MathML: remove unrequired <mrow>s, support more commands.

Support additional commands from the AMS math-guide.

Remove <mrow>, if it is single child and the parent inferres an mrow
or if it has only one child element.

tex_number(): do not return trailing delimiter.

Use class "mathscr" instead of hard-codes font name for \mathscr.

git-svn-id: https://svn.code.sf.net/p/docutils/code/trunk@8756 929543f6-e4f2-0310-98a6-ba3bd3dd1d04

6 files changed, 220 insertions, 264 deletions

diff --git a/docutils/docs/user/mathematics.txt b/docutils/docs/user/mathematics.txt
index 61f324a1d..0132015b5 100644
--- a/docutils/docs/user/mathematics.txt
+++ b/docutils/docs/user/mathematics.txt
@@ -118,7 +118,7 @@ The "narrow" accents are intended for a single-letter base.
 .. class:: colwidths-auto
 
   =========== =============  =========== =============  ============== ================
-  `\acute{x}` ``\acute{x}``  `\dot{t}`   ``\dot{t}``    `\hat{H}`      ``\hat{H}``
+  `\acute{x}` ``\acute{x}``  `\dot{t}`   ``\dot{t}``    `\hat{x}`      ``\hat{x}``
   `\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}``
@@ -190,28 +190,22 @@ Pairing delimiters
 
   =============== =================   ========================= ===========================
   `( )`           ``( )``             `\langle \rangle`         ``\langle \rangle``
-  `[ ]`           ``[ ]``             `\lceil \rceil`           ``\lceil \rceil``
+  `[ ]`           ``[ ]``             `\lceil  \rceil`          ``\lceil \rceil``
   `\{ \}`         ``\{ \}``           `\lfloor \rfloor`         ``\lfloor \rfloor``
-  `\lvert \rvert` ``\lvert \rvert``   `\lVert \rVert`           ``\lVert \rVert``
+  `\lvert \rvert` ``\lvert \rvert``   `\lgroup \rgroup`         ``\lgroup \rgroup``
+  `\lVert \rVert` ``\lVert \rVert``   `\lmoustache \rmoustache` ``\lmoustache \rmoustache``
   =============== =================   ========================= ===========================
 
-.. The "math-guide" also lists macros for parts of extensible delimiters:
-
-   =============  =  =============  =  ============  =
-   `\lmoustache`  ⎰  `\rmoustache`  ⎱  `\bracevert`  ⎪
-   `\lgroup`      ⟮  `\rgroup`      ⟯  `\arrowvert`  ⏐
-   ..                                  `\Arrowvert`  ‖
-   =============  =  =============  =  ============  =
 
 Nonpairing delimiters
 ~~~~~~~~~~~~~~~~~~~~~
 .. class:: colwidths-auto
 
-  ===========  ===========================
-  `|`  ``|``   `\vert`      ``\vert``
-  `\|` ``\|``  `\Vert`      ``\Vert``
-  `/`  ``/``   `\backslash` ``\backslash``
-  ===========  ===========================
+  ==== ======  ============ ==============  ============ ==============
+  `|`  ``|``   `\vert`      ``\vert``       `\arrowvert` ``\arrowvert``
+  `\|` ``\|``  `\Vert`      ``\Vert``       `\Arrowvert` ``\Arrowvert``
+  `/`  ``/``   `\backslash` ``\backslash``  `\bracevert` ``\bracevert``
+  ==== ======  ============ ==============  ============ ==============
 
 The use of ``|`` and ``\|`` for pairs of vertical bars may produce
 incorrect spacing, e.g., ``|k|=|-k|`` produces `|k| = |−k|` and
@@ -229,6 +223,37 @@ Vertical Arrows
   `\updownarrow` ``\updownarrow``  `\Updownarrow` ``\Updownarrow``
   ===============================  ======================================
 
+Functions (named operators)
+---------------------------
+.. class:: colwidths-auto
+
+  ========= ===========  ========= ===========  ============= ================
+  `\arccos` ``\arccos``  `\gcd`    ``\gcd``     `\Pr`         ``\Pr``
+  `\arcsin` ``\arcsin``  `\hom`    ``\hom``     `\projlim`    ``\projlim``
+  `\arctan` ``\arctan``  `\inf`    ``\inf``     `\sec`        ``\sec``
+  `\arg`    ``\arg``     `\injlim` ``\injlim``  `\sin`        ``\sin``
+  `\cos`    ``\cos``     `\ker`    ``\ker``     `\sinh`       ``\sinh``
+  `\cosh`   ``\cosh``    `\lg`     ``\lg``      `\sup`        ``\sup``
+  `\cot`    ``\cot``     `\lim`    ``\lim``     `\tan`        ``\tan``
+  `\coth`   ``\coth``    `\liminf` ``\liminf``  `\tanh`       ``\tanh``
+  `\csc`    ``\csc``     `\limsup` ``\limsup``  `\varlimsup`  ``\varlimsup``
+  `\deg`    ``\deg``     `\ln`     ``\ln``      `\varliminf`  ``\varliminf``
+  `\det`    ``\det``     `\log`    ``\log``     `\varprojlim` ``\varprojlim``
+  `\dim`    ``\dim``     `\max`    ``\max``     `\varinjlim`  ``\varinjlim``
+  `\exp`    ``\exp``     `\min`    ``\min``
+  ========= ===========  ========= ===========  ============= ================
+
+Named operators outside the above list can be typeset with
+``\operatorname{name}``, e.g.
+
+.. math:: \operatorname{sgn}(-3) = -1.
+
+The ``\DeclareMathOperator`` command can only be used in the
+`LaTeX preamble`_.
+
+.. _LaTeX preamble: latex.html#latex-preamble
+
+
 Greek letters
 -------------
 
@@ -243,16 +268,16 @@ formulas and not supported by LaTeX.
 
   ========== ============  ========== ============  ========== ============  ============== ===============
   `\Gamma`   ``\Gamma``    `\alpha`   ``\alpha``    `\mu`      ``\mu``       `\omega`       ``\omega``
-  `\Delta`   ``\Delta``    `\beta`    ``\beta``     `\nu`      ``\nu``       `\backepsilon` ``\backepsilon``
-  `\Lambda`  ``\Lambda``   `\gamma`   ``\gamma``    `\xi`      ``\xi``       `\digamma`     ``\digamma``
-  `\Omega`   ``\Omega``    `\delta`   ``\delta``    `\pi`      ``\pi``       `\varepsilon`  ``\varepsilon``
-  `\Phi`     ``\Phi``      `\epsilon` ``\epsilon``  `\rho`     ``\rho``      `\varkappa`    ``\varkappa``
-  `\Pi`      ``\Pi``       `\zeta`    ``\zeta``     `\sigma`   ``\sigma``    `\varphi`      ``\varphi``
-  `\Psi`     ``\Psi``      `\eta`     ``\eta``      `\tau`     ``\tau``      `\varpi`       ``\varpi``
-  `\Sigma`   ``\Sigma``    `\theta`   ``\theta``    `\upsilon` ``\upsilon``  `\varrho`      ``\varrho``
-  `\Theta`   ``\Theta``    `\iota`    ``\iota``     `\phi`     ``\phi``      `\varsigma`    ``\varsigma``
-  `\Upsilon` ``\Upsilon``  `\kappa`   ``\kappa``    `\chi`     ``\chi``      `\vartheta`    ``\vartheta``
-  `\Xi`      ``\Xi``       `\lambda`  ``\lambda``   `\psi`     ``\psi``
+  `\Delta`   ``\Delta``    `\beta`    ``\beta``     `\nu`      ``\nu``       `\digamma`     ``\digamma``
+  `\Lambda`  ``\Lambda``   `\gamma`   ``\gamma``    `\xi`      ``\xi``       `\backepsilon` ``\backepsilon``
+  `\Phi`     ``\Phi``      `\delta`   ``\delta``    `\pi`      ``\pi``       `\varepsilon`  ``\varepsilon``
+  `\Pi`      ``\Pi``       `\epsilon` ``\epsilon``  `\rho`     ``\rho``      `\varkappa`    ``\varkappa``
+  `\Psi`     ``\Psi``      `\zeta`    ``\zeta``     `\sigma`   ``\sigma``    `\varphi`      ``\varphi``
+  `\Sigma`   ``\Sigma``    `\eta`     ``\eta``      `\tau`     ``\tau``      `\varpi`       ``\varpi``
+  `\Theta`   ``\Theta``    `\theta`   ``\theta``    `\upsilon` ``\upsilon``  `\varrho`      ``\varrho``
+  `\Upsilon` ``\Upsilon``  `\iota`    ``\iota``     `\phi`     ``\phi``      `\varsigma`    ``\varsigma``
+  `\Xi`      ``\Xi``       `\kappa`   ``\kappa``    `\chi`     ``\chi``      `\vartheta`    ``\vartheta``
+  `\Omega`   ``\Omega``    `\lambda`  ``\lambda``   `\psi`     ``\psi``
   ========== ============  ========== ============  ========== ============  ============== ===============
 
 __ http://mirrors.ctan.org/macros/latex/contrib/isomath/isomath.html#table-2
@@ -262,20 +287,21 @@ Letterlike symbols
 .. class:: colwidths-auto
 
 ========== ============  ============= ===============  ========= ===========  =========== =============
-`\aleph`   ``\aleph``    `\forall`     ``\forall``      `\hbar`   ``\hbar``    `\ell`      ``\ell``   
-`\beth`    ``\beth``     `\complement` ``\complement``  `\hslash` ``\hslash``  `\wp`       ``\wp``      
-`\gimel`   ``\gimel``    `\exists`     ``\exists``      `\Im`     ``\Im``      `\Re`       ``\Re``      
+`\aleph`   ``\aleph``    `\forall`     ``\forall``      `\hbar`   ``\hbar``    `\ell`      ``\ell``
+`\beth`    ``\beth``     `\complement` ``\complement``  `\hslash` ``\hslash``  `\wp`       ``\wp``
+`\gimel`   ``\gimel``    `\exists`     ``\exists``      `\Im`     ``\Im``      `\Re`       ``\Re``
 `\daleth`  ``\daleth``   `\Finv`       ``\Finv``        `\imath`  ``\imath``   `\circledR` ``\circledR``
 `\partial` ``\partial``  `\Game`       ``\Game``        `\Bbbk`   ``\Bbbk``    `\circledS` ``\circledS``
-`\eth`     ``\eth``                                                            `\mho`      ``\mho``     
+`\eth`     ``\eth``                                                            `\mho`      ``\mho``
 ========== ============  ============= ===============  ========= ===========  =========== =============
 
 
 Mathematical Alphabets
 ----------------------
 
-For mathematical variables where style variations are important semantically,
-select an appropriate *math alphabet* [#]_.
+Mathematical alphabets select a combination of font attributes (shape,
+weight, family) [#]_. They are intended for mathematical variables where
+style variations are important semantically.
 
 .. class:: colwidths-auto
 
@@ -321,6 +347,11 @@ in line with the International Standard [ISO-80000-2].
 
    .. math:: \mathbfit{r}^2=x^2+y^2+z^2.
 
+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}`.
+
 
 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
@@ -350,46 +381,18 @@ Miscellaneous symbols
 ==================== ======================  ================ ==================  ================= ===================
 
 
-Named operators
----------------
-.. class:: colwidths-auto
-
-  ========= ===========  ========= ===========  ============= ================
-  `\arccos` ``\arccos``  `\gcd`    ``\gcd``     `\Pr`         ``\Pr``
-  `\arcsin` ``\arcsin``  `\hom`    ``\hom``     `\projlim`    ``\projlim``
-  `\arctan` ``\arctan``  `\inf`    ``\inf``     `\sec`        ``\sec``
-  `\arg`    ``\arg``     `\injlim` ``\injlim``  `\sin`        ``\sin``
-  `\cos`    ``\cos``     `\ker`    ``\ker``     `\sinh`       ``\sinh``
-  `\cosh`   ``\cosh``    `\lg`     ``\lg``      `\sup`        ``\sup``
-  `\cot`    ``\cot``     `\lim`    ``\lim``     `\tan`        ``\tan``
-  `\coth`   ``\coth``    `\liminf` ``\liminf``  `\tanh`       ``\tanh``
-  `\csc`    ``\csc``     `\limsup` ``\limsup``  `\varlimsup`  ``\varlimsup``
-  `\deg`    ``\deg``     `\ln`     ``\ln``      `\varliminf`  ``\varliminf``
-  `\det`    ``\det``     `\log`    ``\log``     `\varprojlim` ``\varprojlim``
-  `\dim`    ``\dim``     `\max`    ``\max``     `\varinjlim`  ``\varinjlim``
-  `\exp`    ``\exp``     `\min`    ``\min``
-  ========= ===========  ========= ===========  ============= ================
-
-Named operators outside the above list can be typeset with
-``\operatorname{name}``, e.g.
-
-.. math:: \operatorname{sgn}(-3) = -1.
-
-The ``\DeclareMathOperator`` command can only be used in the
-`LaTeX preamble`_.
-
-.. _LaTeX preamble: latex.html#latex-preamble
-
 Punctuation
 -----------
 .. class:: colwidths-auto
 
-======== ===============
-`\colon` ``\colon`` [#]_
-`\cdots` ``\cdots``
-`\ddots` ``\ddots``
-`\ddots` ``\ddots``
-======== ===============
+=== =====  ======== ===============  ======== ==========
+`.` ``.``  `!`      ``!``            `?`      ``?``
+`/` ``/``  `\colon` ``\colon`` [#]_  `\dotsb` ``\dotsb``
+`|` ``|``  `\cdots` ``\cdots``       `\dotsc` ``\dotsc``
+`'` ``'``  `\ddots` ``\ddots``       `\dotsi` ``\dotsi``
+`;` ``;``  `\ldots` ``\ldots``       `\dotsm` ``\dotsm``
+`:` ``:``  `\vdots` ``\vdots``       `\dotso` ``\dotso``
+=== =====  ======== ===============  ======== ==========
 
 .. [#] Punctuation (not ratio):
        Compare spacing in `a\colon b\to c` to `a:b = c`.
@@ -582,6 +585,9 @@ Result:
 
 .. TODO: small matrices, matrices with delimiters built in?
 
+   The environments pmatrix, bmatrix, Bmatrix, vmatrix, and Vmatrix have
+   (respectively) ( ), [ ], { }, | |, and k k delimiters built in.
+
 For piecewise function definitions there is a cases environment:
 
 .. math::
@@ -596,19 +602,22 @@ Horizontal space
 
 .. class:: colwidths-auto
 
-  =================  ==================  =============
-  :m:`|\qquad|`      ``|\qquad|``        2 em
-  :m:`|\quad|`       ``|\quad|``         1 em
-  :m:`|\;|`          ``|\;|``            thick
-  :m:`|\ |`          ``|\ |``            standard
-  :m:`|~|`           ``|~|``             non-break
-  :m:`|\:|`          ``|\:|``            medium
-  :m:`|\,|`          ``|\,|``            thin
-  :m:`|  |`          ``|  |``            none
-  :m:`|\!|`          ``|\!|``            thin negative
-  `|\hspace{1ex}|`   ``|\hspace{1ex}|``  custom
-  =================  ==================  =============
-
+  =====================  ========  =======================
+  :m:`|\qquad|`                    ``|\qquad|`` (2em)
+  :m:`|\quad|`                     ``|\quad|``  (1em)
+  :m:`|~|`               ``|~|``   ``|\nobreakspace|``
+  :m:`|\ |`              ``|\ |``  escaped space
+  :m:`|\;|`              ``|\;|``  ``|\thickspace|``
+  :m:`|\:|`              ``|\:|``  ``|\medspace|``
+  :m:`|\,|`              ``|\,|``  ``|\thinspace|``
+  :m:`|  |`              ``|  |``  regular space (ignored)
+  :m:`|\!|`              ``|\!|``  ``|\negthinspace|``
+  :m:`|\negmedspace|`              ``|\negmedspace|``
+  :m:`|\negthickspace|`            ``|\negthickspace|``
+  `|\hspace{1ex}|`                 ``|\hspace{1ex}|``
+  =====================  ========  =======================
+
+.. TODO: \phantom \hphantom, \vphantom
 
 Roots and Fractions
 -------------------
@@ -623,6 +632,8 @@ Roots and Fractions
   ``\frac``  ``\frac{1}{1-x}``       `\frac{1}{1-x}`
   =========  ====================  ==================
 
+.. TODO: \dfrac, \tfrac, \binom, \dbinom, \tbinom
+
 Text
 ====
 
@@ -638,22 +649,11 @@ Whitespace is kept inside the argument:
 
 Currently, math in text is not supported by LaTeX2MathML.
 
+.. TODO: Math inside text: ``n - 1 \text{if $n$ is odd}``.
 
-ToDo
-====
-
-internal LaTeX2MathML
-
-* Math inside text: ``n - 1 \text{if $n$ is odd}``.
-* Remove circular refs.
-* Document ``\circledS``, \circledR, implement other characters
-  in the short-math-guide.pdf but not in the
-  Unicode `Mathematical Character Repertoire`__
-
-__ http://www.unicode.org/reports/tr25/
 
 Tests
-==========
+=====
 
 Font changes
 ------------
@@ -670,14 +670,7 @@ MathML), leaving some symbols unchanged:
 
 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
+\mathbb\Gamma \mathbb{\Pi} \mathbb {\Sigma} \mathbb\gamma \mathbb\pi}`.
 
 Inferred <mrow>s in MathML
 ~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -707,3 +700,5 @@ Sub- and superscript may be given in any order:
 `x_i^j = x^j_i` and `\int_0^1 = \int^1_0`.
 
 Double exponent: `x^{10}^4`, `r_T_\mathrm{in}` and `x_i^n^2`.
+
+Binary vs. unary minus operator: `a - b = -c`
diff --git a/docutils/docutils/utils/math/latex2mathml.py b/docutils/docutils/utils/math/latex2mathml.py
index 0793fa4bf..fda5d1792 100644
--- a/docutils/docutils/utils/math/latex2mathml.py
+++ b/docutils/docutils/utils/math/latex2mathml.py
@@ -57,7 +57,7 @@ greek_capitals = {
     'Gamma':u'\u0393', 'Lambda':u'\u039b'}
 
 # functions -> <mi>
-functions = dict((name, name) for name in 
+functions = dict((name, name) for name in
                  ('arccos', 'arcsin', 'arctan', 'arg', 'cos',  'cosh',
                   'cot',    'coth',   'csc',    'deg', 'det',  'dim',
                   'exp',    'gcd',    'hom',    'inf', 'ker',  'lg',
@@ -73,7 +73,7 @@ functions.update({# functions with a space in the name
                   'operatorname': None})
 
 # function with limits, use <mo> to allow "movablelimits" attribute
-functions_with_limits = dict((name, name) for name in 
+functions_with_limits = dict((name, name) for name in
                              ('lim', 'sup', 'inf', 'max', 'min'))
 
 # math font selection -> <mi mathvariant=...> or <mstyle mathvariant=...>
@@ -114,10 +114,16 @@ operators.update({# negated symbols without pre-composed Unicode character
                   'nsubseteqq': u'\u2AC5\u0338', # ⫅̸
                   'nsupseteqq': u'\u2AC6\u0338', # ⫆̸
                   # alias commands:
-                  'lvert': u'|',      # pairing delimiters
-                  'lVert': u'\u2016', # ‖
-                  'rvert': u'|',
-                  'rVert': u'\u2016',
+                  'lvert':      u'|',      # left  |
+                  'lVert':      u'\u2016', # left  ‖
+                  'rvert':      u'|',      # right |
+                  'rVert':      u'\u2016', # right ‖
+                  'Arrowvert':  u'\u2016', # ‖
+                  'dotsb':      u'\u22ef', # ⋯ with binary operators/relations
+                  'dotsc':      u'\u2026', # … with commas
+                  'dotsi':      u'\u22ef', # ⋯ with integrals
+                  'dotsm':      u'\u22ef', # ⋯ multiplication dots
+                  'dotso':      u'\u2026', # … other dots
                  })
 
 # special cases
@@ -132,14 +138,14 @@ small_operators = {# mathsize='75%'
                    'shortparallel':  u'\u2225', # ∥
                    'nshortmid':      u'\u2224', # ∤
                    'nshortparallel': u'\u2226', # ∦
-                   'smallfrown': u'\u2322', # ⌢ FROWN
-                   'smallsmile': u'\u2323', # ⌣ SMILE
-                   'smallint':   u'\u222b', # ∫ INTEGRAL
+                   'smallfrown':     u'\u2322', # ⌢ FROWN
+                   'smallsmile':     u'\u2323', # ⌣ SMILE
+                   'smallint':       u'\u222b', # ∫ INTEGRAL
                   }
 
 # Operators and functions with limits
-# over/under in display formulas and in index position inline
-sumintprod = [operators[name] for name in
+# above/below in display formulas and in index position inline
+with_limits = [operators[name] for name in
               ('coprod', 'fatsemi', 'fint', 'iiiint', 'iiint',
                'iint', 'int', 'oiint', 'oint', 'ointctrclockwise',
                'prod', 'sqint', 'sum', 'varointclockwise',
@@ -249,11 +255,6 @@ mathbb = {u'Γ': u'\u213E',    # ℾ
           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
          }
 
 
@@ -369,12 +370,6 @@ class math(object):
 # >>> math(CLASS='bold').xml_starttag()
 # '<math class="bold">'
 
-class mrow(math):
-    """Group sub-expressions as a horizontal row."""
-
-# >>> mrow(displaystyle='false')
-# mrow(displaystyle='false')
-
 class mtable(math): pass
 
 # >>> mtable(displaystyle='true')
@@ -382,13 +377,41 @@ class mtable(math): pass
 # >>> math(mtable(displaystyle='true')).toprettyxml()
 # '<math>\n  <mtable displaystyle="true">\n  </mtable>\n</math>'
 
+class mrow(math):
+    """Group sub-expressions as a horizontal row."""
+
+    def close(self):
+        """Close element and return first non-full parent or None.
+
+        Remove <mrow>, if it is single child and the parent inferres an mrow
+        or if it has only one child element.
+        """
+        parent = self.parent
+        if isinstance(parent, MathRowInferred) and parent.nchildren == 1:
+            parent.nchildren = None
+            parent.children = self.children
+            return parent.close()
+        if len(self) == 1:
+            try:
+                parent.children[parent.children.index(self)] = self.children[0]
+            except (AttributeError, ValueError):
+                return self.children[0]
+        return super(mrow, self).close()
+
+# >>> mrow(displaystyle='false')
+# mrow(displaystyle='false')
+
 # 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
+class MathRowInferred(math):
+    """Base class for elements treating content as a single inferred mrow."""
+class mtr(MathRowInferred): pass
+class mtd(MathRowInferred): pass
+class mstyle(MathRowInferred):
+    nchildren = 1
+class msqrt(MathRowInferred):
+    nchildren = 1
 
 class MathToken(math):
     """Token Element: contains data instead of children.
@@ -511,23 +534,27 @@ def tex_cmdname(string):
 # ('', '')
 
 def tex_number(string):
-    """Return first number literal and remainder of `string`.
+    """Return leading number literal and remainder of `string`.
 
     >>> tex_number('123.4')
     ('123.4', '')
 
     """
-    m = re.match(r'([0-9.,]+)(.*)', string)
+    m = re.match(r'([0-9.,]*[0-9]+)(.*)', string)
     if m is None:
         return '', string
     return m.group(1), m.group(2)
 
 # Test:
 #
-# >>> tex_number(' 123.4')
-# ('', ' 123.4')
-# >>> tex_number('23,400')
-# ('23,400', '')
+# >>> tex_number(' 23.4b') # leading whitespace -> no number
+# ('', ' 23.4b')
+# >>> tex_number('23,400/2') # comma separator included
+# ('23,400', '/2')
+# >>> tex_number('23. 4/2') # trailing separator not included
+# ('23', '. 4/2')
+# >>> tex_number('4, 2') # trailing separator not included
+# ('4', ', 2')
 # >>> tex_number('1 000.4')
 # ('1', ' 000.4')
 
@@ -650,15 +677,15 @@ def parse_latex_math(node, string):
         elif c.isdigit():
             number, string = tex_number(string)
             node = node.append(mn(c+number))
-        elif c in "/()[]|":
-            node = node.append(mo(c, stretchy='false'))
-        # use dedicated mathematical operator characters
         elif c in anomalous_chars:
+            # characters with a special meaning in LaTeX math mode
             node = node.append(mo(anomalous_chars[c]))
+        elif c in "/()[]|":
+            node = node.append(mo(c, stretchy='false'))
         elif c in "+*=<>,.!?';@":
             node = node.append(mo(c))
         else:
-            raise SyntaxError(u'Illegal character: "%s"' % c)
+            raise SyntaxError(u'Unsupported character: "%s"' % c)
     return node
 
 # Test:
@@ -673,6 +700,8 @@ def parse_latex_math(node, string):
 # math(msqrt(mn('2')), mo('≠'), mn('3'))
 # >>> parse_latex_math(math(), '\\sqrt{2 + 3} < 3')
 # math(msqrt(mn('2'), mo('+'), mn('3')), mo('<'), mn('3'))
+# >>> parse_latex_math(math(), '\\sqrt[3]{2 + 3}')
+# math(mroot(mrow(mn('2'), mo('+'), mn('3')), mn('3')))
 # >>> parse_latex_math(math(), '\max_x') # function takes limits
 # math(munder(mi('max', movablelimits='true'), mi('x')))
 # >>> parse_latex_math(math(), 'x^j_i') # ensure correct order: base, sub, sup
@@ -701,10 +730,10 @@ def handle_cmdname(name, node, string):
 
     if name in letters:
         if name in greek_capitals:
-            node = node.append(mi(greek_capitals[name], CLASS='capital-greek'))
             # upright in "TeX style" but MathML sets them italic ("ISO style").
             # CSS styling does not change the font style in Firefox 78.
             # Use 'mathvariant="normal"'?
+            node = node.append(mi(greek_capitals[name], CLASS='capital-greek'))
         else:
             node = node.append(mi(letters[name]))
         return node, string
@@ -718,7 +747,7 @@ def handle_cmdname(name, node, string):
             new_node = mi(arg, mathvariant='normal')
         else:
             new_node = mi(functions[name])
-        # compound function symbols:
+        # embellished function names:
         if name == 'varliminf':    # \underline\lim
             new_node = munder(new_node, mo(u'_'))
         elif name == 'varlimsup':  # \overline\lim
@@ -738,36 +767,27 @@ def handle_cmdname(name, node, string):
     if name in math_alphabets:
         arg, remainder = tex_token(string)
         if arg[0] == '\\':
-            if name == 'mathbb':
-                # mathvariant="double-struck" is ignored for Greek letters
-                # (tested in Firefox 78). Use literal Unicode characters.
-                arg = mathbb.get(arg, arg)
-            # convert single letters (so they can be set with <mi>)
+            # convert single letters (so the isalpha() test below works).
             arg = letters.get(arg[1:], arg)
-
+        if name == 'mathbb':
+            # mathvariant="double-struck" is ignored for Greek letters
+            # (tested in Firefox 78). Use literal Unicode characters.
+            arg = mathbb.get(arg, arg)
         if name == 'boldsymbol':
             attributes = {'style': 'font-weight: bold'}
         else:
             attributes = {'mathvariant': math_alphabets[name]}
         if name == 'mathscr':
-            # alternative script letter shapes
-            attributes['style'] = 'font-family: STIX'
+            attributes['class'] = 'mathscr'
 
-        # one symbol (single letter, name, or number)
-        if arg.isalpha():
+        # one symbol (single letter, name, or ⅀)
+        if arg.isalpha() or arg == u'\u2140':
             node = node.append(mi(arg, **attributes))
             return node, remainder
-        if arg.replace('.', '').replace(',', '').isdigit():
-            node = node.append(mn(arg, **attributes))
-            return node, remainder
-        if len(arg) == 1 and arg != '{':
-            node = node.append(mo(arg, **attributes))
-            return node, remainder
-
         # Wrap in <style>
         style = mstyle(**attributes)
         node.append(style)
-        return style, string[1:] # take of the opening '{', <mrow> is inferred
+        return style, string
 
 
     # operator, fence, or separator  ->  <mo>
@@ -798,7 +818,7 @@ def handle_cmdname(name, node, string):
             row = mrow()
             node.append(row)
             node = row
-        if delimiter: # may be empty (source '.')
+        if delimiter: # may be empty
             node.append(mo(delimiter))
         if name == 'right':
             node = node.close()
@@ -813,7 +833,6 @@ def handle_cmdname(name, node, string):
         return node, string
 
     # arbitrary text (usually comments)  ->  <mtext>
-
     if name in ('text', 'mbox', 'textrm'):
         arg, string = tex_token(string)
         text = re.sub('(^ | $)', u'\u00a0', arg)
@@ -821,7 +840,6 @@ def handle_cmdname(name, node, string):
         return node, string
 
     # horizontal space -> <mspace>
-
     if name in spaces:
         node = node.append(mspace(width='%s'%spaces[name]))
         return node, string
@@ -835,18 +853,14 @@ def handle_cmdname(name, node, string):
     # ==================================
 
     if name == 'sqrt':
-        # TODO: optional arg -> <mroot> <mn>2</mn> <mn>3</mn> </mroot>
-        degree, string = tex_optarg(string)
-        if degree:
+        radix, string = tex_optarg(string)
+        if radix:
             indexnode = mrow()
-            parse_latex_math(indexnode, degree)
             new_node = mroot(indexnode, switch=True)
+            parse_latex_math(indexnode, radix)
+            indexnode.close()
         else:
             new_node = msqrt()
-            if string.startswith('{'): # argument is a group
-                string = string[1:] # mrow implied, skip opening bracket
-            else: # no group, enclose only one element
-                new_node.nchildren = 1
         node.append(new_node)
         return new_node, string
 
@@ -977,8 +991,7 @@ def handle_script_or_limit(node, c):
             new_node = msubsup(*child.children, switch=True)
         elif isinstance(child, mover):
             new_node = munderover(*child.children, switch=True)
-        # elif isinstance(child, MathToken) and child.data in sumintprod:
-        elif getattr(child, 'data', '') in sumintprod:
+        elif getattr(child, 'data', '') in with_limits:
             child.attributes['movablelimits'] = 'true'
             new_node = munder(child)
         else:
@@ -988,7 +1001,7 @@ def handle_script_or_limit(node, c):
             new_node = msubsup(*child.children)
         elif isinstance(child, munder):
             new_node = munderover(*child.children)
-        elif isinstance(child, MathToken) and child.data in sumintprod:
+        elif getattr(child, 'data', '') in with_limits:
             child.attributes['movablelimits'] = 'true'
             new_node = mover(child)
         else:
diff --git a/docutils/docutils/utils/math/tex2unichar.py b/docutils/docutils/utils/math/tex2unichar.py
index 52d990199..3630793e5 100644
--- a/docutils/docutils/utils/math/tex2unichar.py
+++ b/docutils/docutils/utils/math/tex2unichar.py
@@ -295,6 +295,7 @@ mathord = {
     'angle': u'\u2220', # ∠ ANGLE
     'aquarius': u'\u2652', # ♒ AQUARIUS
     'aries': u'\u2648', # ♈ ARIES
+    'arrowvert': u'\u23d0', # ⏐ VERTICAL LINE EXTENSION
     'ast': u'*', # * ASTERISK
     'backepsilon': u'\u03f6', # ϶ GREEK REVERSED LUNATE EPSILON SYMBOL
     'backprime': u'\u2035', # ‵ REVERSED PRIME
@@ -307,6 +308,7 @@ mathord = {
     'blacksquare': u'\u25fc', # ◼ BLACK MEDIUM SQUARE
     'bot': u'\u22a5', # ⊥ UP TACK
     'boy': u'\u2642', # ♂ MALE SIGN
+    'bracevert': u'\u23aa', # ⎪ CURLY BRACKET EXTENSION
     'cancer': u'\u264b', # ♋ CANCER
     'capricornus': u'\u2651', # ♑ CAPRICORN
     'cdots': u'\u22ef', # ⋯ MIDLINE HORIZONTAL ELLIPSIS
@@ -347,6 +349,7 @@ mathord = {
     'leftturn': u'\u21ba', # ↺ ANTICLOCKWISE OPEN CIRCLE ARROW
     'leo': u'\u264c', # ♌ LEO
     'libra': u'\u264e', # ♎ LIBRA
+    'lmoustache': u'\u23b0', # ⎰ UPPER LEFT OR LOWER RIGHT CURLY BRACKET SECTION
     'lnot': u'\xac', # ¬ NOT SIGN
     'lozenge': u'\u25ca', # ◊ LOZENGE
     'male': u'\u2642', # ♂ MALE SIGN
@@ -369,6 +372,7 @@ mathord = {
     'quarternote': u'\u2669', # ♩ QUARTER NOTE
     'rightmoon': u'\u263d', # ☽ FIRST QUARTER MOON
     'rightturn': u'\u21bb', # ↻ CLOCKWISE OPEN CIRCLE ARROW
+    'rmoustache': u'\u23b1', # ⎱ UPPER RIGHT OR LOWER LEFT CURLY BRACKET SECTION
     'sagittarius': u'\u2650', # ♐ SAGITTARIUS
     'saturn': u'\u2644', # ♄ SATURN
     'scorpio': u'\u264f', # ♏ SCORPIUS
diff --git a/docutils/docutils/writers/html5_polyglot/plain.css b/docutils/docutils/writers/html5_polyglot/plain.css
index 599b74364..0b85c5c5e 100644
--- a/docutils/docutils/writers/html5_polyglot/plain.css
+++ b/docutils/docutils/writers/html5_polyglot/plain.css
@@ -265,6 +265,9 @@ pre.code .inserted, code .inserted { background-color: #A3D289}
 mtable.align > mtr > mtd { /* emulate AMS "align" environment. */
   text-align: left;   
 }
+mstyle.mathscr, mi.mathscr {
+  font-family: STIX;
+}
 
 /* Epigraph           */
 /* Highlights         */
diff --git a/docutils/docutils/writers/html5_polyglot/responsive.css b/docutils/docutils/writers/html5_polyglot/responsive.css
index 4dbc43e37..551240f2d 100644
--- a/docutils/docutils/writers/html5_polyglot/responsive.css
+++ b/docutils/docutils/writers/html5_polyglot/responsive.css
@@ -345,6 +345,9 @@ table.align-right {
 mtable.align > mtr > mtd { /* emulate AMS "align" environment. */
   text-align: left;   
 }
+mstyle.mathscr, mi.mathscr {
+  font-family: STIX;
+}
 
 /* Adaptive page layout */
 /* ==================== */
diff --git a/docutils/test/functional/expected/math_output_mathml.html b/docutils/test/functional/expected/math_output_mathml.html
index b5c8f7e31..11eb52fe4 100644
--- a/docutils/test/functional/expected/math_output_mathml.html
+++ b/docutils/test/functional/expected/math_output_mathml.html
@@ -33,12 +33,8 @@ role specificator, <math xmlns="http://www.w3.org/1998/Math/MathML">
   </msub>
   <mo>=</mo>
   <mfrac>
-    <mrow>
-      <mi>π</mi>
-    </mrow>
-    <mrow>
-      <mn>4</mn>
-    </mrow>
+    <mi>π</mi>
+    <mn>4</mn>
   </mfrac>
   <msup>
     <mi>d</mi>
@@ -57,9 +53,7 @@ role specificator, <math xmlns="http://www.w3.org/1998/Math/MathML">
         <mo stretchy="false">)</mo>
         <mo>=</mo>
         <mfrac>
-          <mrow>
-            <mn>1</mn>
-          </mrow>
+          <mn>1</mn>
           <mrow>
             <mn>1</mn>
             <mo>+</mo>
@@ -68,9 +62,7 @@ role specificator, <math xmlns="http://www.w3.org/1998/Math/MathML">
             <mrow>
               <mo>(</mo>
               <mfrac>
-                <mrow>
-                  <mi>ε</mi>
-                </mrow>
+                <mi>ε</mi>
                 <mrow>
                   <msub>
                     <mi>k</mi>
@@ -97,12 +89,8 @@ role specificator, <math xmlns="http://www.w3.org/1998/Math/MathML">
         <mi>N</mi>
         <mo>=</mo>
         <mfrac>
-          <mrow>
-            <mtext>number of apples</mtext>
-          </mrow>
-          <mrow>
-            <mn>7</mn>
-          </mrow>
+          <mtext>number of apples</mtext>
+          <mn>7</mn>
         </mfrac>
       </mtd>
     </mtr>
@@ -177,9 +165,7 @@ For example, the following sum and integral with limits:</p>
         <mi>x</mi>
         <mo>=</mo>
         <mfrac>
-          <mrow>
-            <mn>1</mn>
-          </mrow>
+          <mn>1</mn>
           <mrow>
             <mi>n</mi>
             <mo>+</mo>
@@ -216,9 +202,7 @@ For example, the following sum and integral with limits:</p>
             <mn>1</mn>
             <mo stretchy="false">)</mo>
           </mrow>
-          <mrow>
-            <mn>2</mn>
-          </mrow>
+          <mn>2</mn>
         </mfrac>
       </mtd>
     </mtr>
@@ -236,9 +220,7 @@ directives:</p>
         <mi>i</mi>
         <mi>ℏ</mi>
         <mfrac>
-          <mrow>
-            <mo>∂</mo>
-          </mrow>
+          <mo>∂</mo>
           <mrow>
             <mo>∂</mo>
             <mi>t</mi>
@@ -247,9 +229,7 @@ directives:</p>
         <mi class="capital-greek">Ψ</mi>
         <mo>=</mo>
         <mover accent="true">
-          <mrow>
-            <mi>H</mi>
-          </mrow>
+          <mi>H</mi>
           <mo>ˆ</mo>
         </mover>
         <mi class="capital-greek">Ψ</mi>
@@ -274,100 +254,76 @@ physical system changes in time.</p>
 <tbody>
 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="true">
-    <mrow>
-      <mi>a</mi>
-    </mrow>
+    <mi>a</mi>
     <mo>´</mo>
   </mover>
 </math>      <span class="docutils literal">\acute{a}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="true">
-    <mrow>
-      <mi>t</mi>
-    </mrow>
+    <mi>t</mi>
     <mo>˙</mo>
   </mover>
 </math>        <span class="docutils literal">\dot{t}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="true">
-    <mrow>
-      <mi>γ</mi>
-    </mrow>
+    <mi>γ</mi>
     <mo>ˆ</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">
   <mover accent="true">
-    <mrow>
-      <mi>a</mi>
-    </mrow>
+    <mi>a</mi>
     <mo>`</mo>
   </mover>
 </math>      <span class="docutils literal">\grave{a}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="true">
-    <mrow>
-      <mi>t</mi>
-    </mrow>
+    <mi>t</mi>
     <mo>¨</mo>
   </mover>
 </math>       <span class="docutils literal">\ddot{t}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="true">
-    <mrow>
-      <mi>α</mi>
-    </mrow>
+    <mi>α</mi>
     <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">
   <mover accent="true">
-    <mrow>
-      <mi>x</mi>
-    </mrow>
+    <mi>x</mi>
     <mo>˘</mo>
   </mover>
 </math>      <span class="docutils literal">\breve{x}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="true">
-    <mrow>
-      <mi>t</mi>
-    </mrow>
+    <mi>t</mi>
     <mo>⃛</mo>
   </mover>
 </math>      <span class="docutils literal">\dddot{t}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="false">
-    <mrow>
-      <mi>ı</mi>
-    </mrow>
+    <mi>ı</mi>
     <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">
   <mover accent="true">
-    <mrow>
-      <mi>a</mi>
-    </mrow>
+    <mi>a</mi>
     <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">
   <mover accent="true">
-    <mrow>
-      <mi>a</mi>
-    </mrow>
+    <mi>a</mi>
     <mo>ˉ</mo>
   </mover>
 </math>        <span class="docutils literal">\bar{a}</span></p></td>
 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
   <mover accent="false">
-    <mrow>
-      <mi>R</mi>
-    </mrow>
+    <mi>R</mi>
     <mo>→</mo>
   </mover>
 </math>        <span class="docutils literal">\vec{R}</span></p></td>
@@ -411,9 +367,7 @@ physical system changes in time.</p>
                 <mrow>
                   <msub>
                     <mi>ω</mi>
-                    <mrow>
-                      <mi>x</mi>
-                    </mrow>
+                    <mi>x</mi>
                   </msub>
                   <mo>=</mo>
                   <mn>0</mn>
@@ -435,9 +389,7 @@ physical system changes in time.</p>
                   <mo>−</mo>
                   <mo>∞</mo>
                 </mrow>
-                <mrow>
-                  <mo>∞</mo>
-                </mrow>
+                <mo>∞</mo>
               </munderover>
               <mi>s</mi>
               <mo stretchy="false">(</mo>
@@ -449,17 +401,13 @@ physical system changes in time.</p>
                   <mi mathvariant="normal">i</mi>
                   <msub>
                     <mi>ω</mi>
-                    <mrow>
-                      <mi>x</mi>
-                    </mrow>
+                    <mi>x</mi>
                   </msub>
                   <mi>x</mi>
                 </mrow>
               </msup>
               <mi mathvariant="normal">d</mi>
-              <mrow>
-                <mi>x</mi>
-              </mrow>
+              <mi>x</mi>
             </mrow>
             <mrow>
               <munderover>
@@ -468,18 +416,14 @@ physical system changes in time.</p>
                   <mo>−</mo>
                   <mo>∞</mo>
                 </mrow>
-                <mrow>
-                  <mo>∞</mo>
-                </mrow>
+                <mo>∞</mo>
               </munderover>
               <mi>s</mi>
               <mo stretchy="false">(</mo>
               <mi>x</mi>
               <mo stretchy="false">)</mo>
               <mi mathvariant="normal">d</mi>
-              <mrow>
-                <mi>x</mi>
-              </mrow>
+              <mi>x</mi>
             </mrow>
           </mfrac>
           <mo>)</mo>
@@ -500,9 +444,7 @@ physical system changes in time.</p>
       <mtd>
         <msub>
           <mi>s</mi>
-          <mrow>
-            <mi mathvariant="normal">out</mi>
-          </mrow>
+          <mi mathvariant="normal">out</mi>
         </msub>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
@@ -512,9 +454,7 @@ physical system changes in time.</p>
         <mo>=</mo>
         <msub>
           <mi>s</mi>
-          <mrow>
-            <mi mathvariant="normal">in</mi>
-          </mrow>
+          <mi mathvariant="normal">in</mi>
         </msub>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
@@ -541,9 +481,7 @@ physical system changes in time.</p>
         <mo>∫</mo>
         <msub>
           <mi>s</mi>
-          <mrow>
-            <mi mathvariant="normal">in</mi>
-          </mrow>
+          <mi mathvariant="normal">in</mi>
         </msub>
         <mo stretchy="false">(</mo>
         <mi>x</mi>