Integer(2))_(0,)" -> "Integer(2)_(0, 1)";
+    "Mul(Symbol('x'), Symbol('y'))_(1,)" -> "Symbol('x')_(1, 0)";
+    "Mul(Symbol('x'), Symbol('y'))_(1,)" -> "Symbol('y')_(1, 1)";
     }
 
 .. note::
@@ -82,16 +83,16 @@ expression, 2, we got ``Integer(2)``.  ``Integer`` is the SymPy class for
 integers.  It is similar to the Python built-in type ``int``, except that
 ``Integer`` plays nicely with other SymPy types.
 
-When we write ``2**x``, this creates a ``Pow`` object.  ``Pow`` is short for
+When we write ``x**2``, this creates a ``Pow`` object.  ``Pow`` is short for
 "power".
 
-    >>> srepr(2**x)
-    "Pow(Integer(2), Symbol('x'))"
+    >>> srepr(x**2)
+    "Pow(Symbol('x'), Integer(2))"
 
-We could have created the same object by calling ``Pow(2, x)``
+We could have created the same object by calling ``Pow(x, 2)``
 
-    >>> Pow(2, x)
-    2**x
+    >>> Pow(x, 2)
+    x**2
 
 Note that in the ``srepr`` output, we see ``Integer(2)``, the SymPy version of
 integers, even though technically, we input ``2``, a Python int.  In general,
@@ -104,7 +105,7 @@ function that does this is ``sympify`` [#sympify-fn]_.
     >>> type(sympify(2))
     <class 'sympy.core.numbers.Integer'>
 
-We have seen that ``2**x`` is represented as ``Pow(2, x)``.  What about
+We have seen that ``x**2`` is represented as ``Pow(x, 2)``.  What about
 ``x*y``?  As we might expect, this is the multiplication of ``x`` and ``y``.
 The SymPy class for multiplication is ``Mul``.
 
@@ -116,13 +117,13 @@ Thus, we could have created the same object by writing ``Mul(x, y)``.
     >>> Mul(x, y)
     x*y
 
-Now we get to our final expression, ``2**x + x*y``.  This is the addition of
-our last two objects, ``Pow(2, x)``, and ``Mul(x, y)``.  The SymPy class for
+Now we get to our final expression, ``x**2 + x*y``.  This is the addition of
+our last two objects, ``Pow(x, 2)``, and ``Mul(x, y)``.  The SymPy class for
 addition is ``Add``, so, as you might expect, to create this object, we use
-``Add(Pow(2, x), Mul(x, y))``.
+``Add(Pow(x, 2), Mul(x, y))``.
 
-    >>> Add(Pow(2, x), Mul(x, y))
-    2**x + x*y
+    >>> Add(Pow(x, 2), Mul(x, y))
+    x**2 + x*y
 
 SymPy expression trees can have many branches, and can be quite deep or quite
 broad.  Here is a more complicated example

doc/src/tutorial/matrices.rst

@@ -151,7 +151,7 @@ raise it to the ``-1`` power.
     >>> N**-1
     Traceback (most recent call last):
     ...
-    ValueError: Matrix det == 0; not invertible.
+    NonInvertibleMatrixError: Matrix det == 0; not invertible.
 
 To take the transpose of a Matrix, use ``T``.
 
@@ -427,7 +427,7 @@ guaranteed to be accurate in some limited domain of numerics and symbols,
 and any complicated expressions beyond its decidability are treated as ``None``,
 which behaves similarly to logical ``False``.
 
-The list of methods using zero testing procedures are as followings.
+The list of methods using zero testing procedures are as follows:
 
 ``echelon_form`` , ``is_echelon`` , ``rank`` , ``rref`` , ``nullspace`` ,
 ``eigenvects`` , ``inverse_ADJ`` , ``inverse_GE`` , ``inverse_LU`` ,

doc/src/tutorial/printing.rst

@@ -221,6 +221,7 @@ imported from ``sympy.printing.mathml``.
 ``print_mathml()`` prints the output.  If you want the string, use the
 function ``mathml()``.
 
+
 Dot
 ---
 
@@ -229,27 +230,33 @@ format, which can be rendered with Graphviz.  See the
 :ref:`tutorial-manipulation` section for some examples of the output of this
 printer.
 
+Here is an example of the raw output of the ``dotprint()`` function
+
     >>> from sympy.printing.dot import dotprint
     >>> from sympy.abc import x
-    >>> print(dotprint(x+2)) 
+    >>> print(dotprint(x+2))
     digraph{
+    <BLANKLINE>
     # Graph style
     "ordering"="out"
     "rankdir"="TD"
+    <BLANKLINE>
     #########
     # Nodes #
     #########
-    "Add(Integer(2), Symbol(x))_()" ["color"="black", "label"="Add", "shape"="ellipse"];
+    <BLANKLINE>
+    "Add(Integer(2), Symbol('x'))_()" ["color"="black", "label"="Add", "shape"="ellipse"];
     "Integer(2)_(0,)" ["color"="black", "label"="2", "shape"="ellipse"];
-    "Symbol(x)_(1,)" ["color"="black", "label"="x", "shape"="ellipse"];
+    "Symbol('x')_(1,)" ["color"="black", "label"="x", "shape"="ellipse"];
+    <BLANKLINE>
     #########
     # Edges #
     #########
-    "Add(Integer(2), Symbol(x))_()" -> "Integer(2)_(0,)";
-    "Add(Integer(2), Symbol(x))_()" -> "Symbol(x)_(1,)";
+    <BLANKLINE>
+    "Add(Integer(2), Symbol('x'))_()" -> "Integer(2)_(0,)";
+    "Add(Integer(2), Symbol('x'))_()" -> "Symbol('x')_(1,)";
     }
 
-
 .. rubric:: Footnotes
 
 .. [#srepr-fn] SymPy does not use the Python builtin ``repr()`` function for

doc/src/tutorial/solvers.rst

@@ -110,7 +110,7 @@ In the ``solveset`` module, the non linear system of equations is solved using
 	>>> nonlinsolve([x**2 + 1, y**2 + 1], [x, y])
 	{(-ⅈ, -ⅈ), (-ⅈ, ⅈ), (ⅈ, -ⅈ), (ⅈ, ⅈ)}
 
-3. When both real and complex solution is present:
+3. When both real and complex solution are present:
 
 	>>> from sympy import sqrt
 	>>> system = [x**2 - 2*y**2 -2, x*y - 2]
@@ -118,17 +118,11 @@ In the ``solveset`` module, the non linear system of equations is solved using
 	>>> nonlinsolve(system, vars)
 	{(-2, -1), (2, 1), (-√2⋅ⅈ, √2⋅ⅈ), (√2⋅ⅈ, -√2⋅ⅈ)}
 
-	>>> n = Dummy('n')
 	>>> system = [exp(x) - sin(y), 1/y - 3]
-	>>> real_soln = (log(sin(S(1)/3)), S(1)/3)
-	>>> img_lamda = Lambda(n, 2*n*I*pi + Mod(log(sin(S(1)/3)), 2*I*pi))
-	>>> complex_soln = (ImageSet(img_lamda, S.Integers), S(1)/3)
-	>>> soln = FiniteSet(real_soln, complex_soln)
-	>>> nonlinsolve(system, [x, y]) == soln
-	True
+	>>> nonlinsolve(system, vars)
+	{({2⋅n⋅ⅈ⋅π + log(sin(1/3)) | n ∊ ℤ}, 1/3)}
 
-4. If non linear system of equations is Positive dimensional system (A system with
-infinitely many solutions is said to be positive-dimensional):
+4. When the system is positive-dimensional system (has infinitely many solutions):
 
 	>>> nonlinsolve([x*y, x*y - x], [x, y])
 	{(0, y)}
@@ -148,14 +142,14 @@ infinitely many solutions is said to be positive-dimensional):
    ``solve`` can be used for such cases:
 
    >>> solve([x**2 - y**2/exp(x)], [x, y], dict=True)
-   ⎡⎧             ⎛y⎞⎫⎤
-   ⎢⎨x: 2⋅LambertW⎜─⎟⎬⎥
-   ⎣⎩             ⎝2⎠⎭⎦
+   ⎡⎧      ⎛-y ⎞⎫  ⎧      ⎛y⎞⎫⎤
+   ⎢⎨x: 2⋅W⎜───⎟⎬, ⎨x: 2⋅W⎜─⎟⎬⎥
+   ⎣⎩      ⎝ 2 ⎠⎭  ⎩      ⎝2⎠⎭⎦
 
    3. Currently ``nonlinsolve`` is not properly capable of solving the system of equations
    having trigonometric functions.
 
-   ``solve`` can be used for such cases(not all solution):
+   ``solve`` can be used for such cases (but does not give all solution):
 
    >>> solve([sin(x + y), cos(x - y)], [x, y])
    ⎡⎛-3⋅π   3⋅π⎞  ⎛-π   π⎞  ⎛π  3⋅π⎞  ⎛3⋅π  π⎞⎤
@@ -185,7 +179,7 @@ multiplicity 1 and ``3`` is a root of multiplicity 2.
    ``solve`` can be used for such cases:
 
    >>> solve(x*exp(x) - 1, x )
-   [LambertW(1)]
+   [W(1)]
 
 
 .. _tutorial-dsolve:

examples/advanced/autowrap_ufuncify.py

@@ -30,7 +30,6 @@ if not plt:
 
 import mpmath
 from sympy.utilities.autowrap import ufuncify
-from sympy.utilities.lambdify import implemented_function
 from sympy import symbols, legendre, pprint
 
 

examples/advanced/dense_coding_example.py

@@ -2,11 +2,9 @@
 
 """Demonstration of quantum dense coding."""
 
-from sympy import sqrt, pprint
+from sympy import pprint
 from sympy.physics.quantum import qapply
 from sympy.physics.quantum.gate import H, X, Z, CNOT
-from sympy.physics.quantum.qubit import Qubit
-from sympy.physics.quantum.circuitplot import circuit_plot
 from sympy.physics.quantum.grover import superposition_basis
 
 

examples/advanced/fem.py

@@ -15,7 +15,7 @@ $ python fem.py
 
 """
 
-from sympy import symbols, Symbol, factorial, Rational, zeros, div, eye, \
+from sympy import symbols, Symbol, factorial, Rational, zeros, eye, \
     integrate, diff, pprint, reduced
 
 x, y, z = symbols('x,y,z')

examples/advanced/pidigits.py

@@ -7,10 +7,9 @@ computation of the digits of pi.
 """
 
 from mpmath import libmp, pi
-from mpmath import functions as mpf_funs
 
 import math
-from time import clock
+from sympy.core.compatibility import clock
 import sys
 
 
@@ -70,9 +69,9 @@ def calculateit(func, base, n, tofile):
 def interactive():
     """Simple function to interact with user"""
     print("Compute digits of pi with SymPy\n")
-    base = input("Which base? (2-36, 10 for decimal) \n> ")
-    digits = input("How many digits? (enter a big number, say, 10000)\n> ")
-    tofile = raw_input("Output to file? (enter a filename, or just press enter\nto print directly to the screen) \n> ")
+    base = int(input("Which base? (2-36, 10 for decimal) \n> "))
+    digits = int(input("How many digits? (enter a big number, say, 10000)\n> "))
+    tofile = input("Output to file? (enter a filename, or just press enter\nto print directly to the screen) \n> ")
     if tofile:
         tofile = open(tofile, "w")
     calculateit(pi, base, digits, tofile)

examples/advanced/pyglet_plotting.py

@@ -3,16 +3,15 @@
 """
 Plotting Examples
 
-Suggested Usage:    python -i plotting.py
+Suggested Usage:    python -i pyglet_plotting.py
 """
 
 
-from sympy import symbols
+from sympy import symbols, sin, cos, pi, sqrt
+from sympy.core.compatibility import range, clock
 from sympy.plotting.pygletplot import PygletPlot
-from sympy import sin, cos, pi, sqrt, exp
-from sympy.core.compatibility import range
 
-from time import sleep, clock
+from time import sleep
 
 
 def main():

examples/advanced/qft.py

@@ -15,8 +15,8 @@ SymPy, but that's a long journey.
 
 """
 
-from sympy import Basic, exp, Symbol, sin, Rational, I, Mul, Matrix, \
-    ones, sqrt, pprint, simplify, Eq, sympify
+from sympy import Basic, Symbol, Matrix, \
+    ones, sqrt, pprint, Eq, sympify
 
 from sympy.physics import msigma, mgamma
 

examples/advanced/relativity.py

@@ -13,8 +13,8 @@ something is not clear, like what the Ricci tensor is, etc.
 
 """
 
-from sympy import (exp, Symbol, sin, Rational, Derivative, dsolve, Function,
-                  Matrix, Eq, pprint, Pow, classify_ode, solve)
+from sympy import (exp, Symbol, sin, dsolve, Function,
+                  Matrix, Eq, pprint, solve)
 
 
 def grad(f, X):

examples/beginner/limits_examples.py

@@ -23,7 +23,7 @@ def main():
 
     show( limit(x*(sqrt(x**2 + 1) - x), x, oo), Rational(1)/2 )
 
-    show( limit(x - sqrt(x**3 - 1), x, oo), Rational(0) )
+    show( limit(x - sqrt3(x**3 - 1), x, oo), Rational(0) )
 
     show( limit(log(1 + exp(x))/x, x, -oo), Rational(0) )
 

examples/intermediate/coupled_cluster.py

@@ -12,7 +12,7 @@ from sympy.physics.secondquant import (AntiSymmetricTensor, wicks,
         F, Fd, NO, evaluate_deltas, substitute_dummies, Commutator,
         simplify_index_permutations, PermutationOperator)
 from sympy import (
-    symbols, expand, pprint, Rational, latex, Dummy
+    symbols, Rational, latex, Dummy
 )
 
 pretty_dummies_dict = {

examples/intermediate/mplot2d.py

@@ -9,7 +9,7 @@ import sys
 
 from sample import sample
 
-from sympy import log, pi, sqrt, sin, Symbol
+from sympy import sqrt, Symbol
 from sympy.core.compatibility import is_sequence
 from sympy.external import import_module
 

examples/intermediate/mplot3d.py

@@ -9,7 +9,7 @@ import sys
 
 from sample import sample
 
-from sympy import sin, Symbol
+from sympy import Symbol
 from sympy.external import import_module
 
 

examples/intermediate/partial_differential_eqs.py

@@ -5,7 +5,7 @@
 Demonstrates various ways to solve partial differential equations
 """
 
-from sympy import symbols, Eq, Function, pde_separate, pprint, sin, cos, latex
+from sympy import symbols, Eq, Function, pde_separate, pprint, sin, cos
 from sympy import Derivative as D
 
 
@@ -20,7 +20,7 @@ def main():
     eq = Eq(D(Xi(r, phi, theta), r, 2) + 2/r * D(Xi(r, phi, theta), r) +
             1/(r**2 * sin(phi)**2) * D(Xi(r, phi, theta), theta, 2) +
             cos(phi)/(r**2 * sin(phi)) * D(Xi(r, phi, theta), phi) +
-            1/r**2 * D(Xi(r, phi, theta), phi, 2))
+            1/r**2 * D(Xi(r, phi, theta), phi, 2), 0)
     pprint(eq)
 
     pprint("We can either separate this equation in regards with variable r:")

examples/intermediate/sample.py

@@ -21,7 +21,7 @@ def sample2d(f, x_args):
     try:
         f = sympify(f)
     except SympifyError:
-        raise ValueError("f could not be interpretted as a SymPy function")
+        raise ValueError("f could not be interpreted as a SymPy function")
     try:
         x, x_min, x_max, x_n = x_args
     except (TypeError, IndexError):

examples/intermediate/vandermonde.py

@@ -6,7 +6,7 @@ Demonstrates matrix computations using the Vandermonde matrix.
   * https://en.wikipedia.org/wiki/Vandermonde_matrix
 """
 
-from sympy import Matrix, pprint, Rational, sqrt, symbols, Symbol, zeros
+from sympy import Matrix, pprint, Rational, symbols, Symbol, zeros
 from sympy.core.compatibility import range
 
 

examples/notebooks/Macaulay_resultant.ipynb

@@ -44,7 +44,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "There are a number of steps needed to contruct matrix $A$. Let us consider an example from https://dl.acm.org/citation.cfm?id=550525 to \n",
+    "There are a number of steps needed to construct matrix $A$. Let us consider an example from https://dl.acm.org/citation.cfm?id=550525 to \n",
     "show the construction."
    ]
   },

examples/notebooks/Sylvester_resultant.ipynb

@@ -68,7 +68,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "From the definition, it is clear that the resultant will equal zero if and only if $p$ and $q$ have at least one common root. Thus, the resultant becomes very usefull in identifying whether common roots exist. "
+    "From the definition, it is clear that the resultant will equal zero if and only if $p$ and $q$ have at least one common root. Thus, the resultant becomes very useful in identifying whether common roots exist. "
    ]
   },
   {

release/Dockerfile

@@ -3,7 +3,7 @@ FROM continuumio/anaconda3
 WORKDIR /root
 
 RUN apt-get update \
-    && apt-get install -y libc6-i386 libc6 linux-headers-amd64 git make zip graphviz inkscape texlive-xetex texlive-fonts-recommended texlive-latex-extra librsvg2-bin docbook2x latexmk \
+    && apt-get install -y libc6-i386 libc6 linux-headers-amd64 git make zip graphviz inkscape texlive-xetex texlive-fonts-recommended texlive-latex-extra librsvg2-bin docbook2x latexmk libatlas-dev libatlas-base-dev liblapack-dev gfortran gcc \
     && apt-get -y clean
 
 RUN conda config --add channels conda-forge

release/README.md

@@ -24,6 +24,12 @@ First, make sure that you have done the following things
 - Push the release branch up to origin, and make a pull request for it against
   master.
 
+- Create the release notes page for the new release on the wiki. See
+  https://github.com/sympy/sympy-bot/issues/26. The easiest way to do this is
+  to copy the old release notes to a new page and remove all the changes, and
+  update the version number. The formatting on the release notes page is
+  important as otherwise the bot will fail, so it is best to do it this way.
+
 It is important to create a new branch because that lets master continue as
 normal. The release script will automatically checkout the release branch from
 origin, which is why you need to push it (it determines what the release
@@ -54,9 +60,9 @@ script can take about an hour or so to run (depending on how long the tests
 take). Every time you re-run the script, it pulls from the branch and runs
 everything from scratch.
 
-At the end it will print two things, the list of authors, and the md5 sums.
+At the end it will print two things, the list of authors, and the sha256 sums.
 Copy the list of authors into the release notes. You should verify that the
-md5 sums of the release files are the same as what are printed.
+sha256 sums of the release files are the same as what are printed.
 
 # Tagging the release
 
@@ -138,3 +144,9 @@ Once you have it working, push the changes up to Dockerhub
     docker push sympy/sympy-release
 
 You'll need access to the sympy org, ask Aaron or Ondřej if you need it.
+
+It is usually not necessary to rebuild the Docker container. The container
+first pulls the latest version of the release branch before running rever
+(see `pull_and_run_rever.sh`), so unless you modify that script, or change the
+packages that are installed in the container, it should not be necessary to
+rebuild it.

release/rever.xsh

@@ -33,16 +33,20 @@ $ACTIVITIES = [
     'mailmap_update',
     'test_sympy',
     'source_tarball',
+    'wheel',
     'build_docs',
     'copy_release_files',
     'compare_tar_against_git',
     'test_tarball27',
-    'test_tarball34',
     'test_tarball35',
     'test_tarball36',
     'test_tarball37',
+    'test_wheel27',
+    'test_wheel35',
+    'test_wheel36',
+    'test_wheel37',
     'print_authors',
-    'md5',
+    'sha256',
     # 'tag',
 ]
 
@@ -70,8 +74,8 @@ def mailmap_update():
 @activity
 def test_sympy():
     with run_in_conda_env(['mpmath', 'matplotlib>=2.2', 'numpy', 'scipy', 'theano',
-        'ipython', 'gmpy2', 'fastcache', 'symengine', 'libgfortran', 'libgcc',
-        'gcc', 'cython', 'tensorflow', 'llvmlite', 'wurlitzer', 'autowrap',
+        'ipython', 'gmpy2', 'fastcache', 'symengine', 'libgfortran', 'cython',
+        'tensorflow', 'llvmlite', 'wurlitzer', 'autowrap',
         'python-symengine=0.3.*', 'numexpr', 'antlr-python-runtime>=4.7,<4.8',
         'antlr>=4.7,<4.8'], 'sympy-tests'):
 
@@ -83,9 +87,16 @@ def source_tarball():
         # Assumes this is run in Docker and git is already clean
         ./setup.py sdist --keep-temp
 
+
+@activity(deps={'_version', 'mailmap_update', 'test_sympy'})
+def wheel():
+    with run_in_conda_env(['mpmath', 'python=3.6', 'setuptools', 'pip', 'wheel'], 'sympy-release'):
+        # Assumes this is run in Docker and git is already clean
+        ./setup.py bdist_wheel --universal --keep-temp
+
 @activity(deps={'_version'})
 def build_docs():
-    with run_in_conda_env(['sphinx', 'docutils', 'numpy', 'mpmath'],
+    with run_in_conda_env(['sphinx', 'docutils', 'numpy', 'mpmath', 'matplotlib'],
         envname='sympy-release-docs'):
 
         cd doc
@@ -108,7 +119,7 @@ def build_docs():
         cd ../../../
 
 
-@activity(deps={'source_tarball', 'build_docs'})
+@activity(deps={'source_tarball', 'wheel', 'build_docs'})
 def copy_release_files():
     ls dist
     cp dist/* /root/release/
@@ -117,10 +128,6 @@ def copy_release_files():
 def test_tarball27():
     test_tarball('2.7')
 
-@activity(deps={'source_tarball'})
-def test_tarball34():
-    test_tarball('3.4')
-
 @activity(deps={'source_tarball'})
 def test_tarball35():
     test_tarball('3.5')
@@ -133,6 +140,22 @@ def test_tarball36():
 def test_tarball37():
     test_tarball('3.7')
 
+@activity(deps={'wheel'})
+def test_wheel27():
+    test_wheel('2.7')
+
+@activity(deps={'wheel'})
+def test_wheel35():
+    test_wheel('3.5')
+
+@activity(deps={'wheel'})
+def test_wheel36():
+    test_wheel('3.6')
+
+@activity(deps={'wheel'})
+def test_wheel37():
+    test_wheel('3.7')
+
 @activity(deps={'source_tarball'})
 def compare_tar_against_git():
     """
@@ -176,7 +199,7 @@ def compare_tar_against_git():
     if fail:
         sys.exit(red("Non-whitelisted files found or not found in the tarball"))
 
-@activity(deps={'source_tarball'})
+@activity(deps={'source_tarball', 'wheel'})
 def print_authors():
     """
     Print authors text to put at the bottom of the release notes
@@ -200,18 +223,18 @@ Thanks to everyone who contributed to this release!
         print("- " + name)
     print()
 
-@activity(deps={'source_tarball', 'build_docs'})
-def md5():
+@activity(deps={'source_tarball', 'wheel', 'build_docs'})
+def sha256():
     """
-    Print the md5 sums of the release files
+    Print the sha256 sums of the release files
     """
-    _md5(print_=True)
+    _sha256(print_=True)
 
-def _md5(print_=True, local=False):
+def _sha256(print_=True, local=False):
     if local:
-        out = $(md5sum @(release_files()))
+        out = $(shasum -a 256 @(release_files()))
     else:
-        out = $(md5sum /root/release/*)
+        out = $(shasum -a 256 /root/release/*)
     # Remove the release/ part for printing. Useful for copy-pasting into the
     # release notes.
     out = [i.split() for i in out.strip().split('\n')]
@@ -220,7 +243,12 @@ def _md5(print_=True, local=False):
         print(out)
     return out
 
-@activity(deps={'mailmap_update', 'md5', 'print_authors', 'source_tarball', 'build_docs', 'compare_tar_against_git', 'test_tarball27', 'test_tarball34', 'test_tarball35', 'test_tarball36', 'test_sympy'})
+@activity(deps={'mailmap_update', 'sha256', 'print_authors',
+                'source_tarball', 'wheel', 'build_docs',
+                'compare_tar_against_git', 'test_tarball27',
+                'test_tarball35', 'test_tarball36', 'test_wheel27',
+                'test_wheel35', 'test_wheel36',
+                'test_wheel37', 'test_sympy'})
 def release():
     pass
 
@@ -254,16 +282,32 @@ def test_tarball(py_version):
     Test that the tarball can be unpacked and installed, and that sympy
     imports in the install.
     """
+    if py_version not in {'2.7', '3.5', '3.6', '3.7'}: # TODO: Add win32
+        raise ValueError("release must be one of 2.7, 3.5, 3.6, or 3.7 not %s" % py_version)
+
+
+    with run_in_conda_env(['python=%s' % py_version], 'test-install-%s' % py_version):
+        cp @('/root/release/{source}'.format(**tarball_format)) @("releasetar.tar.gz".format(**tarball_format))
+        tar xvf releasetar.tar.gz
+
+        cd @("{source-orig-notar}".format(**tarball_format))
+        python setup.py install
+        python -c "import sympy; print(sympy.__version__); print('sympy installed successfully')"
+        python -m isympy --help
+        isympy --help
+
+def test_wheel(py_version):
+    """
+    Test that the wheel can be installed, and that sympy imports in the install.
+    """
     if py_version not in {'2.7', '3.4', '3.5', '3.6', '3.7'}: # TODO: Add win32
         raise ValueError("release must be one of 2.7, 3.4, 3.5, 3.6, or 3.7 not %s" % py_version)
 
 
     with run_in_conda_env(['python=%s' % py_version], 'test-install-%s' % py_version):
-        cp @('/root/release/{source}'.format(**tarball_format)) @("releasetar.tar".format(**tarball_format))
-        tar xvf releasetar.tar
+        cp @('/root/release/{wheel}'.format(**tarball_format)) @("{wheel}".format(**tarball_format))
+        pip install @("{wheel}".format(**tarball_format))
 
-        cd @("/root/{source-orig-notar}".format(**tarball_format))
-        python setup.py install
         python -c "import sympy; print(sympy.__version__); print('sympy installed successfully')"
         python -m isympy --help
         isympy --help
@@ -277,6 +321,7 @@ def get_tarball_name(file):
     source-orig:       The original name of the source tarball
     source-orig-notar: The name of the untarred directory
     source:            The source tarball (after renaming)
+    wheel:             The wheel
     html:              The name of the html zip
     html-nozip:        The name of the html, without ".zip"
     pdf-orig:          The original name of the pdf file
@@ -298,6 +343,8 @@ def get_tarball_name(file):
             name += ".{extension}"
     elif file == 'pdf-orig':
         name = "sympy-{version}.pdf"
+    elif file == 'wheel':
+        name = 'sympy-{version}-py2.py3-none-any.whl'
     else:
         raise ValueError(file + " is not a recognized argument")
 
@@ -309,6 +356,7 @@ tarball_name_types = {
     'source-orig',
     'source-orig-notar',
     'source',
+    'wheel',
     'html',
     'html-nozip',
     'pdf-orig',
@@ -541,7 +589,7 @@ def _GitHub_release(username=None, user='sympy', token=None,
 
         print(green("Done"))
 
-    # TODO: download the files and check that they have the right md5 sum
+    # TODO: download the files and check that they have the right sha256 sum
 
 def _size(print_=True):
     """
@@ -565,8 +613,8 @@ def table():
 
     tarball_formatter_dict['version'] = shortversion
 
-    md5s = [i.split('\t') for i in _md5(print_=False, local=True).split('\n')]
-    md5s_dict = {name: md5 for md5, name in md5s}
+    sha256s = [i.split('\t') for i in _sha256(print_=False, local=True).split('\n')]
+    sha256s_dict = {name: sha256 for sha256, name in sha256s}
 
     sizes = [i.split('\t') for i in _size(print_=False).split('\n')]
     sizes_dict = {name: size for size, name in sizes}
@@ -589,7 +637,7 @@ def table():
 
     with tag('table'):
         with tag('tr'):
-            for headname in ["Filename", "Description", "size", "md5"]:
+            for headname in ["Filename", "Description", "size", "sha256"]:
                 with tag("th"):
                     table.append(headname)
 
@@ -605,7 +653,7 @@ def table():
                 with tag('td'):
                     table.append(sizes_dict[name])
                 with tag('td'):
-                    table.append(md5s_dict[name])
+                    table.append(sha256s_dict[name])
 
     out = ' '.join(table)
     return out
@@ -622,7 +670,7 @@ See https://github.com/sympy/sympy/wiki/release-notes-for-{shortversion} for the
 {htmltable}
 
 **Note**: Do not download the **Source code (zip)** or the **Source code (tar.gz)**
-files above.
+files below.
 """
     out = out.format(shortversion=shortversion, htmltable=htmltable)
     print(blue("Here are the release notes to copy into the GitHub release "
@@ -829,6 +877,7 @@ def check_tag_exists():
 
 descriptions = OrderedDict([
     ('source', "The SymPy source installer.",),
+    ('wheel', "A wheel of the package.",),
     ('html', '''Html documentation. This is the same as
 the <a href="https://docs.sympy.org/latest/index.html">online documentation</a>.''',),
     ('pdf', '''Pdf version of the <a href="https://docs.sympy.org/latest/index.html"> html documentation</a>.''',),
@@ -980,13 +1029,16 @@ git_whitelist = {
     '.gitattributes',
     '.gitignore',
     '.mailmap',
-    # Travis
+    # Travis and CI
     '.travis.yml',
     '.ci/durations.json',
     '.ci/generate_durations_log.sh',
     '.ci/parse_durations_log.py',
     '.ci/blacklisted.json',
     '.editorconfig',
+    '.coveragerc',
+    'codecov.yml',
+    'pytest.ini',
     # Code of conduct
     'CODE_OF_CONDUCT.md',
     # Pull request template
@@ -1058,8 +1110,6 @@ git_whitelist = {
     # This is just a distribute version of setup.py. Used mainly for setup.py
     # develop, which we don't care about in the release tarball
     'setupegg.py',
-    # Example on how to use tox to test Sympy. For development.
-    'tox.ini.sample',
     # pytest stuff
     'conftest.py',
     # Encrypted deploy key for deploying dev docs to GitHub

setup.py

@@ -33,8 +33,12 @@ import sys
 import os
 import shutil
 import glob
+import subprocess
 
-mpmath_version = '0.19'
+from distutils.command.sdist import sdist
+
+
+min_mpmath_version = '0.19'
 
 # This directory
 dir_setup = os.path.dirname(os.path.realpath(__file__))
@@ -58,11 +62,11 @@ except ImportError:
     from distutils.version import LooseVersion
     try:
         import mpmath
-        if mpmath.__version__ < LooseVersion(mpmath_version):
+        if mpmath.__version__ < LooseVersion(min_mpmath_version):
             raise ImportError
     except ImportError:
         print("Please install the mpmath package with a version >= %s"
-              % mpmath_version)
+              % min_mpmath_version)
         sys.exit(-1)
 
 PY3 = sys.version_info[0] > 2
@@ -122,6 +126,8 @@ modules = [
     'sympy.parsing.autolev._antlr',
     'sympy.parsing.autolev.test-examples',
     'sympy.parsing.autolev.test-examples.pydy-example-repo',
+    'sympy.parsing.c',
+    'sympy.parsing.fortran',
     'sympy.parsing.latex',
     'sympy.parsing.latex._antlr',
     'sympy.physics',
@@ -304,6 +310,37 @@ class antlr(Command):
             sys.exit(-1)
 
 
+class sdist_sympy(sdist):
+    def run(self):
+        # Fetch git commit hash and write down to commit_hash.txt before
+        # shipped in tarball.
+        commit_hash = None
+        commit_hash_filepath = 'doc/commit_hash.txt'
+        try:
+            commit_hash = \
+                subprocess.check_output(['git', 'rev-parse', 'HEAD'])
+            commit_hash = commit_hash.decode('ascii')
+            commit_hash = commit_hash.rstrip()
+            print('Commit hash found : {}.'.format(commit_hash))
+            print('Writing it to {}.'.format(commit_hash_filepath))
+        except:
+            pass
+
+        if commit_hash:
+            with open(commit_hash_filepath, 'w') as f:
+                f.write(commit_hash)
+
+        super(sdist_sympy, self).run()
+
+        try:
+            os.remove(commit_hash_filepath)
+            print(
+                'Successfully removed temporary file {}.'
+                .format(commit_hash_filepath))
+        except OSError as e:
+            print("Error deleting %s - %s." % (e.filename, e.strerror))
+
+
 # Check that this list is uptodate against the result of the command:
 # python bin/generate_test_list.py
 tests = [
@@ -409,6 +446,7 @@ if __name__ == '__main__':
                     'clean': clean,
                     'audit': audit,
                     'antlr': antlr,
+                    'sdist': sdist_sympy,
                     },
           classifiers=[
             'License :: OSI Approved :: BSD License',
@@ -420,14 +458,15 @@ if __name__ == '__main__':
             'Programming Language :: Python :: 2',
             'Programming Language :: Python :: 2.7',
             'Programming Language :: Python :: 3',
-            'Programming Language :: Python :: 3.4',
             'Programming Language :: Python :: 3.5',
             'Programming Language :: Python :: 3.6',
+            'Programming Language :: Python :: 3.7',
+            'Programming Language :: Python :: 3.8',
             'Programming Language :: Python :: Implementation :: CPython',
             'Programming Language :: Python :: Implementation :: PyPy',
             ],
           install_requires=[
-            'mpmath>=%s' % mpmath_version,
+            'mpmath>=%s' % min_mpmath_version,
             ],
           **extra_kwargs
           )

sympy/__init__.py

@@ -80,7 +80,7 @@ from .algebras import *
 # from combinatorics import *
 # This module is slow to import:
 #from physics import units
-from .plotting import plot, textplot, plot_backends, plot_implicit
+from .plotting import plot, textplot, plot_backends, plot_implicit, plot_parametric
 from .printing import *
 from .interactive import init_session, init_printing
 

sympy/abc.py

@@ -27,6 +27,28 @@ you still need to use ``Symbol('foo')`` or ``symbols('foo')``.
 You can freely mix usage of ``sympy.abc`` and ``Symbol``/``symbols``, though
 sticking with one and only one way to get the symbols does tend to make the code
 more readable.
+
+The module also defines some special names to help detect which names clash
+with the default SymPy namespace.
+
+``_clash1`` defines all the single letter variables that clash with
+SymPy objects; ``_clash2`` defines the multi-letter clashing symbols;
+and ``_clash`` is the union of both. These can be passed for ``locals``
+during sympification if one desires Symbols rather than the non-Symbol
+objects for those names.
+
+Examples
+========
+
+>>> from sympy import S
+>>> from sympy.abc import _clash1, _clash2, _clash
+>>> S("Q & C", locals=_clash1)
+C & Q
+>>> S('pi(x)', locals=_clash2)
+pi(x)
+>>> S('pi(C, Q)', locals=_clash)
+pi(C, Q)
+
 """
 
 from __future__ import print_function, division
@@ -70,50 +92,20 @@ _greek = list(greeks) # make a copy, so we can mutate it
 _greek.remove("lambda")
 _greek.append("lamda")
 
-def clashing():
-    """Return the clashing-symbols dictionaries.
+ns = {}
+exec_('from sympy import *', ns)
+_clash1 = {}
+_clash2 = {}
+while ns:
+    _k, _ = ns.popitem()
+    if _k in _greek:
+        _clash2[_k] = Symbol(_k)
+        _greek.remove(_k)
+    elif _k in _latin:
+        _clash1[_k] = Symbol(_k)
+        _latin.remove(_k)
+_clash = {}
+_clash.update(_clash1)
+_clash.update(_clash2)
 
-    ``clash1`` defines all the single letter variables that clash with
-    SymPy objects; ``clash2`` defines the multi-letter clashing symbols;
-    and ``clash`` is the union of both. These can be passed for ``locals``
-    during sympification if one desires Symbols rather than the non-Symbol
-    objects for those names.
-
-    Examples
-    ========
-
-    >>> from sympy import S
-    >>> from sympy.abc import _clash1, _clash2, _clash
-    >>> S("Q & C", locals=_clash1)
-    And(C, Q)
-    >>> S('pi(x)', locals=_clash2)
-    pi(x)
-    >>> S('pi(C, Q)', locals=_clash)
-    pi(C, Q)
-
-    Note: if changes are made to the docstring examples they can only
-    be tested after removing "clashing" from the list of deleted items
-    at the bottom of this file which removes this function from the
-    namespace.
-    """
-
-    ns = {}
-    exec_('from sympy import *', ns)
-    clash1 = {}
-    clash2 = {}
-    while ns:
-        k, _ = ns.popitem()
-        if k in _greek:
-            clash2[k] = Symbol(k)
-            _greek.remove(k)
-        elif k in _latin:
-            clash1[k] = Symbol(k)
-            _latin.remove(k)
-    clash = {}
-    clash.update(clash1)
-    clash.update(clash2)
-    return clash1, clash2, clash
-
-_clash1, _clash2, _clash = clashing()
-
-del _latin, _greek, clashing, Symbol
+del _latin, _greek, Symbol, _k