MathML: support more functions and symbols.

- Support emellished identifiers,
- support more functions and symbols from "amsmath",
- map HYPHEN-MINUS -> MINUS SIGN and COLON -> RATIO im math context,
- simplify doctests with starred import,
- dont wrap content in <mrow> when it is inferred by an element
  (let these elements inherit from "mrow").

- tex2unichar: Fix/extend character mappings.

git-svn-id: https://svn.code.sf.net/p/docutils/code/trunk@8748 929543f6-e4f2-0310-98a6-ba3bd3dd1d04

4 files changed, 508 insertions, 367 deletions

diff --git a/docutils/docutils/utils/math/latex2mathml.py b/docutils/docutils/utils/math/latex2mathml.py
index 5a3bce492..769ced771 100644
--- a/docutils/docutils/utils/math/latex2mathml.py
+++ b/docutils/docutils/utils/math/latex2mathml.py
@@ -22,7 +22,7 @@
 #
 # Usage:
 #
-# >>> import latex2mathml as l2m
+# >>> from latex2mathml import *
 
 import collections
 import re
@@ -54,12 +54,17 @@ greek_capitals = {
 functions = ['arccos', 'arcsin', 'arctan', 'arg', 'cos',  'cosh',
              'cot',    'coth',   'csc',    'deg', 'det',  'dim',
              'exp',    'gcd',    'hom',    'inf', 'ker',  'lg',
-             'lim',    'liminf', 'limsup', 'ln',  'log',  'max',
-             'min',    'Pr',     'sec',    'sin', 'sinh', 'sup',
-             'tan',    'tanh',   'injlim', 'varinjlim',   'projlim',
-             'varlimsup', 'varliminf', 'varprojlim']
-
-# font selection -> <mi mathvariant=...>
+             'lim',    'ln',     'log',    'max', 'min',  'Pr',
+             'sec',    'sin',    'sinh',   'sup', 'tan',  'tanh']
+functions = dict((name, name) for name in functions)
+functions.update({# functions with a space in the name
+                  'liminf': u'lim\u202finf', 'limsup': u'lim\u202fsup',
+                  'injlim': u'inj\u202flim', 'projlim': u'proj\u202flim',
+                  # embellished function names (see handle_keyword() below)
+                  'varlimsup': 'lim', 'varliminf': 'lim',
+                  'varprojlim': 'lim', 'varinjlim': 'lim'})
+
+# math font selection -> <mi mathvariant=...> or <mstyle mathvariant=...>
 math_alphabets = {# 'cmdname': 'mathvariant value'  # package
                   'boldsymbol': 'bold',
                   'mathbb': 'double-struck',        # amssymb
@@ -79,19 +84,6 @@ math_alphabets = {# 'cmdname': 'mathvariant value'  # package
                   #              bold-sans-serif
                  }
 
-# blackboar bold (Greek characters not working with "mathvariant" (Firefox 78)
-mathbb = {u'Γ': u'\u213E',    # ℾ
-          u'Π': u'\u213F',    # ℿ
-          u'Σ': u'\u2140',    # ⅀
-          u'γ': u'\u213D',    # ℽ
-          u'π': u'\u213C',    # ℼ
-          r'\Gamma': u'\u213E', # ℾ
-          r'\Pi':    u'\u213F', # ℿ
-          r'\Sigma': u'\u2140', # ⅀
-          r'\gamma': u'\u213D', # ℽ
-          r'\pi':    u'\u213C', # ℼ
-         }
-
 # operator, fence, or separator -> <mo>
 
 operators = tex2unichar.mathbin         # Binary symbols
@@ -101,24 +93,58 @@ operators.update(tex2unichar.mathop)    # Variable-sized symbols
 operators.update(tex2unichar.mathopen)  # Braces
 operators.update(tex2unichar.mathclose) # Braces
 operators.update(tex2unichar.mathfence)
-
-# >>> '{' in l2m.operators.values()
+operators.update({# negated symbols without pre-composed Unicode character
+                  'nleqq':      u'\u2266\u0338', # ≦̸
+                  'ngeqq':      u'\u2267\u0338', # ≧̸
+                  'nleqslant':  u'\u2a7d\u0338', # ⩽̸
+                  'ngeqslant':  u'\u2a7e\u0338', # ⩾̸
+                  'nsubseteqq': u'\u2AC5\u0338', # ⫅̸
+                  'nsupseteqq': u'\u2AC6\u0338', # ⫆̸
+                 })
+
+# >>> '{' in operators.values()
 # True
 
 # special cases
 
+thick_operators = {# style='font-weight: bold;'
+                   'thicksim':   u'\u223C', # ∼
+                   'thickapprox':u'\u2248', # ≈
+                  }
+
+small_operators = {# mathsize='75%'
+                   'shortmid':       u'\u2223', # ∣
+                   'shortparallel':  u'\u2225', # ∥
+                   'nshortmid':      u'\u2224', # ∤
+                   'nshortparallel': u'\u2226', # ∦
+                   'smallfrown': u'\u2322', # ⌢ FROWN
+                   'smallsmile': u'\u2323', # ⌣ SMILE
+                   'smallint':   u'\u222b', # ∫ INTEGRAL
+                  }
+
+left_delimiters = {# rspace='0', lspace='0.22em'
+                   'lvert': '|',
+                   'lVert': u'\u2016' # ‖ DOUBLE VERTICAL LINE
+                  }
+
+right_delimiters = {# lspace='0', rspace='0.22em'
+                    'rvert': '|',
+                    'rVert': u'\u2016', # ‖ DOUBLE VERTICAL LINE
+                   }
+
 sumintprod = ''.join([operators[symbol] for symbol in
                       ['sum', 'int', 'oint', 'prod']])
 
-# >>> print(l2m.sumintprod)
+# >>> print(sumintprod)
 # ∑∫∮∏
 
-#
+# pre-composed characters for negated symbols
+# see https://www.w3.org/TR/xml-entity-names/#combining
 negatables = {'=': u'\u2260',
               r'\in': u'\u2209',
               r'\equiv': u'\u2262'}
 
-# cmds/characters allowed in left/right cmds
+# extensible delimiters allowed in left/right cmds
 stretchables = {'(': '(',
                 ')': ')',
                 '[': '[',
@@ -147,7 +173,7 @@ for (key, value) in tex2unichar.mathclose.items():
 #                          **tex2unichar.mathfence}.items():
 #         stretchables['\\'+key] = value
 
-# >>> print(' '.join(sorted(set(l2m.stretchables.values()))))
+# >>> print(' '.join(sorted(set(stretchables.values()))))
 #  ( ) / [ \ ] { | } ‖ ↑ ↓ ↕ ⇑ ⇓ ⇕ ⌈ ⌉ ⌊ ⌋ ⌜ ⌝ ⌞ ⌟ ⟅ ⟆ ⟦ ⟧ ⟨ ⟩ ⟮ ⟯ ⦇ ⦈
 
 
@@ -171,33 +197,53 @@ spaces = {'qquad':         '2em',       # two \quad
 
 # accents -> <mover>
 #        TeX        spacing    combining
-over = {'acute':    u'\u00B4', # u'\u0301',
-        'bar':      u'\u00AF', # u'\u0304',
-        'breve':    u'\u02D8', # u'\u0306',
-        'check':    u'\u02C7', # u'\u030C',
-        'dot':      u'\u02D9', # u'\u0307',
-        'ddot':     u'\u00A8', # u'\u0308',
-        'dddot':               u'\u20DB',
+over = {'acute':    u'´',      # u'\u0301',
+        'bar':      u'-',      # u'\u0304',
+        'breve':    u'˘',      # u'\u0306',
+        'check':    u'ˇ',      # u'\u030C',
+        'dot':      u'·',      # u'\u0307',
+        'ddot':     u'··',     # u'\u0308',
+        'dddot':    u'···',    # u'\u20DB',
         'grave':    u'`',      # u'\u0300',
         'hat':      u'^',      # u'\u0302',
-        'mathring': u'\u02DA', # u'\u030A',
-        'overleftrightarrow':  u'\u20e1',
-        # 'overline':        # u'\u0305',
-        'tilde':    u'\u02DC', # u'\u0303',
-        'vec':               u'\u20D7'}
+        'mathring': u'°',      # u'\u030A',
+        'tilde':    u'\u223C', # u'\u0303',
+        'vec':                 u'\u20D7',
+       }
+
+wideover = {'overbrace':            u'\u23DE', # TOP CURLY BRACKET
+            'overleftarrow':        u'\u2190',
+            'overleftrightarrow':   u'\u2194',
+            'overline':             u'¯',
+            'overrightarrow':       u'\u2192',
+            'widehat':              u'^',
+            'widetilde':            u'~'}
+wideunder = {'underbrace':          u'\u23DF',
+             'underleftarrow':      u'\u2190',
+             'underleftrightarrow': u'\u2194',
+             'underline':           u'_',
+             'underrightarrow':     u'\u2192'}
+
+# Character translations
+# ----------------------
+# characters with preferred alternative in mathematical use
+anomalous_chars = {'-': u'\u2212', # HYPHEN-MINUS -> MINUS SIGN
+                   ':': u'\u2236', # COLON -> RATIO
+                  }
 
+# blackboard bold (Greek characters not working with "mathvariant" (Firefox 78)
+mathbb = {u'Γ': u'\u213E',    # ℾ
+          u'Π': u'\u213F',    # ℿ
+          u'Σ': u'\u2140',    # ⅀
+          u'γ': u'\u213D',    # ℽ
+          u'π': u'\u213C',    # ℼ
+          r'\Gamma': u'\u213E', # ℾ
+          r'\Pi':    u'\u213F', # ℿ
+          r'\Sigma': u'\u2140', # ⅀
+          r'\gamma': u'\u213D', # ℽ
+          r'\pi':    u'\u213C', # ℼ
+         }
 
-# all supported math-characters:
-#mathcharacters = dict(letters)
-#mathcharacters.update(operators)
-#mathcharacters.update(tex2unichar.space)
-#
-## >>> l2m.mathcharacters['alpha']
-## 'α'
-## >>> l2m.mathcharacters['{']
-## '{'
-## >>> l2m.mathcharacters['pm']
-## '±'
 
 # MathML element classes
 # ----------------------
@@ -205,8 +251,10 @@ over = {'acute':    u'\u00B4', # u'\u0301',
 class math(object):
     """Base class for MathML elements."""
 
-    nchildren = 1000000
-    """Required/Supported number of children"""
+    nchildren = None
+    """Expected number of children or None"""
+    parent = None
+    """Parent node in MathML DOM tree."""
     _level = 0 # indentation level (static class variable)
 
     def __init__(self, children=None, inline=None, **kwargs):
@@ -216,7 +264,7 @@ class math(object):
 
         self.children = []
         if children is not None:
-            if not isinstance(children, list):
+            if not isinstance(children, (list, tuple)):
                 children = [children]
             for child in children:
                 self.append(child)
@@ -226,7 +274,6 @@ class math(object):
             self.attributes['xmlns'] = 'http://www.w3.org/1998/Math/MathML'
         if inline is False:
             self.attributes['display'] = 'block'
-            # self.attributes['displaystyle'] = 'true'
         # sort kwargs for predictable functional tests
         # as self.attributes.update(kwargs) does not keep order in Python < 3.6
         for key in sorted(kwargs.keys()):
@@ -242,8 +289,8 @@ class math(object):
 
     def full(self):
         """Room for more children?"""
-
-        return len(self.children) >= self.nchildren
+        return (self.nchildren is not None
+                and len(self.children) >= self.nchildren)
 
     def append(self, child):
         """append(child) -> element
@@ -255,7 +302,7 @@ class math(object):
         self.children.append(child)
         child.parent = self
         node = self
-        while node.full():
+        while node is not None and node.full():
             node = node.parent
         return node
 
@@ -310,42 +357,55 @@ class math(object):
             last_child = child
         return xml
 
-# >>> l2m.math(l2m.mn(2))
+# >>> math(mn(2))
 # math(mn(2))
-# >>> l2m.math(l2m.mn(2)).xml()
+# >>> math(mn(2)).xml()
 # ['<math>', '\n  ', '<mn>', '2', '</mn>', '\n', '</math>']
 #
-# >>> l2m.math(id='eq3')
+# >>> math(id='eq3')
 # math(id='eq3')
-# >>> l2m.math(id='eq3').xml()
+# >>> math(id='eq3').xml()
 # ['<math id="eq3">', '\n', '</math>']
 #
 # use CLASS to get "class" in XML
-# >>> l2m.math(CLASS='test')
+# >>> math(CLASS='test')
 # math(CLASS='test')
-# >>> l2m.math(CLASS='test').xml()
+# >>> math(CLASS='test').xml()
 # ['<math class="test">', '\n', '</math>']
 
-# >>> l2m.math(inline=True)
+# >>> math(inline=True)
 # math(xmlns='http://www.w3.org/1998/Math/MathML')
-# >>> l2m.math(inline=True).xml()
+# >>> math(inline=True).xml()
 # ['<math xmlns="http://www.w3.org/1998/Math/MathML">', '\n', '</math>']
-# >>> l2m.math(inline=False)
+# >>> math(inline=False)
 # math(xmlns='http://www.w3.org/1998/Math/MathML', display='block')
-# >>> l2m.math(inline=False).xml()
+# >>> math(inline=False).xml()
 # ['<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">', '\n', '</math>']
 
-class mrow(math): pass
+class mrow(math):
+    """Group sub-expressions as a horizontal row.
+    """
+    def __init__(self, children=None, nchildren=None, **kwargs):
+        self.nchildren = nchildren
+        math.__init__(self, children)
+        self.attributes = kwargs
 
-# >>> l2m.mrow(displaystyle='false')
+# >>> mrow(displaystyle='false')
 # mrow(displaystyle='false')
 
 class mtable(math): pass
 
-# >>> l2m.mtable(displaystyle='true')
+# >>> mtable(displaystyle='true')
 # mtable(displaystyle='true')
-# >>> l2m.math(l2m.mtable(displaystyle='true')).xml()
+# >>> math(mtable(displaystyle='true')).xml()
 # ['<math>', '\n  ', '<mtable displaystyle="true">', '\n  ', '</mtable>', '\n', '</math>']
+
+
+# The elements <msqrt>, <mstyle>, <merror>, <mpadded>, <mphantom>, <menclose>,
+# <mtd>, <mscarry>, and <math> treat their contents as a single inferred mrow
+# formed from all their children.
+class msqrt(mrow): pass
+class mstyle(mrow): pass
 class mtr(mrow): pass
 class mtd(mrow): pass
 
@@ -367,9 +427,9 @@ class mn(mx): pass
 class mo(mx): pass
 class mtext(mx): pass
 
-# >>> l2m.mo(u'<')
+# >>> mo(u'<')
 # mo('<')
-# >>> l2m.mo(u'<').xml()
+# >>> mo(u'<').xml()
 # ['<mo>', '&lt;', '</mo>']
 
 class msub(math):
@@ -378,9 +438,6 @@ class msub(math):
 class msup(math):
     nchildren = 2
 
-class msqrt(math):
-    nchildren = 1
-
 class mroot(math):
     nchildren = 2
 
@@ -403,18 +460,11 @@ class msubsup(math):
 class mspace(math):
     nchildren = 0
 
-class mstyle(math):
-    def __init__(self, children=None, nchildren=None, **kwargs):
-        if nchildren is not None:
-            self.nchildren = nchildren
-        math.__init__(self, children)
-        self.attributes = kwargs
-
 class mover(math):
     nchildren = 2
-    def __init__(self, children=None, reversed=False):
+    def __init__(self, children=None, reversed=False, **kwargs):
         self.reversed = reversed
-        math.__init__(self, children)
+        math.__init__(self, children, **kwargs)
 
     def xml(self):
         if self.reversed:
@@ -422,7 +472,10 @@ class mover(math):
             self.reversed = False
         return math.xml(self)
 
-class munder(math):
+# >>> mover(children=[mi('lim'), mo('-')], accent='false')
+# mover(mi('lim'), mo('-'), accent='false')
+
+class munder(mover):
     nchildren = 2
 
 class munderover(math):
@@ -440,11 +493,11 @@ class munderover(math):
 def tex_cmdname(string):
     """Return leading TeX command name from `string`.
 
-      >>> l2m.tex_cmdname('name2') # up to first non-letter
+      >>> tex_cmdname('name2') # up to first non-letter
       ('name', '2')
-      >>> l2m.tex_cmdname('name 2') # strip trailing whitespace
+      >>> tex_cmdname('name 2') # strip trailing whitespace
       ('name', '2')
-      >>> l2m.tex_cmdname('_2') # single non-letter character
+      >>> tex_cmdname('_2') # single non-letter character
       ('_', '2')
 
     """
@@ -455,21 +508,15 @@ def tex_cmdname(string):
 
 # Test:
 #
-# >>> l2m.tex_cmdname('name_2') # first non-letter terminates
+# >>> tex_cmdname('name_2') # first non-letter terminates
 # ('name', '_2')
-# >>> l2m.tex_cmdname(' next') # leading whitespace is returned
+# >>> tex_cmdname(' next') # leading whitespace is returned
 # (' ', 'next')
-# >>> l2m.tex_cmdname('1 2') # whitespace after non-letter is kept
+# >>> tex_cmdname('1 2') # whitespace after non-letter is kept
 # ('1', ' 2')
-# >>> l2m.tex_cmdname('') # empty string
+# >>> tex_cmdname('') # empty string
 # ('', '')
 
-
-# TODO: check for Inferred <mrow>s:
-
-# The elements <msqrt>, <mstyle>, <merror>, <mpadded>, <mphantom>, <menclose>,
-# <mtd, mscarry>, and <math> treat their contents as a single inferred mrow
-# formed from all their children
 #
 # --- https://www.w3.org/TR/MathML3/chapter3.html#id.3.1.3.2
 
@@ -478,11 +525,11 @@ def tex_token(string):
 
     Return token and remainder.
 
-      >>> l2m.tex_token('{first simple group} {without brackets}')
+      >>> tex_token('{first simple group} {without brackets}')
       ('first simple group', ' {without brackets}')
-      >>> l2m.tex_token('\\command{without argument}')
+      >>> tex_token('\\command{without argument}')
       ('\\command', '{without argument}')
-      >>> l2m.tex_token(' first non-white character')
+      >>> tex_token(' first non-white character')
       ('f', 'irst non-white character')
 
     """
@@ -505,19 +552,19 @@ def tex_token(string):
 
 # Test:
 #
-# >>> l2m.tex_token('{opening bracket of group with {nested group}}')
+# >>> tex_token('{opening bracket of group with {nested group}}')
 # ('{', 'opening bracket of group with {nested group}}')
-# >>> l2m.tex_token('{group with \\{escaped\\} brackets}')
+# >>> tex_token('{group with \\{escaped\\} brackets}')
 # ('group with \\{escaped\\} brackets', '')
-# >>> l2m.tex_token('{group followed by closing bracket}} from outer group')
+# >>> tex_token('{group followed by closing bracket}} from outer group')
 # ('group followed by closing bracket', '} from outer group')
-# >>> l2m.tex_token(' {skip leading whitespace}')
+# >>> tex_token(' {skip leading whitespace}')
 # ('skip leading whitespace', '')
-# >>> l2m.tex_token('  \\skip{leading whitespace}')
+# >>> tex_token('  \\skip{leading whitespace}')
 # ('\\skip', '{leading whitespace}')
-# >>> l2m.tex_token('\\skip whitespace after macro name')
+# >>> tex_token('\\skip whitespace after macro name')
 # ('\\skip', 'whitespace after macro name')
-# >>> l2m.tex_token('') # empty string.
+# >>> tex_token('') # empty string.
 # ('', '')
 
 
@@ -527,8 +574,8 @@ def parse_latex_math(string, inline=True):
     Return a MathML-tree parsed from `string`.
     Set `inline` to False for displayed math.
 
-      >>> l2m.parse_latex_math('\\alpha')
-      math(mrow(mi('α')), xmlns='http://www.w3.org/1998/Math/MathML')
+      >>> parse_latex_math('\\alpha')
+      math(mi('α'), xmlns='http://www.w3.org/1998/Math/MathML')
 
     """
 
@@ -537,8 +584,8 @@ def parse_latex_math(string, inline=True):
 
     # Set up: tree is the whole tree and node is the current element.
     if inline:
-        node = mrow()
-        tree = math(node, inline=True)
+        node = math(inline=True)
+        tree = node
     else:
         # block: emulate align* environment with a math table
         node = mtd()
@@ -550,7 +597,7 @@ def parse_latex_math(string, inline=True):
         c, string = string[0], string[1:]
 
         if c == ' ':
-            continue
+            continue  # whitespace is ignored in LaTeX math mode
 
         if c == '\\': # start of a LaTeX macro
             cmdname, string = tex_cmdname(string)
@@ -561,7 +608,10 @@ def parse_latex_math(string, inline=True):
             node = node.append(mn(c))
         elif c in "/()[]|":
             node = node.append(mo(c, stretchy='false'))
-        elif c in "+-*=<>,.!?':;@":
+        # use dedicated mathematical operator characters
+        elif c in anomalous_chars:
+            node = node.append(mo(anomalous_chars[c]))
+        elif c in "+*=<>,.!?';@":
             node = node.append(mo(c))
         elif c == '_':
             child = node.delete_child()
@@ -603,11 +653,14 @@ def parse_latex_math(string, inline=True):
 
 # Test:
 
-# >>> l2m.parse_latex_math(' \\sqrt{ \\alpha}')
-# math(mrow(msqrt(mrow(mi('α')))), xmlns='http://www.w3.org/1998/Math/MathML')
-# >>> l2m.parse_latex_math('\\alpha', inline=False)
+# >>> parse_latex_math(' \\sqrt{ \\alpha}')
+# math(msqrt(mi('α')), xmlns='http://www.w3.org/1998/Math/MathML')
+# >>> parse_latex_math('\\alpha', inline=False)
 # math(mtable(mtr(mtd(mi('α'))), CLASS='align', displaystyle='true'), xmlns='http://www.w3.org/1998/Math/MathML', display='block')
-
+# >>> parse_latex_math('\\sqrt 2 \\ne 3')
+# math(msqrt(mn('2')), mo('≠'), mn('3'), xmlns='http://www.w3.org/1998/Math/MathML')
+# >>> parse_latex_math('\\sqrt{2 + 3} < 3')
+# math(msqrt(mn('2'), mo('+'), mn('3')), mo('<'), mn('3'), xmlns='http://www.w3.org/1998/Math/MathML')
 
 def handle_keyword(name, node, string):
     """Process LaTeX macro `name` followed by `string`.
@@ -615,9 +668,9 @@ def handle_keyword(name, node, string):
     If needed, parse `string` for macro argument.
     Return updated current node and remainder:
 
-      >>> l2m.handle_keyword('hbar', l2m.math(), r' \frac')
+      >>> handle_keyword('hbar', math(), r' \frac')
       (math(mi('ℏ')), ' \\frac')
-      >>> l2m.handle_keyword('hspace', l2m.math(), r'{1ex} (x)')
+      >>> handle_keyword('hspace', math(), r'{1ex} (x)')
       (math(mspace(width='1ex')), ' (x)')
 
     """
@@ -637,20 +690,31 @@ def handle_keyword(name, node, string):
             node = node.append(mi(letters[name]))
         return node, string
 
-    if name in functions:
+    if (name in functions or name == 'operatorname'):
         # use <mi> followed by invisible function applicator character
         # (see https://www.w3.org/TR/MathML3/chapter3.html#presm.mi)
-        node = node.append(mi(name))
-        node = node.append(mo('&ApplyFunction;'))
-        return node, string
-
-    if name == 'operatorname':
-        # custom function name ``\operatorname{abs}(x)``
-        arg, string = tex_token(string)
-        node = node.append(mi(arg, mathvariant='normal'))
+        if name == 'operatorname':
+            # custom function name ``\operatorname{abs}(x)``
+            arg, string = tex_token(string)
+            identifier = mi(arg, mathvariant='normal')
+        else:
+            identifier = mi(functions[name])
+        # functions with embellished names
+        if name == 'varliminf':    # \underline\lim
+            identifier = munder([identifier, mo(u'_')], accent='false')
+        elif name == 'varlimsup':  # \overline\lim
+            identifier = mover([identifier, mo(u'¯')], accent='false')
+        elif name == 'varprojlim': # \underleftarrow\lim
+            identifier = munder([identifier, mo(u'\u2190')], accent='false')
+        elif name == 'varinjlim':  # \underrightarrow\lim
+            identifier = munder([identifier, mo(u'\u2192')], accent='false')
+
+        node = node.append(identifier)
+        # TODO: only add ApplyFunction when appropriate (not \sin ^2(x), say)
         node = node.append(mo('&ApplyFunction;')) # '\u2061'
         return node, string
 
+
     if name in math_alphabets:
         arg, remainder = tex_token(string)
         if arg[0] == '\\':
@@ -665,6 +729,8 @@ def handle_keyword(name, node, string):
             kwargs = {'style': 'font-weight: bold'}
         else:
             kwargs = {'mathvariant': math_alphabets[name]}
+        if name == 'mathscr':
+            kwargs['style'] = 'font-family: STIX' # alternative script letter shapes
 
         # one symbol (single letter, name, or number)
         if arg.isalpha():
@@ -685,10 +751,26 @@ def handle_keyword(name, node, string):
 
     # operator, fence, or separator  ->  <mo>
 
-    if name == 'colon': # "normal" colon, not binary operator
+    if name in left_delimiters: # opening delimiters
+        node = node.append(mo(left_delimiters[name], rspace='0'))
+        return node, string
+
+    if name in right_delimiters: # closing delimiters
+        node = node.append(mo(right_delimiters[name], lspace='0', ))
+        return node, string
+
+    if name == 'colon': # trailing punctuation, not binary relation
         node = node.append(mo(':', lspace='0', rspace='0.28em'))
         return node, string
 
+    if name in thick_operators:
+        node = node.append(mo(thick_operators[name], style='font-weight: bold'))
+        return node, string
+
+    if name in small_operators:
+        node = node.append(mo(small_operators[name], mathsize='75%'))
+        return node, string
+
     if name in operators:
         node = node.append(mo(operators[name]))
         return node, string
@@ -714,7 +796,7 @@ def handle_keyword(name, node, string):
         try:
             node = node.append(mo(negatables[arg]))
         except KeyError:
-            raise SyntaxError(u'Expected something to negate: "\\not ..."!')
+            raise SyntaxError(u'"\\not: Cannot negate: %s!'%arg)
         return node, string
 
     # arbitrary text (usually comments)  ->  <mtext>
@@ -741,7 +823,11 @@ def handle_keyword(name, node, string):
     # ==================================
 
     if name == 'sqrt':
-        sqrt = msqrt()
+        if string.startswith('{'): # argument is a group
+            string = string[1:] # mrow implied, skip opening bracket
+            sqrt = msqrt()
+        else: # no group, enclose only one element
+            sqrt = msqrt(nchildren=1)
         node.append(sqrt)
         return sqrt, string
 
@@ -757,8 +843,17 @@ def handle_keyword(name, node, string):
         node = entry
         return node, string
 
-    if name in over:
-        ovr = mover(mo(over[name]), reversed=True)
+    if name in over or name in wideover:
+        try:
+            ovr = mover(mo(over[name]), reversed=True)
+        except KeyError:
+            ovr = mover(mo(wideover[name]), reversed=True, accent='false')
+        node.append(ovr)
+        node = ovr
+        return node, string
+
+    if name in wideunder:
+        ovr = munder(mo(wideunder[name]), reversed=True, accent='false')
         node.append(ovr)
         node = ovr
         return node, string
@@ -794,32 +889,35 @@ def handle_keyword(name, node, string):
     raise SyntaxError(u'Unknown LaTeX command: ' + name)
 
 
-# >>> l2m.handle_keyword('left', l2m.math(), '[a\\right]')
+# >>> handle_keyword('left', math(), '[a\\right]')
 # (mrow(mo('[')), 'a\\right]')
-# >>> l2m.handle_keyword('left', l2m.math(), '. a)') # emtpy \left
+# >>> handle_keyword('left', math(), '. a)') # emtpy \left
 # (mrow(), ' a)')
-# >>> l2m.handle_keyword('left', l2m.math(), '\\uparrow a)') # cmd
+# >>> handle_keyword('left', math(), '\\uparrow a)') # cmd
 # (mrow(mo('↑')), 'a)')
-# >>> l2m.handle_keyword('not', l2m.math(), '\\equiv \\alpha)') # cmd
+# >>> handle_keyword('not', math(), '\\equiv \\alpha)') # cmd
 # (math(mo('≢')), '\\alpha)')
-# >>> l2m.handle_keyword('text', l2m.math(), '{ for } i>0') # group
+# >>> handle_keyword('text', math(), '{ for } i>0') # group
 # (math(mtext('&nbsp;for&nbsp;')), ' i>0')
-# >>> l2m.handle_keyword('text', l2m.math(), '{B}T') # group
+# >>> handle_keyword('text', math(), '{B}T') # group
 # (math(mtext('B')), 'T')
-# >>> l2m.handle_keyword('text', l2m.math(), '{number of apples}}') # group
+# >>> handle_keyword('text', math(), '{number of apples}}') # group
 # (math(mtext('number of apples')), '}')
-# >>> l2m.handle_keyword('text', l2m.math(), 'i \\sin(x)') # single char
+# >>> handle_keyword('text', math(), 'i \\sin(x)') # single char
 # (math(mtext('i')), ' \\sin(x)')
-# >>> l2m.handle_keyword('sin', l2m.math(), '(\\alpha)')
+# >>> handle_keyword('sin', math(), '(\\alpha)')
 # (math(mi('sin'), mo('&ApplyFunction;')), '(\\alpha)')
-# >>> l2m.handle_keyword('sin', l2m.math(), ' \\alpha')
+# >>> handle_keyword('sin', math(), ' \\alpha')
 # (math(mi('sin'), mo('&ApplyFunction;')), ' \\alpha')
-# >>> l2m.handle_keyword('operatorname', l2m.math(), '{abs}(x)')
+# >>> handle_keyword('operatorname', math(), '{abs}(x)')
 # (math(mi('abs', mathvariant='normal'), mo('&ApplyFunction;')), '(x)')
-# >>> l2m.handle_keyword('mathrm', l2m.math(), '\\alpha')
+# >>> handle_keyword('mathrm', math(), '\\alpha')
 # (math(mi('α', mathvariant='normal')), '')
-# >>> l2m.handle_keyword('mathrm', l2m.math(), '{out} = 3')
+# >>> handle_keyword('mathrm', math(), '{out} = 3')
 # (math(mi('out', mathvariant='normal')), ' = 3')
+# >>> handle_keyword('overline', math(), '{981}')
+# (mover(mo('¯'), accent='false'), '{981}')
+
 
 def tex2mathml(tex_math, inline=True):
     """Return string with MathML code corresponding to `tex_math`.
diff --git a/docutils/docutils/utils/math/tex2unichar.py b/docutils/docutils/utils/math/tex2unichar.py
index 434c0e8c3..84001d34a 100644
--- a/docutils/docutils/utils/math/tex2unichar.py
+++ b/docutils/docutils/utils/math/tex2unichar.py
@@ -1,4 +1,4 @@
-# -*- coding: utf-8 -*-
+# -*- coding: utf8 -*-
 
 # LaTeX math to Unicode symbols translation dictionaries.
 # Generated with ``write_tex2unichar.py`` from the data in
@@ -7,30 +7,30 @@
 # Includes commands from: wasysym, stmaryrd, mathdots, mathabx, esint, bbold, amsxtra, amsmath, amssymb, standard LaTeX
 
 mathaccent = {
-    'acute': u'\u0301', # x́ COMBINING ACUTE ACCENT
-    'bar': u'\u0304', # x̄ COMBINING MACRON
-    'breve': u'\u0306', # x̆ COMBINING BREVE
-    'check': u'\u030c', # x̌ COMBINING CARON
+    'acute': u'\u0301', #  ́ COMBINING ACUTE ACCENT
+    'bar': u'\u0304', #  ̄ COMBINING MACRON
+    'breve': u'\u0306', #  ̆ COMBINING BREVE
+    'check': u'\u030c', #  ̌ COMBINING CARON
     'ddddot': u'\u20dc', # x⃜ COMBINING FOUR DOTS ABOVE
     'dddot': u'\u20db', # x⃛ COMBINING THREE DOTS ABOVE
-    'ddot': u'\u0308', # ẍ COMBINING DIAERESIS
-    'dot': u'\u0307', # ẋ COMBINING DOT ABOVE
-    'grave': u'\u0300', # x̀ COMBINING GRAVE ACCENT
-    'hat': u'\u0302', # x̂ COMBINING CIRCUMFLEX ACCENT
-    'mathring': u'\u030a', # x̊ COMBINING RING ABOVE
-    'not': u'\u0338', # x̸ COMBINING LONG SOLIDUS OVERLAY
+    'ddot': u'\u0308', #  ̈ COMBINING DIAERESIS
+    'dot': u'\u0307', #  ̇ COMBINING DOT ABOVE
+    'grave': u'\u0300', #  ̀ COMBINING GRAVE ACCENT
+    'hat': u'\u0302', #  ̂ COMBINING CIRCUMFLEX ACCENT
+    'mathring': u'\u030a', #  ̊ COMBINING RING ABOVE
+    'not': u'\u0338', #  ̸ COMBINING LONG SOLIDUS OVERLAY
     'overleftarrow': u'\u20d6', # x⃖ COMBINING LEFT ARROW ABOVE
     'overleftrightarrow': u'\u20e1', # x⃡ COMBINING LEFT RIGHT ARROW ABOVE
-    'overline': u'\u0305', # x̅ COMBINING OVERLINE
+    'overline': u'\u0305', #  ̅ COMBINING OVERLINE
     'overrightarrow': u'\u20d7', # x⃗ COMBINING RIGHT ARROW ABOVE
-    'tilde': u'\u0303', # x̃ COMBINING TILDE
-    'underbar': u'\u0331', # x̱ COMBINING MACRON BELOW
+    'tilde': u'\u0303', #  ̃ COMBINING TILDE
+    'underbar': u'\u0331', #  ̱ COMBINING MACRON BELOW
     'underleftarrow': u'\u20ee', # x⃮ COMBINING LEFT ARROW BELOW
-    'underline': u'\u0332', # x̲ COMBINING LOW LINE
+    'underline': u'\u0332', #  ̲ COMBINING LOW LINE
     'underrightarrow': u'\u20ef', # x⃯ COMBINING RIGHT ARROW BELOW
     'vec': u'\u20d7', # x⃗ COMBINING RIGHT ARROW ABOVE
-    'widehat': u'\u0302', # x̂ COMBINING CIRCUMFLEX ACCENT
-    'widetilde': u'\u0303', # x̃ COMBINING TILDE
+    'widehat': u'\u0302', #  ̂ COMBINING CIRCUMFLEX ACCENT
+    'widetilde': u'\u0303', #  ̃ COMBINING TILDE
     }
 mathalpha = {
     'Bbbk': u'\U0001d55c', # 𝕜 MATHEMATICAL DOUBLE-STRUCK SMALL K
@@ -54,7 +54,7 @@ mathalpha = {
     'chi': u'\u03c7', # χ GREEK SMALL LETTER CHI
     'daleth': u'\u2138', # ℸ DALET SYMBOL
     'delta': u'\u03b4', # δ GREEK SMALL LETTER DELTA
-    'digamma': u'\u03dc', # Ϝ GREEK LETTER DIGAMMA
+    'digamma': u'\u03dd', # ϝ GREEK SMALL LETTER DIGAMMA
     'ell': u'\u2113', # ℓ SCRIPT SMALL L
     'epsilon': u'\u03f5', # ϵ GREEK LUNATE EPSILON SYMBOL
     'eta': u'\u03b7', # η GREEK SMALL LETTER ETA
@@ -91,7 +91,7 @@ mathalpha = {
     'varUpsilon': u'\U0001d6f6', # 𝛶 MATHEMATICAL ITALIC CAPITAL UPSILON
     'varXi': u'\U0001d6ef', # 𝛯 MATHEMATICAL ITALIC CAPITAL XI
     'varepsilon': u'\u03b5', # ε GREEK SMALL LETTER EPSILON
-    'varkappa': u'\U0001d718', # 𝜘 MATHEMATICAL ITALIC KAPPA SYMBOL
+    'varkappa': u'\u03f0', # ϰ GREEK KAPPA SYMBOL
     'varphi': u'\u03c6', # φ GREEK SMALL LETTER PHI
     'varpi': u'\u03d6', # ϖ GREEK PI SYMBOL
     'varrho': u'\u03f1', # ϱ GREEK RHO SYMBOL
@@ -110,10 +110,12 @@ mathbin = {
     'amalg': u'\u2a3f', # ⨿ AMALGAMATION OR COPRODUCT
     'ast': u'\u2217', # ∗ ASTERISK OPERATOR
     'barwedge': u'\u22bc', # ⊼ NAND
+    'bigcirc': u'\u25ef', # ◯ LARGE CIRCLE
     'bigtriangledown': u'\u25bd', # ▽ WHITE DOWN-POINTING TRIANGLE
     'bigtriangleup': u'\u25b3', # △ WHITE UP-POINTING TRIANGLE
     'bindnasrepma': u'\u214b', # ⅋ TURNED AMPERSAND
     'blacklozenge': u'\u29eb', # ⧫ BLACK LOZENGE
+    'blacktriangle': u'\u25b4', # ▴ BLACK UP-POINTING SMALL TRIANGLE
     'blacktriangledown': u'\u25be', # ▾ BLACK DOWN-POINTING SMALL TRIANGLE
     'blacktriangleleft': u'\u25c2', # ◂ BLACK LEFT-POINTING SMALL TRIANGLE
     'blacktriangleright': u'\u25b8', # ▸ BLACK RIGHT-POINTING SMALL TRIANGLE
@@ -128,7 +130,7 @@ mathbin = {
     'boxplus': u'\u229e', # ⊞ SQUARED PLUS
     'boxslash': u'\u29c4', # ⧄ SQUARED RISING DIAGONAL SLASH
     'boxtimes': u'\u22a0', # ⊠ SQUARED TIMES
-    'bullet': u'\u2219', # ∙ BULLET OPERATOR
+    'bullet': u'\u2022', # • BULLET
     'cap': u'\u2229', # ∩ INTERSECTION
     'cdot': u'\u22c5', # ⋅ DOT OPERATOR
     'circ': u'\u2218', # ∘ RING OPERATOR
@@ -320,9 +322,12 @@ mathord = {
     'dasharrow': u'\u21e2', # ⇢ RIGHTWARDS DASHED ARROW
     'dashleftarrow': u'\u21e0', # ⇠ LEFTWARDS DASHED ARROW
     'dashrightarrow': u'\u21e2', # ⇢ RIGHTWARDS DASHED ARROW
+    'diagdown': u'\u27cd', # ⟍ 
+    'diagup': u'\u27cb', # ⟋ 
     'diameter': u'\u2300', # ⌀ DIAMETER SIGN
     'diamondsuit': u'\u2662', # ♢ WHITE DIAMOND SUIT
     'earth': u'\u2641', # ♁ EARTH
+    'emptyset': u'\u2205', # ∅ EMPTY SET
     'exists': u'\u2203', # ∃ THERE EXISTS
     'female': u'\u2640', # ♀ FEMALE SIGN
     'flat': u'\u266d', # ♭ MUSIC FLAT SIGN
@@ -333,6 +338,7 @@ mathord = {
     'girl': u'\u2640', # ♀ FEMALE SIGN
     'heartsuit': u'\u2661', # ♡ WHITE HEART SUIT
     'infty': u'\u221e', # ∞ INFINITY
+    'invdiameter': u'\u2349', # ⍉ APL FUNCTIONAL SYMBOL CIRCLE BACKSLASH
     'invneg': u'\u2310', # ⌐ REVERSED NOT SIGN
     'jupiter': u'\u2643', # ♃ JUPITER
     'ldots': u'\u2026', # … HORIZONTAL ELLIPSIS
@@ -386,7 +392,7 @@ mathord = {
     'twonotes': u'\u266b', # ♫ BEAMED EIGHTH NOTES
     'uranus': u'\u2645', # ♅ URANUS
     'varEarth': u'\u2641', # ♁ EARTH
-    'varnothing': u'\u2205', # ∅ EMPTY SET
+    'varnothing': u'\u2300', # ⌀ DIAMETER SIGN
     'virgo': u'\u264d', # ♍ VIRGO
     'wasylozenge': u'\u2311', # ⌑ SQUARE LOZENGE
     'wasytherefore': u'\u2234', # ∴ THEREFORE
@@ -397,7 +403,6 @@ mathover = {
     'wideparen': u'\u23dc', # ⏜ TOP PARENTHESIS
     }
 mathradical = {
-    'sqrt': u'\u221a', # √ SQUARE ROOT
     'sqrt[3]': u'\u221b', # ∛ CUBE ROOT
     'sqrt[4]': u'\u221c', # ∜ FOURTH ROOT
     }
@@ -476,6 +481,7 @@ mathrel = {
     'gg': u'\u226b', # ≫ MUCH GREATER-THAN
     'ggcurly': u'\u2abc', # ⪼ DOUBLE SUCCEEDS
     'ggg': u'\u22d9', # ⋙ VERY MUCH GREATER-THAN
+    'gggtr': u'\u22d9', # ⋙ VERY MUCH GREATER-THAN
     'gnapprox': u'\u2a8a', # ⪊ GREATER-THAN AND NOT APPROXIMATE
     'gneq': u'\u2a88', # ⪈ GREATER-THAN AND SINGLE-LINE NOT EQUAL TO
     'gneqq': u'\u2269', # ≩ GREATER-THAN BUT NOT EQUAL TO
@@ -523,6 +529,7 @@ mathrel = {
     'll': u'\u226a', # ≪ MUCH LESS-THAN
     'llcurly': u'\u2abb', # ⪻ DOUBLE PRECEDES
     'lll': u'\u22d8', # ⋘ VERY MUCH LESS-THAN
+    'llless': u'\u22d8', # ⋘ VERY MUCH LESS-THAN
     'lnapprox': u'\u2a89', # ⪉ LESS-THAN AND NOT APPROXIMATE
     'lneq': u'\u2a87', # ⪇ LESS-THAN AND SINGLE-LINE NOT EQUAL TO
     'lneqq': u'\u2268', # ≨ LESS-THAN BUT NOT EQUAL TO
@@ -585,6 +592,7 @@ mathrel = {
     'preccurlyeq': u'\u227c', # ≼ PRECEDES OR EQUAL TO
     'preceq': u'\u2aaf', # ⪯ PRECEDES ABOVE SINGLE-LINE EQUALS SIGN
     'precnapprox': u'\u2ab9', # ⪹ PRECEDES ABOVE NOT ALMOST EQUAL TO
+    'precneqq': u'\u2ab5', # ⪵ PRECEDES ABOVE NOT EQUAL TO
     'precnsim': u'\u22e8', # ⋨ PRECEDES BUT NOT EQUIVALENT TO
     'precsim': u'\u227e', # ≾ PRECEDES OR EQUIVALENT TO
     'propto': u'\u221d', # ∝ PROPORTIONAL TO
@@ -623,6 +631,7 @@ mathrel = {
     'succcurlyeq': u'\u227d', # ≽ SUCCEEDS OR EQUAL TO
     'succeq': u'\u2ab0', # ⪰ SUCCEEDS ABOVE SINGLE-LINE EQUALS SIGN
     'succnapprox': u'\u2aba', # ⪺ SUCCEEDS ABOVE NOT ALMOST EQUAL TO
+    'succneqq': u'\u2ab6', # ⪶ SUCCEEDS ABOVE NOT EQUAL TO
     'succnsim': u'\u22e9', # ⋩ SUCCEEDS BUT NOT EQUIVALENT TO
     'succsim': u'\u227f', # ≿ SUCCEEDS OR EQUIVALENT TO
     'supset': u'\u2283', # ⊃ SUPERSET OF
diff --git a/docutils/test/functional/expected/math_output_mathml.html b/docutils/test/functional/expected/math_output_mathml.html
index 5cb03d5a1..d5f95a3bf 100644
--- a/docutils/test/functional/expected/math_output_mathml.html
+++ b/docutils/test/functional/expected/math_output_mathml.html
@@ -14,31 +14,27 @@
 
 <p>Docutils supports inline math with the prefix or postfix <span class="docutils literal">:math:</span>
 role specificator, <math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mi>n</mi><mo>!</mo><mo>+</mo><mi>sin</mi><mo>&ApplyFunction;</mo><mo stretchy="false">(</mo>
-    <msubsup>
-      <mi>x</mi><mi>n</mi><mn>2</mn>
-    </msubsup>
-    <mo stretchy="false">)</mo>
-  </mrow>
+  <mi>n</mi><mo>!</mo><mo>+</mo><mi>sin</mi><mo>&ApplyFunction;</mo><mo stretchy="false">(</mo>
+  <msubsup>
+    <mi>x</mi><mi>n</mi><mn>2</mn>
+  </msubsup>
+  <mo stretchy="false">)</mo>
 </math> and <math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <msub>
-      <mi>A</mi><mtext>c</mtext>
-    </msub>
-    <mo>=</mo>
-    <mfrac>
-      <mrow>
-        <mi>π</mi>
-      </mrow>
-      <mrow>
-        <mn>4</mn>
-      </mrow>
-    </mfrac>
-    <msup>
-      <mi>d</mi><mn>2</mn>
-    </msup>
-  </mrow>
+  <msub>
+    <mi>A</mi><mtext>c</mtext>
+  </msub>
+  <mo>=</mo>
+  <mfrac>
+    <mrow>
+      <mi>π</mi>
+    </mrow>
+    <mrow>
+      <mn>4</mn>
+    </mrow>
+  </mfrac>
+  <msup>
+    <mi>d</mi><mn>2</mn>
+  </msup>
 </math>, as well as displayed math via the
 <cite>math</cite> directive:</p>
 <div>
@@ -132,9 +128,7 @@ See <a class="reference internal" href="#eq-m">eq:M</a> and <a class="reference
 </math>
 </div>
 <p>is <math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mo stretchy="false">|</mo><mi mathvariant="bold">M</mi><mo stretchy="false">|</mo><mo>=</mo><mi>a</mi><mi>d</mi><mo>-</mo><mi>b</mi><mi>c</mi>
-  </mrow>
+  <mo stretchy="false">|</mo><mi mathvariant="bold">M</mi><mo stretchy="false">|</mo><mo>=</mo><mi>a</mi><mi>d</mi><mo>−</mo><mi>b</mi><mi>c</mi>
 </math>.</p>
 <p>More than one display math block can be put in one math directive.
 For example, the following sum and integral with limits:</p>
@@ -220,9 +214,7 @@ directives:</p>
 </math>
 </div>
 <p>with the <em>wave function</em> <math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mi class="capital-greek">Ψ</mi>
-  </mrow>
+  <mi class="capital-greek">Ψ</mi>
 </math>, describes how the quantum state of a
 physical system changes in time.</p>
 <dl>
@@ -235,127 +227,103 @@ physical system changes in time.</p>
 </colgroup>
 <tbody>
 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>a</mi>
-      </mrow>
-      <mo>´</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>a</mi>
+    </mrow>
+    <mo>´</mo>
+  </mover>
 </math>      <span class="docutils literal">\acute{a}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>t</mi>
-      </mrow>
-      <mo>˙</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>t</mi>
+    </mrow>
+    <mo>·</mo>
+  </mover>
 </math>        <span class="docutils literal">\dot{t}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>γ</mi>
-      </mrow>
-      <mo>^</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>γ</mi>
+    </mrow>
+    <mo>^</mo>
+  </mover>
 </math>   <span class="docutils literal"><span class="pre">\hat{\gamma}</span></span></p></td>
 </tr>
 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>a</mi>
-      </mrow>
-      <mo>`</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>a</mi>
+    </mrow>
+    <mo>`</mo>
+  </mover>
 </math>      <span class="docutils literal">\grave{a}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>t</mi>
-      </mrow>
-      <mo>¨</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>t</mi>
+    </mrow>
+    <mo>··</mo>
+  </mover>
 </math>       <span class="docutils literal">\ddot{t}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>α</mi>
-      </mrow>
-      <mo>˜</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>α</mi>
+    </mrow>
+    <mo>∼</mo>
+  </mover>
 </math> <span class="docutils literal"><span class="pre">\tilde{\alpha}</span></span></p></td>
 </tr>
 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>x</mi>
-      </mrow>
-      <mo>˘</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>x</mi>
+    </mrow>
+    <mo>˘</mo>
+  </mover>
 </math>      <span class="docutils literal">\breve{x}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>t</mi>
-      </mrow>
-      <mo>⃛</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>t</mi>
+    </mrow>
+    <mo>···</mo>
+  </mover>
 </math>      <span class="docutils literal">\dddot{t}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>ı</mi>
-      </mrow>
-      <mo>⃗</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>ı</mi>
+    </mrow>
+    <mo>⃗</mo>
+  </mover>
 </math>   <span class="docutils literal"><span class="pre">\vec{\imath}</span></span></p></td>
 </tr>
 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>a</mi>
-      </mrow>
-      <mo>ˇ</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>a</mi>
+    </mrow>
+    <mo>ˇ</mo>
+  </mover>
 </math>      <span class="docutils literal">\check{a}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>a</mi>
-      </mrow>
-      <mo>¯</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>a</mi>
+    </mrow>
+    <mo>-</mo>
+  </mover>
 </math>        <span class="docutils literal">\bar{a}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
-  <mrow>
-    <mover>
-      <mrow>
-        <mi>R</mi>
-      </mrow>
-      <mo>⃗</mo>
-    </mover>
-  </mrow>
+  <mover>
+    <mrow>
+      <mi>R</mi>
+    </mrow>
+    <mo>⃗</mo>
+  </mover>
 </math>        <span class="docutils literal">\vec{R}</span></p></td>
 </tr>
 </tbody>
@@ -403,7 +371,7 @@ physical system changes in time.</p>
               <munderover>
                 <mo>∫</mo>
                 <mrow>
-                  <mo>-</mo><mo>∞</mo>
+                  <mo>−</mo><mo>∞</mo>
                 </mrow>
                 <mrow>
                   <mo>∞</mo>
@@ -432,7 +400,7 @@ physical system changes in time.</p>
               <munderover>
                 <mo>∫</mo>
                 <mrow>
-                  <mo>-</mo><mo>∞</mo>
+                  <mo>−</mo><mo>∞</mo>
                 </mrow>
                 <mrow>
                   <mo>∞</mo>
@@ -480,7 +448,7 @@ physical system changes in time.</p>
         <msub>
           <mi>s</mi><mi>δ</mi>
         </msub>
-        <mo stretchy="false">(</mo><mi>x</mi><mo>-</mo><mi>x</mi><mo>'</mo><mo stretchy="false">)</mo>
+        <mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mi>x</mi><mo>'</mo><mo stretchy="false">)</mo>
       </mtd>
     </mtr>
     <mtr>
@@ -498,7 +466,7 @@ physical system changes in time.</p>
         <msub>
           <mi>s</mi><mi>δ</mi>
         </msub>
-        <mo stretchy="false">(</mo><mi>x</mi><mo>-</mo><mi>x</mi><mo>'</mo><mo stretchy="false">)</mo><mi mathvariant="normal">d</mi><mi>x</mi><mo>'</mo>
+        <mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mi>x</mi><mo>'</mo><mo stretchy="false">)</mo><mi mathvariant="normal">d</mi><mi>x</mi><mo>'</mo>
       </mtd>
     </mtr>
   </mtable>
@@ -516,7 +484,7 @@ physical system changes in time.</p>
           <mtable>
             <mtr>
               <mtd>
-                <mo>-</mo><mn>1</mn>
+                <mo>−</mo><mn>1</mn>
               </mtd>
               <mtd>
                 <mi>x</mi><mo>&lt;</mo><mn>0</mn>
diff --git a/docutils/test/functional/input/data/comprehensive-math-test.txt b/docutils/test/functional/input/data/comprehensive-math-test.txt
index 4324709f1..a696789ef 100644
--- a/docutils/test/functional/input/data/comprehensive-math-test.txt
+++ b/docutils/test/functional/input/data/comprehensive-math-test.txt
@@ -136,23 +136,35 @@ Accents
 .. class:: colwidths-auto
 
   =========== =============  =========== =============  ============== ================
-  `\acute{x}` ``\acute{x}``  `\dot{x}`   ``\dot{x}``    `\hat{H}`      ``\hat{H}``
-  `\bar{v}`   ``\bar{v}``    `\ddot{x}`  ``\ddot{x}``   `\mathring{x}` ``\mathring{x}``
-  `\breve{x}` ``\breve{x}``  `\dddot{x}` ``\dddot{x}``  `\tilde{n}`    ``\tilde{n}``
-  `\check{x}` ``\check{x}``  `\grave{x}` ``\grave{x}``  `\vec{R}`      ``\vec{R}``
+  `\acute{x}` ``\acute{x}``  `\dot{t}`   ``\dot{t}``    `\hat{H}`      ``\hat{H}``
+  `\bar{v}`   ``\bar{v}``    `\ddot{t}`  ``\ddot{t}``   `\mathring{x}` ``\mathring{x}``
+  `\breve{x}` ``\breve{x}``  `\dddot{t}` ``\dddot{t}``  `\tilde{n}`    ``\tilde{n}``
+  `\check{x}` ``\check{x}``  `\grave{x}` ``\grave{x}``  `\vec{x}`      ``\vec{x}``
   =========== =============  =========== =============  ============== ================
 
 When adding an accent to an i or j in math, dotless variants can be
 obtained with ``\imath`` and ``\jmath``: `\bar \imath`, `\hat{\jmath}`
+(MathML drops the dot automatically).
+
+For adornment that span multiple symbols, see `top and bottom
+embellishments`_.
+
+Font switches
+-------------
+
+TeX’s *math alphabets* correspond to the
+:t:`mathematical alphanumeric symbols` block in Unicode and the
+"mathvariant" `style attribute`__ in MathML. They are “to be used for
+mathematical variables where style variations are important
+semantically”.
+
+__ https://developer.mozilla.org/en-US/docs/Web/MathML/Attribute
 
-alphabets
----------
 .. class:: colwidths-auto
 
   ===============  ============================  ==========================
   command          example                       result
   ===============  ============================  ==========================
-  ``\boldsymbol``  ``\boldsymbol{\alpha + 3}``   `\boldsymbol{\alpha + 3}`
   ``\mathbf``      ``\mathbf{r}^2=x^2+y^2+z^2``  `\mathbf{r}^2=x^2+y^2+z^2`
   ``\mathbb``      ``\mathbb{R \subset C}``      `\mathbb{R \subset C}`
   ``\mathcal``     ``\mathcal{F}f(x)``           `\mathcal{F}f(x)`
@@ -160,14 +172,40 @@ alphabets
   ``\mathit``      ``\mathit{\Gamma}``           `\mathit{\Gamma}`
   ``\mathrm``      ``s_\mathrm{out}``            `s_\mathrm{out}`
   ``\mathsf``      ``\mathsf x``                 `\mathsf x`
-  ``\mathtt``      ``\mathtt{0.12}``              `\mathtt{0.12}`
+  ``\mathtt``      ``\mathtt{0.12}``             `\mathtt{0.12}`
   ===============  ============================  ==========================
 
-.. with isomath:
-                  'mathbfit': 'bold-italic',        # isomath
-                  'mathsfit': 'sans-serif-italic',  # isomath
-                  'mathsfbfit': 'sans-serif-bold-italic',  # isomath
-   with mathrsfs, ...       'mathscr'
+Additional alphabets are defined in LaTeX packages, e.g.
+
+.. class:: colwidths-auto
+
+  ===========  =============  ======================
+  TeX command  LaTeX package  MathML "mathvariant"
+  ===========  =============  ======================
+  mathbfit     isomath_       bold-italic
+  mathsfit     isomath_       sans-serif-italic
+  mathsfbfit   isomath_       sans-serif-bold-italic
+  mathscr      mathrsfs_      script
+  ===========  =============  ======================
+.. _isomath: https://www.ctan.org/pkg/isomath
+.. _mathrsfs: https://www.ctan.org/pkg/mathrsfs
+
+This can be used to typeset vector symbols in **bold** *italic*
+in line with the International Standard [ISO-80000-2].
+``\mathbfit{r}^2=x^2+y^2+z^2`` becomes
+
+.. math:: \mathbfit{r}^2=x^2+y^2+z^2.
+
+
+
+In contrast to the math alphabet selectors, ``\boldsymbol`` only changes
+the *font weight*. In LaTeX, it can be used to get a bold version of any
+mathematical symbol (for other output formats, results are mixed):
+
+.. math::
+     \boldsymbol{abs(x) \pm \alpha \approx 3 \Gamma \quad \forall x \in R}
+
+
 
 
 Arrows
@@ -201,27 +239,26 @@ Binary operators
 .. class:: colwidths-auto
 
   ================== ====================  ================= ===================  ================== ====================
-  `*`                ``*``                 `\circledast`     ``\circledast``      `\odot`            ``\odot``
-  `+`                ``+``                 `\circledcirc`    ``\circledcirc``     `\ominus`          ``\ominus``
-  `-`                ``-``                 `\circleddash`    ``\circleddash``     `\oplus`           ``\oplus``
-  `:`                ``:``                 `\cup`            ``\cup``             `\oslash`          ``\oslash``
-  `\Cap`             ``\Cap``              `\curlyvee`       ``\curlyvee``        `\otimes`          ``\otimes``
-  `\Cup`             ``\Cup``              `\curlywedge`     ``\curlywedge``      `\pm`              ``\pm``
-  `\amalg`           ``\amalg``            `\dagger`         ``\dagger``          `\rightthreetimes` ``\rightthreetimes``
-  `\ast`             ``\ast``              `\ddagger`        ``\ddagger``         `\rtimes`          ``\rtimes``
-  `\bigcirc`         ``\bigcirc``          `\diamond`        ``\diamond``         `\setminus`        ``\setminus``
-  `\bigtriangledown` ``\bigtriangledown``  `\div`            ``\div``             `\smallsetminus`   ``\smallsetminus``
-  `\bigtriangleup`   ``\bigtriangleup``    `\divideontimes`  ``\divideontimes``   `\sqcap`           ``\sqcap``
-  `\boxdot`          ``\boxdot``           `\dotplus`        ``\dotplus``         `\sqcup`           ``\sqcup``
-  `\boxminus`        ``\boxminus``         `\doublebarwedge` ``\doublebarwedge``  `\star`            ``\star``
-  `\boxplus`         ``\boxplus``          `\gtrdot`         ``\gtrdot``          `\times`           ``\times``
-  `\boxtimes`        ``\boxtimes``         `\intercal`       ``\intercal``        `\triangleleft`    ``\triangleleft``
-  `\bullet`          ``\bullet``           `\leftthreetimes` ``\leftthreetimes``  `\triangleright`   ``\triangleright``
-  `\cap`             ``\cap``              `\lessdot`        ``\lessdot``         `\uplus`           ``\uplus``
-  `\cdot`            ``\cdot``             `\ltimes`         ``\ltimes``          `\vee`             ``\vee``
-  `\centerdot`       ``\centerdot``        `\mp`             ``\mp``              `\veebar`          ``\veebar``
-  `\circ`            ``\circ``                                                    `\wedge`           ``\wedge``
-  ..                                                                              `\wr`              ``\wr``
+  `*`                ``*``                 `\circledast`     ``\circledast``      `\ominus`          ``\ominus``
+  `+`                ``+``                 `\circledcirc`    ``\circledcirc``     `\oplus`           ``\oplus``
+  `-`                ``-``                 `\circleddash`    ``\circleddash``     `\oslash`          ``\oslash``
+  `:`                ``:``                 `\cup`            ``\cup``             `\otimes`          ``\otimes``
+  `\Cap`             ``\Cap``              `\curlyvee`       ``\curlyvee``        `\pm`              ``\pm``
+  `\Cup`             ``\Cup``              `\curlywedge`     ``\curlywedge``      `\rightthreetimes` ``\rightthreetimes``
+  `\amalg`           ``\amalg``            `\dagger`         ``\dagger``          `\rtimes`          ``\rtimes``
+  `\ast`             ``\ast``              `\ddagger`        ``\ddagger``         `\setminus`        ``\setminus``
+  `\bigcirc`         ``\bigcirc``          `\diamond`        ``\diamond``         `\smallsetminus`   ``\smallsetminus``
+  `\bigtriangledown` ``\bigtriangledown``  `\div`            ``\div``             `\sqcap`           ``\sqcap``
+  `\bigtriangleup`   ``\bigtriangleup``    `\divideontimes`  ``\divideontimes``   `\sqcup`           ``\sqcup``
+  `\boxdot`          ``\boxdot``           `\dotplus`        ``\dotplus``         `\star`            ``\star``
+  `\boxminus`        ``\boxminus``         `\doublebarwedge` ``\doublebarwedge``  `\times`           ``\times``
+  `\boxplus`         ``\boxplus``          `\gtrdot`         ``\gtrdot``          `\triangleleft`    ``\triangleleft``
+  `\boxtimes`        ``\boxtimes``         `\intercal`       ``\intercal``        `\triangleright`   ``\triangleright``
+  `\bullet`          ``\bullet``           `\leftthreetimes` ``\leftthreetimes``  `\uplus`           ``\uplus``
+  `\cap`             ``\cap``              `\lessdot`        ``\lessdot``         `\vee`             ``\vee``
+  `\cdot`            ``\cdot``             `\ltimes`         ``\ltimes``          `\veebar`          ``\veebar``
+  `\centerdot`       ``\centerdot``        `\mp`             ``\mp``              `\wedge`           ``\wedge``
+  `\circ`            ``\circ``             `\odot`            ``\odot``           `\wr`              ``\wr``
   ================== ====================  ================= ===================  ================== ====================
 
 
@@ -264,7 +301,7 @@ Letterlike symbols
 `\mho`  ``\mho``    `\complement` ``\complement``  `\gimel`  ``\gimel``   `\hslash`  ``\hslash``
 `\Bbbk` ``\Bbbk``   `\Finv`       ``\Finv``        `\daleth` ``\daleth``  `\imath`   ``\imath``
 `\ell`    ``\ell``  `\Game`       ``\Game``        `\nabla`  ``\nabla``   `\partial` ``\partial``
-`\wp`    ``\wp``                                   
+`\wp`    ``\wp``
 ======= ==========  ============= ===============  ========= ===========  ========== ============
 
 
@@ -365,7 +402,18 @@ Use ``.`` for "empty" delimiters:
 Top and bottom embellishments
 -----------------------------
 
-TODO
+Visually similar to accents_ but generally applied to multiple symbols.
+
+.. class:: colwidths-auto
+
+  ========================== ============================  =========================== =============================
+  `\widetilde{abi}`          ``\widetilde{abi}``           `\widehat{abi}`             ``\widehat{abi}``
+  `\overline{abi}`           ``\overline{abi}``            `\underline{abi}`           ``\underline{abi}``
+  `\overbrace{abi}`          ``\overbrace{abi}``           `\underbrace{abi}`          ``\underbrace{abi}``
+  `\overleftarrow{abi}`      ``\overleftarrow{abi}``       `\underleftarrow{abi}`      ``\underleftarrow{abi}``
+  `\overrightarrow{abi}`     ``\overrightarrow{abi}``      `\underrightarrow{abi}`     ``\underrightarrow{abi}``
+  `\overleftrightarrow{abi}` ``\overleftrightarrow{abi}``  `\underleftrightarrow{abi}` ``\underleftrightarrow{abi}``
+  ========================== ============================  =========================== =============================
 
 Extensible arrows
 -----------------
@@ -416,47 +464,65 @@ internal LaTeX2MathML
 
 * Shorthands for combined named operators
 
-  ===============  =================
-  `\liminf`        ``\liminf``
-  `\limsup`        ``\limsup``
-  `\injlim`        ``\injlim``
-  `\projlim`       ``\projlim``
-  `\varinjlim`     ``\varinjlim``
-  `\varliminf`     ``\varliminf``
-  `\varlimsup`     ``\varlimsup``
-  `\varprojlim`    ``\varprojlim``
-  ===============  =================
+  ==========  ============  =============  ===============  ==================
+  `\liminf`   ``\liminf``   `\varliminf`   ``\varliminf``   `\underline{\lim}`
+  `\limsup`   ``\limsup``   `\varlimsup`   ``\varlimsup``   `\overline{\lim}`
+  `\injlim`   ``\injlim``   `varinjlim`    ``\varinjlim``
+  `\projlim`  ``\projlim``  `varprojlim`   ``\varprojlim``
+  ==========  ============  =============  ===============  ==================
 
 * Implement ``\circledS``? (in short-math-guide.pdf but not in mathematical Unicode characters)
 
-  ``\widetilde{xxx}``
-  ``\widehat{xxx}``
-
 
 Tests
 ==========
 
+Font changes
+------------
 
-LICR macros in different alphabets:
+Math alphabet macros change the default alphabet ("mathvariant" in
+MathML), leaving some symbols unchanged:
 
-.. math::
+:normal: `abs(x) \pm \alpha \approx 3 \Gamma  \quad \forall x \in R`
+:mathrm: `\mathrm{abs(x) \pm \alpha \approx 3 \Gamma  \quad \forall x \in R}`
+:mathit: `\mathit{abs(x) \pm \alpha \approx 3 \Gamma  \quad \forall x \in R}`
+:mathsf: `\mathsf{abs(x) \pm \alpha \approx 3 \Gamma  \quad \forall x \in R}`
+:mathbb: `\mathbb{abs(x) \pm \alpha \approx 3 \Gamma  \quad \forall x \in R}`
+:mathbf: `\mathbf{abs(x) \pm \alpha \approx 3 \Gamma  \quad \forall x \in R`
 
-   \text{normal: } &
-     abs(x) \pm \alpha \approx \Gamma \forall x \in R \bigstar \\
-   \text{mathrm: } &
-     \mathrm{abs(x) \pm \alpha \approx \Gamma \forall x \in R \bigstar} \\
-   \text{mathit: } &
-     \mathit{abs(x) \pm \alpha \approx \Gamma \forall x \in R \bigstar} \\
-   \text{mathsf: } &
-     \mathsf{abs(x) \pm \alpha \approx \Gamma \forall x \in R \bigstar} \\
-   \text{mathbb: } &
-     \mathbb{abs(x) \pm \alpha \approx \Gamma \forall x \in R \bigstar} \\
-   \text{mathbf: } &
-     \mathbf{abs(x) \pm \alpha \approx \Gamma \forall x \in R \bigstar} \\
-   \text{boldsymbol: } &
-     \boldsymbol{abs(x) \pm \alpha \approx \Gamma \forall x \in R \bigstar}
-
-All blackboard-bold characters:
+Unicode supports the following blackboard-bold characters:
 `\mathbb{a \ldots z A \ldots Z 0 \ldots 9
 \mathbb\Gamma \mathbb{\Pi} \mathbb {\Sigma}\mathbb\gamma \mathbb\pi}`.
 
+The package mathrsfs_ (and some drop-in replacements) define the ``\mathscr``
+macro that selects a differently shaped "script" alphabet.
+Compare `\mathscr{A, B, …, Z, a, b, …, z}` 
+with `\mathcal{A, B, …, Z, a, b, …, z}`.
+
+.. _rsfs: https://ctan.org/pkg/mathrsfs
+
+Inferred <mrow>s in MathML
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The elements <msqrt>, <mstyle>, <merror>, <mpadded>, <mphantom>, <menclose>,
+<mtd, mscarry>, and <math> treat their contents as a single inferred mrow
+formed from all their children.
+
+.. math:: a = \sqrt 2, b = \sqrt{1+x^2}, c = \sqrt\frac{sin(x)}{23}
+
+inline: :math:`a = \sqrt 2, b = \sqrt{1+x^2}, c = \sqrt\frac{sin(x)}{23}`.
+
+Accents vs. embellishments
+--------------------------
+
+MathML drops dots on "i" and "j" with accents:
+
+.. math:: \vec i \ne \overrightarrow i 
+          \text{ and } \vec\lim \ne \overrightarrow\lim.
+
+Accents should be nearer to the base (in Firefox 78, it's vice versa!):
+
+.. math:: \vec a \vec l \ne \overrightarrow a \overrightarrow l
+
+          \bar a \bar l \ne \overline a \overline l
+