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+single character inline equation. (valid=True)
+.
+$a$
+.
+<p><eq>a</eq></p>
+.
+
+inline equation with single greek character (valid=True)
+.
+$\\varphi$
+.
+<p><eq>\\varphi</eq></p>
+.
+
+simple equation starting and ending with numbers. (valid=True)
+.
+$1+1=2$
+.
+<p><eq>1+1=2</eq></p>
+.
+
+simple equation including special html character. (valid=True)
+.
+$1+1<3$
+.
+<p><eq>1+1<3</eq></p>
+.
+
+equation including backslashes. (valid=True)
+.
+$a \\backslash$
+.
+<p><eq>a \\backslash</eq></p>
+.
+
+use of currency symbol (valid=True)
+.
+You get 3$ if you solve $1+2$
+.
+<p>You get 3$ if you solve <eq>1+2</eq></p>
+.
+
+use of currency symbol (valid=True)
+.
+If you solve $1+2$ you get $3
+.
+<p>If you solve <eq>1+2</eq> you get $3</p>
+.
+
+inline fraction (valid=True)
+.
+$\\frac{1}{2}$
+.
+<p><eq>\\frac{1}{2}</eq></p>
+.
+
+inline column vector (valid=True)
+.
+$\\begin{pmatrix}x\\\\y\\end{pmatrix}$
+.
+<p><eq>\\begin{pmatrix}x\\\\y\\end{pmatrix}</eq></p>
+.
+
+inline bold vector notation (valid=True)
+.
+${\\tilde\\bold e}_\\alpha$
+.
+<p><eq>{\\tilde\\bold e}_\\alpha</eq></p>
+.
+
+exponentiation (valid=True)
+.
+$a^{b}$
+.
+<p><eq>a^{b}</eq></p>
+.
+
+conjugate complex (valid=True)
+.
+$a^\*b$ with $a^\*$
+.
+<p><eq>a^\*b</eq> with <eq>a^\*</eq></p>
+.
+
+Inline multi-line (valid=True)
+.
+a $a
+\not=1$ b
+.
+<p>a <eq>a
+\not=1</eq> b</p>
+.
+
+Inline multi-line with newline (valid=False)
+.
+a $a
+
+\not=1$ b
+.
+<p>a $a</p>
+<p>\not=1$ b</p>
+.
+
+single block equation, greek index (valid=True)
+.
+$$e_\\alpha$$
+.
+<section>
+<eqn>e_\\alpha</eqn>
+</section>
+.
+
+display equation on its own single line. (valid=True)
+.
+$$1+1=2$$
+.
+<section>
+<eqn>1+1=2</eqn>
+</section>
+.
+
+inline equation followed by block equation. (valid=True)
+.
+${e}_x$
+
+$$e_\\alpha$$
+.
+<p><eq>{e}_x</eq></p>
+<section>
+<eqn>e_\\alpha</eqn>
+</section>
+.
+
+underline tests (valid=True)
+.
+$$c{\\bold e}_x = a{\\bold e}_\\alpha - b\\tilde{\\bold e}_\\alpha$$
+.
+<section>
+<eqn>c{\\bold e}_x = a{\\bold e}_\\alpha - b\\tilde{\\bold e}_\\alpha</eqn>
+</section>
+.
+
+non-numeric character before opening $ or
+after closing $ or both is allowed. (valid=True)
+.
+a$1+1=2$
+$1+1=2$b
+c$x$d
+.
+<p>a<eq>1+1=2</eq>
+<eq>1+1=2</eq>b
+c<eq>x</eq>d</p>
+.
+
+following dollar character '$' is allowed. (valid=True)
+.
+$x$ $ 
+.
+<p><eq>x</eq> $</p>
+.
+
+consecutive inline equations. (valid=True)
+.
+$x$ $y$
+.
+<p><eq>x</eq> <eq>y</eq></p>
+.
+
+inline equation after '-' sign in text. (valid=True)
+.
+so-what is $x$
+.
+<p>so-what is <eq>x</eq></p>
+.
+
+display equation with line breaks. (valid=True)
+.
+$$
+1+1=2
+$$
+.
+<section>
+<eqn>
+1+1=2
+</eqn>
+</section>
+.
+
+multiple equations (valid=True)
+.
+$$
+a = 1
+$$
+
+$$
+b = 2
+$$
+.
+<section>
+<eqn>
+a = 1
+</eqn>
+</section>
+<section>
+<eqn>
+b = 2
+</eqn>
+</section>
+.
+
+equation followed by a labelled equation (valid=True)
+.
+$$
+a = 1
+$$
+
+$$
+b = 2
+$$ (1)
+.
+<section>
+<eqn>
+a = 1
+</eqn>
+</section>
+<section>
+<eqn>
+b = 2
+</eqn>
+</section>
+.
+
+multiline equation. (valid=True)
+.
+$$\\begin{matrix}
+ f & = & 2 + x + 3 \\ 
+ & = & 5 + x 
+\\end{matrix}$$
+.
+<section>
+<eqn>\\begin{matrix}
+ f & = & 2 + x + 3 \\ 
+ & = & 5 + x 
+\\end{matrix}</eqn>
+</section>
+.
+
+vector equation. (valid=True)
+.
+$$\\begin{pmatrix}x_2 \\\\ y_2 \\end{pmatrix} = 
+\\begin{pmatrix} A & B \\\\ C & D \\end{pmatrix}\\cdot
+\\begin{pmatrix} x_1 \\\\ y_1 \\end{pmatrix}$$
+.
+<section>
+<eqn>\\begin{pmatrix}x_2 \\\\ y_2 \\end{pmatrix} = 
+\\begin{pmatrix} A & B \\\\ C & D \\end{pmatrix}\\cdot
+\\begin{pmatrix} x_1 \\\\ y_1 \\end{pmatrix}</eqn>
+</section>
+.
+
+display equation with equation number. (valid=True)
+.
+$$f(x) = x^2 - 1$$ (1)
+.
+<section>
+<eqn>f(x) = x^2 - 1</eqn>
+</section>
+.
+
+inline equation following code section. (valid=True)
+.
+`code`$a-b$
+.
+<p><code>code</code><eq>a-b</eq></p>
+.
+
+equation following code block. (valid=True)
+.
+```
+code
+```
+$$a+b$$
+.
+<pre><code>code
+</code></pre>
+<section>
+<eqn>a+b</eqn>
+</section>
+.
+
+numbered equation following code block. (valid=True)
+.
+```
+code
+```
+$$a+b$$(1)
+.
+<pre><code>code
+</code></pre>
+<section>
+<eqn>a+b</eqn>
+</section>
+.
+
+Equations in list. (valid=True)
+.
+1. $1+2$
+2. $2+3$
+    1. $3+4$
+.
+<ol>
+<li><eq>1+2</eq></li>
+<li><eq>2+3</eq>
+<ol>
+<li><eq>3+4</eq></li>
+</ol>
+</li>
+</ol>
+.
+
+Inline sum. (valid=True)
+.
+$\\sum\_{i=1}^n$
+.
+<p><eq>\\sum\_{i=1}^n</eq></p>
+.
+
+Sum without equation number. (valid=True)
+.
+$$\\sum\_{i=1}^n$$
+.
+<section>
+<eqn>\\sum\_{i=1}^n</eqn>
+</section>
+.
+
+Sum with equation number. (valid=True)
+.
+$$\\sum\_{i=1}\^n$$ \(2\)
+.
+<section>
+<eqn>\\sum\_{i=1}\^n</eqn>
+</section>
+.
+
+equation number always vertically aligned. (valid=True)
+.
+$${\\bold e}(\\varphi) = \\begin{pmatrix}
+\\cos\\varphi\\\\\\sin\\varphi
+\\end{pmatrix}$$ (3)
+.
+<section>
+<eqn>{\\bold e}(\\varphi) = \\begin{pmatrix}
+\\cos\\varphi\\\\\\sin\\varphi
+\\end{pmatrix}</eqn>
+</section>
+.
+
+inline equations in blockquote. (valid=True)
+.
+> see $a = b + c$ 
+> $c^2=a^2+b^2$ (2) 
+> $c^2=a^2+b^2$ 
+.
+<blockquote>
+<p>see <eq>a = b + c</eq>
+<eq>c^2=a^2+b^2</eq> (2)
+<eq>c^2=a^2+b^2</eq></p>
+</blockquote>
+.
+
+display equation in blockquote. (valid=True)
+.
+> formula
+>
+> $$ a+b=c$$ (2)
+>
+> in blockquote. 
+.
+<blockquote>
+<p>formula</p>
+<section>
+<eqn> a+b=c</eqn>
+</section>
+<p>in blockquote.</p>
+</blockquote>
+.
+
+mixed syntax:
+.
+$$
+a=1 \\
+b=2
+$$ (abc)
+
+- ab $c=1$ d
+.
+<section>
+<eqn>
+a=1 \\
+b=2
+</eqn>
+</section>
+<ul>
+<li>ab <eq>c=1</eq> d</li>
+</ul>
+.
+
+escaped dollars '\\$' are interpreted as
+dollar '$' characters. (valid=True)
+.
+\\$1+1=2$
+$1+1=2\\$
+.
+<p>\$1+1=2$
+$1+1=2\$</p>
+.
+
+empty line between text and display formula is required. (valid=False)
+.
+some text
+ \$\\$a+b=c\$\$
+.
+<p>some text
+$\$a+b=c$$</p>
+.
+
+whitespace character after opening $
+or before closing $ is not allowed. (valid=False)
+.
+$ $
+$ x$
+$x $
+.
+<p>$ $
+$ x$
+$x $</p>
+.