diff --git a/src/latest.tex b/src/latest.tex
index 315a9af..769e7f2 100644
--- a/src/latest.tex
+++ b/src/latest.tex
@@ -71,7 +71,8 @@
\textbullet\quad20200831 / 2.3: Update for language and more structure to chemistry markup.\\
\textbullet\quad20200917 / 2.4: Added programming markup.\\
\textbullet\quad20200928 / 2.5: Clarifications and updated code appearance.\\
- \textbullet\quad20220202 / 2.6: (current version) Clarifications for xml:lang, tables and identifiers/text.\\
+ \textbullet\quad20220202 / 2.6: Clarifications for xml:lang, tables and identifiers/text.\\
+ \textbullet\quad20230331 / 3.0: (current version) Removed namespace for math expressions\\
\bigskip
}
\end{quote}
@@ -99,7 +100,7 @@ \section{The fundamental requirements}
\begin{itemize}
\item All mathematical expressions --~both inline and block~-- shall be marked up, along with the general EPUB markup, using \emph{MathML Presentation Markup}, as specified in ''Mathematical Markup Language (MathML) Version 3.0 2nd Edition''\footnote{See~\url{https://www.w3.org/TR/MathML3/}}.
- \item The language of the generated text is reliant on which \emph{xml:lang}-attribute is set. Thus there must exist an ancestor of the expression with the \emph{xml:lang}-attribute, for example: \element{} or \element{...
}. A math element itself cannot contain a \element{xml:lang} attribute.
+ \item The language of the generated text is reliant on which \emph{xml:lang}-attribute is set. Thus there must exist an ancestor of the expression with the \emph{xml:lang}-attribute, for example: \element{} or \element{}. A math element itself cannot contain a \element{xml:lang} attribute.
\item Whenever applicable, the requirements in this document must be respected.
\textbf{For mathematical expressions that are not covered in this document, the personnel involved in the markup process is encouraged to do MathML markup based on a good understanding of mathematics, combined with a solid knowledge of the set of MathML elements and attributes.}
@@ -109,16 +110,16 @@ \section{The fundamental requirements}
\item All MathML markup must be annotated with an AsciiMath expression that represents the mathematical expression printed in the book. Thus, the complete markup of any given mathematical expression must be coded according to the following scheme:
\begin{lstlisting}[language=HTML, caption={Default MathML markup}]
-
-
-
+
+
[MathML markup]
-
-
-
+
+
+
\end{lstlisting}
The \markup{[MathML markup]} is, obviously, the MathML markup that represents the mathematical expression in question, and \markup{[AsciiMath markup]} is the AciiMath version of the same expression.
@@ -177,13 +178,13 @@ \subsection{The display attribute}
\begin{codeblock}
\footnotesize
\begin{verbatimtab}[3]
-
- x
- =
-
- 2
-
-
+
\end{verbatimtab}
\end{codeblock}
};
@@ -214,48 +215,48 @@ \subsection{The display attribute}
A completely different interpretation is that the expression represents a function, $a$, with one argument, namely the sum of $t$ and $\varphi$.
It is extremely important that the interpretation is clearly indicated in the MathML markup. If the expression represents a multiplication operation, this should be clarified by use of the MathML operator
-\verb||. And similar, the representation of a function must be clarified by using
-\verb||.
+\verb||. And similar, the representation of a function must be clarified by using
+\verb||.
So, even though this:
\begin{lstlisting}[language=HTML]
-
- a
- (
- t
- +
- φ
- )
-
+
\end{lstlisting}
in many cases would be perfectly good markup of the expression above, NLB require the markup to be either
\begin{lstlisting}[language=HTML]
-
- a
-
-
-
- t
- +
- φ
-
-
-
+
\end{lstlisting}
for the ''multiplication interpretation'', or
\begin{lstlisting}[language=HTML]
-
- a
-
-
-
- t
- +
- φ
-
-
-
+
\end{lstlisting}
for the ''function interpretation''. Note that the only difference is the choice of entity in line~3.
@@ -312,31 +313,31 @@ \subsection{Use of invisible operators}
where it is quite clear from the context that multiplication is involved, we \emph{require} that these multiplications are added to the markup. Thus, expression 4 must be marked up as
\begin{lstlisting}[language=HTML, caption={Invisible multiplication}]
-
-
- x
- +
- y
-
-
-
-
-
- x
- -
- y
-
-
+
+
+ x
+ +
+ y
+
+
+
+
+
+ x
+ -
+ y
+
+
\end{lstlisting}
while expression 5 must be represented with the following markup:
\begin{lstlisting}[language=HTML, caption={Function application and invisible multiplication}]
-2
-
-
- sin
-
- ɑ
-
+2
+
+
+ sin
+
+ ɑ
+
\end{lstlisting}
Note the use of \entity{\#8290} in line~8 and line~2 respectively in these markup snippets.
@@ -358,84 +359,84 @@ \subsection{Markup of less than, less than or equal, greater than and greater th
\bigskip
\begin{lstlisting}[language=HTML, caption={$9 < 10$}]
-
- 9
- <
- 10
-
+
+ 9
+ <
+ 10
+
\end{lstlisting}
\bigskip
\begin{lstlisting}[language=HTML, caption={$10 > 9$}]
-
- 10
- >
- 9
-
+
+ 10
+ >
+ 9
+
\end{lstlisting}
\bigskip
\begin{lstlisting}[language=HTML, caption={$9 \leq 9$}]
-
- 9
- ≤
- 9
-
+
+ 9
+ ≤
+ 9
+
\end{lstlisting}
\bigskip
\begin{lstlisting}[language=HTML, caption={$9 \geq 9$}]
-
- 9
- ≥
- 9
-
+
+ 9
+ ≥
+ 9
+
\end{lstlisting}
\subsection{Markup of parenthesis}
-Parenthesis shall not be marked up using \verb|(| and \verb|)|. Rather the MathML element \element{mfenced} must be used.
+Parenthesis shall not be marked up using \verb|(| and \verb|)|. Rather the MathML element \element{mfenced} must be used.
The \element{mfenced} should contain attribute defining what type of parenthesis it, as follows:
\begin{lstlisting}[language=HTML]
-
- x
-
+
+ x
+
\end{lstlisting}
This is done to clarify what parenthesis we are dealing with.\\
\bigskip
There are other parentesis to be aware of:
\begin{lstlisting}[language=HTML, caption={Square bracket}]
-
- x
-
+
+ x
+
\end{lstlisting}
\begin{lstlisting}[language=HTML, caption={Curly bracket}]
-
- x
-
+
+ x
+
\end{lstlisting}
This is trivial when there is only one element inside the parenthesis, such as $g(x)$, which should be marked up as
\begin{lstlisting}[language=HTML]
-
- g
-
-
- x
-
-
+
+ g
+
+
+ x
+
+
\end{lstlisting}
However, when the content of the parenthesis consists of multiple parts, such as $3 \cdot (4 + 9)$, the content of the \element{mfenced} element must be placed inside an \element{mrow} element:
\begin{lstlisting}[language=HTML]
-3
-⋅
-
-
- 4
- +
- 9
-
-
+3
+⋅
+
+
+ 4
+ +
+ 9
+
+
\end{lstlisting}
A more complex example, involving nested parenthesis, is
\begin{equation}
@@ -443,39 +444,39 @@ \subsection{Markup of parenthesis}
\end{equation}
The correct markup of this expression would be
\begin{lstlisting}[language=HTML]
-4
-⋅
-
-
- x
- +
- x
- ⋅
-
-
- x
- +
- a
-
-
-
-
-⋅
-
-
- x
- -
- x
- ⋅
-
-
- x
- -
- b
-
-
-
-
+4
+⋅
+
+
+ x
+ +
+ x
+ ⋅
+
+
+ x
+ +
+ a
+
+
+
+
+⋅
+
+
+ x
+ -
+ x
+ ⋅
+
+
+ x
+ -
+ b
+
+
+
+
\end{lstlisting}
@@ -489,14 +490,14 @@ \subsection{Markup of the absolute value}
\begin{equation}|-2| = 2\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML, caption={Absolute values}]
-
-
- -
- 2
-
-
-=
-2
+
+
+ -
+ 2
+
+
+=
+2
\end{lstlisting}
while the more complex expression
\begin{equation}
@@ -504,33 +505,33 @@ \subsection{Markup of the absolute value}
\end{equation}
must be marked up as follows:
\begin{lstlisting}[language=HTML]
-
-
- cos
-
-
- x
- 2
-
-
-
-=
-
-
-
-
- 1
- +
-
- cos
-
- x
-
-
- 2
-
-
-
+
+
+ cos
+
+
+ x
+ 2
+
+
+
+=
+
+
+
+
+ 1
+ +
+
+ cos
+
+ x
+
+
+ 2
+
+
+
\end{lstlisting}
\subsection{Markup of number of degrees}
@@ -539,10 +540,10 @@ \subsection{Markup of number of degrees}
For a positive number, the required markup is simple:
\begin{lstlisting}[language=HTML]
-
- [numeric value]
- °
-
+
+ [numeric value]
+ °
+
\end{lstlisting}
\listofdemands{
@@ -555,13 +556,13 @@ \subsection{Markup of number of degrees}
\medskip
For a negative value, the required markup is a bit more complex:
\begin{lstlisting}[language=HTML]
-
-
- -
- [numeric value]
-
- °
-
+
+
+ -
+ [numeric value]
+
+ °
+
\end{lstlisting}
\listofdemands{
@@ -579,20 +580,20 @@ \subsection{Markup of number of degrees}
The required markup for this kind of angular measurement is either:
\begin{lstlisting}[language=HTML]
-
- [numeric value]
- g
-
+
+ [numeric value]
+ g
+
\end{lstlisting}
or
\begin{lstlisting}[language=HTML]
-
-
- -
- [numeric value]
-
- g
-
+
+
+ -
+ [numeric value]
+
+ g
+
\end{lstlisting}
depending on the value, as described above.
@@ -605,70 +606,70 @@ \subsection{Markup of number of degrees}
\end{equation}
is
\begin{lstlisting}[language=HTML]
-
- 0
- °
-
-
-C
-=
-
- 32
- °
-
-
-F
-=
-273
-
-K
+
+ 0
+ °
+
+
+C
+=
+
+ 32
+ °
+
+
+F
+=
+273
+
+K
\end{lstlisting}
Note the use of the \element{mspace} element to insert proper visual spacing between values and the relevant unit.
For clarity, one could use the following markup instead:
\begin{lstlisting}[language=HTML]
-
-
- 0
- °
-
-
- C
-
-=
-
-
- 32
- °
-
-
- F
-
-
- =
- 273
-
- K
-
+
+
+ 0
+ °
+
+
+ C
+
+=
+
+
+ 32
+ °
+
+
+ F
+
+
+ =
+ 273
+
+ K
+
\end{lstlisting}
The only difference is the extra \element{mrow} elements that are used to group together the different parts of the expression.
The expression $T_0 = \ang{-273,15}\;\text{C}$ must be represented by the following markup:
\begin{lstlisting}[language=HTML]
-
- T
- 0
-
-=
-
-
- -
- 273,15
-
- °
-
-
-C
+
+ T
+ 0
+
+=
+
+
+ -
+ 273,15
+
+ °
+
+
+C
\end{lstlisting}
As a final example, the expression \begin{equation}
@@ -676,39 +677,39 @@ \subsection{Markup of number of degrees}
\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
- sin
-
-
- 45
- °
-
-
-=
-
- sin
-
-
- 50
- g
-
-
-=
-
- sin
-
-
- π
- 4
-
-
-=
-
- 1
-
- 2
-
-
+
+ sin
+
+
+ 45
+ °
+
+
+=
+
+ sin
+
+
+ 50
+ g
+
+
+=
+
+ sin
+
+
+ π
+ 4
+
+
+=
+
+ 1
+
+ 2
+
+
\end{lstlisting}
\end{examples}
@@ -717,21 +718,21 @@ \subsection{Markup of square roots and higher-order roots}
The square root must be marked up using the MathML element \element{msqrt}. As the square root of a mathematical expression can be looked upon as a function with \emph{one} argument, one could expect that the \element{sqrt} element always should have \emph{exactly on}e child.
This would require that $\sqrt{a + b}$ should be marked up as
\begin{lstlisting}[language=HTML]
-
-
- a
- +
- b
-
-
+
+
+ a
+ +
+ b
+
+
\end{lstlisting}
And this is indeed perfectly good markup, but the simpler form
\begin{lstlisting}[language=HTML]
-
- a
- +
- b
-
+
+ a
+ +
+ b
+
\end{lstlisting}
would work just as well.
@@ -740,28 +741,28 @@ \subsection{Markup of square roots and higher-order roots}
Thus, the expression \begin{equation}\sqrt[3]{8} =2\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
- 8
- 3
-
-=
-2
+
+ 8
+ 3
+
+=
+2
\end{lstlisting}
and the expression \begin{equation}\sqrt[n]{x}=x^{1/n} \end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
- x
- n
-
-=
-
- x
-
- 1
- n
-
-
+
+ x
+ n
+
+=
+
+ x
+
+ 1
+ n
+
+
\end{lstlisting}
\subsection{Markup of exponentiation}
@@ -780,50 +781,50 @@ \subsection{Markup of vectors}
\bigskip
For vector notation with arrows we require the following markup:
\begin{lstlisting}[language=HTML]
-
+
[a single element representing the vector]
- →
-
+ →
+
\end{lstlisting}
\begin{examples}
The very simple expression $\vec{v}$ must be represented by
\begin{lstlisting}[language=HTML]
-
- v
- →
-
+
+ v
+ →
+
\end{lstlisting}
Note that the placeholder \markup{[a single element representing the vector]} may represent more complex notation. This means that $\vec{a} = \vec{a_1} + \vec{a_2}$ must be marked up as:
\begin{lstlisting}[language=HTML]
-
- a
- →
-
-=
-
-
- a
- 1
-
- →
-
-+
-
-
- a
- 2
-
- →
-
+
+ a
+ →
+
+=
+
+
+ a
+ 1
+
+ →
+
++
+
+
+ a
+ 2
+
+ →
+
\end{lstlisting}
\end{examples}
\medskip The required markup for vectors represented by a bold font, is to add the \markup{mathvariant} attribute to the \element{mi} element representing the vector. The attribute value \emph{must} be a string containing the substring \markup{bold}, This will typically mean one of \markup{bold}, \markup{bold-italic}, \markup{bold-sans-serif} or \markup{sans-serif-bold-italic}:
\begin{lstlisting}[language=HTML]
-
+
[symbol representing the vector]
-
+
\end{lstlisting}
This means that the expression
\begin{equation}
@@ -831,28 +832,28 @@ \subsection{Markup of vectors}
\end{equation}
can be marked up as
\begin{lstlisting}[language=HTML]
-v
-=
-
- v
- x
-
-
-i
-+
-
- v
- y
-
-
-j
-+
-
- v
- z
-
-
-k
+v
+=
+
+ v
+ x
+
+
+i
++
+
+ v
+ y
+
+
+j
++
+
+ v
+ z
+
+
+k
\end{lstlisting}
Note that another attribute value than \markup{bold} could be used, in order to represent different types of bold font.
@@ -861,29 +862,29 @@ \subsection{Markup of fractions}
Even though the expression $1/2 + 1/2 =1$ could be marked up as
\begin{lstlisting}[language=HTML]
-1
-/
-2
-+
-1
-/
-2
-=
-1
+1
+/
+2
++
+1
+/
+2
+=
+1
\end{lstlisting}
we require the use of \element{mfrac} to represent the fractions:
\begin{lstlisting}[language=HTML]
-
- 1
- 2
-
-+
-
- 1
- 2
-
-=
-1
+
+ 1
+ 2
+
++
+
+ 1
+ 2
+
+=
+1
\end{lstlisting}
Note the use of the \markup{bevelled} attribute to separate the numerator and denominator with a slash rather than with a horizontal line.
@@ -893,16 +894,16 @@ \subsection{Markup of fractions}
\end{equation}
then the \markup{bevelled} attribute should not be used:
\begin{lstlisting}[language=HTML]
-x
-=
-
- 1
-
- a
- +
- b
-
-
+x
+=
+
+ 1
+
+ a
+ +
+ b
+
+
\end{lstlisting}
\bigskip
@@ -914,35 +915,35 @@ \subsection{Lower indices}
For a numeric index, the required markup is
\begin{lstlisting}[language=HTML]
-
-
-
+
+
+
[a single greek letter
or
a single letter in the reqions a-z or A-Z]
-
-
- [one or more integers]
-
+
+
+ [one or more integers]
+
\end{lstlisting}
and for a symbolic index, the required markup is
\begin{lstlisting}[language=HTML]
-
-
-
+
+
+
[a single greek letter
or
a single letter in the reqions a-z or A-Z]
-
-
-
-
+
+
+
+
[a single greek letter
or
a single letter in the reqions a-z or A-Z]
-
-
-
+
+
+
\end{lstlisting}
\begin{examples}
@@ -950,56 +951,56 @@ \subsection{Lower indices}
\begin{equation} A_T = A_1 + A_2 \end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
-
- A
-
- T
-
-=
-
-
- A
-
- 1
-
-+
-
-
- A
-
- 2
-
+
+
+ A
+
+ T
+
+=
+
+
+ A
+
+ 1
+
++
+
+
+ A
+
+ 2
+
\end{lstlisting}
and
\begin{equation} I_\alpha = \frac{I_\beta - I_\gamma}{2} \end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
-
- I
-
- ɑ
-
-=
-
-
-
-
- I
-
- ϐ
-
- -
-
-
- I
-
- γ
-
-
- 2
-
+
+
+ I
+
+ ɑ
+
+=
+
+
+
+
+ I
+
+ ϐ
+
+ -
+
+
+ I
+
+ γ
+
+
+ 2
+
\end{lstlisting}
\end{examples}
@@ -1007,15 +1008,15 @@ \subsection{Lower indices}
\subsection{Markup of functions with one argument}
A mathematical function, such as $f(x)$, $x(t)$, $F(x)$, $\psi (t)$ and similar, must be marked up as follows:
\begin{lstlisting}[language=HTML]
-
-
+
+
[a single greek letter
or
a single letter in the reqions a-z or A-Z]
-
-
- [any one child]
-
+
+
+ [any one child]
+
\end{lstlisting}
\listofdemands{
@@ -1030,44 +1031,44 @@ \subsection{Markup of functions with one argument}
\begin{equation}g(x)\end{equation}
shall be marked up as
\begin{lstlisting}[language=HTML]
-
- g
-
-
- x
-
-
+
+ g
+
+
+ x
+
+
\end{lstlisting}
And similar, the expression
\begin{equation}\psi(t)\end{equation}
shall be marked up as
\begin{lstlisting}[language=HTML]
-
- ψ
-
-
- t
-
-
+
+ ψ
+
+
+ t
+
+
\end{lstlisting}
If the argument to the function is more complicated, such as in
\begin{equation}f(x + \Delta x)\end{equation}
the corresponding markup will also be more complicated:
\begin{lstlisting}[language=HTML]
-
- f
-
-
-
- x
- +
- Δ
- x
-
-
-
+
+ f
+
+
+
+ x
+ +
+ Δ
+ x
+
+
+
\end{lstlisting}
\end{examples}
@@ -1075,15 +1076,15 @@ \subsection{Markup of functions with one argument}
\subsection{Markup of functions with two or more arguments}
A mathematical function with two or more arguments, such as $f(x,y,z)$, $F(x,t)$, $\psi (r, \theta )$ and similar, must be marked up as follows:
\begin{lstlisting}[language=HTML]
-
-
+
+
[a single greek letter
or
a single letter in the reqions a-z or A-Z]
-
-
- [two or more children]
-
+
+
+ [two or more children]
+
\end{lstlisting}
\listofdemands{
@@ -1100,29 +1101,29 @@ \subsection{Markup of functions with two or more arguments}
\begin{equation}f(x,y,z)\end{equation}
shall be marked up as
\begin{lstlisting}[language=HTML]
-
- f
-
-
- x
- y
- z
-
-
+
+ f
+
+
+ x
+ y
+ z
+
+
\end{lstlisting}
And the two-argument function
$\psi (r, \theta )$
shall be marked up as
\begin{lstlisting}[language=HTML]
-
- ψ
-
-
- r
- ϑ
-
-
+
+ ψ
+
+
+ r
+ ϑ
+
+
\end{lstlisting}
\end{examples}
@@ -1130,11 +1131,11 @@ \subsection{Markup of functions with two or more arguments}
\subsection{Markup of named functions}\label{named-functions}
A known mathematical function, such as $\sin \alpha$, $\ln x$, $\arccos(x)$ and similar, must be marked up as follows:
\begin{lstlisting}[language=HTML]
-
- [function name]
-
+
+ [function name]
+
[any one element that represents the argument(s) to the function]
-
+
\end{lstlisting}
\listofdemands{
@@ -1149,19 +1150,19 @@ \subsection{Markup of named functions}\label{named-functions}
\begin{equation}g(\alpha) = \sin \alpha\end{equation}
shall be marked up as
\begin{lstlisting}[language=HTML]
-
- g
-
-
- ɑ
-
-
- =
-
- sin
-
- ɑ
-
+
+ g
+
+
+ ɑ
+
+
+ =
+
+ sin
+
+ ɑ
+
\end{lstlisting}
And, the expression
@@ -1170,67 +1171,67 @@ \subsection{Markup of named functions}\label{named-functions}
\end{equation}
shall be marked up as
\begin{lstlisting}[language=HTML]
-
- ln
-
-
-
- x
-
- y
-
-
-
-=
-
- ln
-
- x
-
-+
-
- ln
-
- y
-
+
+ ln
+
+
+
+ x
+
+ y
+
+
+
+=
+
+ ln
+
+ x
+
++
+
+ ln
+
+ y
+
\end{lstlisting}
\end{examples}
Note that, for an expression on the form $\cos 2 x$, the following markup is \textbf{NOT} correct:
\begin{lstlisting}[language=HTML]
-
- cos
-
- 2
-
- x
-
+
+ cos
+
+ 2
+
+ x
+
\end{lstlisting}
This markup breaks the requirement that the \element{mrow} element must contain exactly three children. Instead, the markup must be as follows:
\begin{lstlisting}[language=HTML]
-
- cos
-
-
- 2
-
- x
-
-
+
+ cos
+
+
+ 2
+
+ x
+
+
\end{lstlisting}
\subsection{Markup of limits and the derivative}
The limit of a mathematical expression must generically be marked up as follows:
\begin{lstlisting}[language=HTML]
-
-
- lim
+
+
+ lim
[element representing the conditions]
-
-
+
+
[one element representing some mathematcal function or expression]
-
+
\end{lstlisting}
\listofdemands{
@@ -1252,33 +1253,33 @@ \subsection{Markup of limits and the derivative}
\end{equation}
shall be marked up as
\begin{lstlisting}[language=HTML]
-
- g
-
-
- x
-
-
-=
-
-
- lim
-
- t
- →
- T
-
-
-
-
- f
-
-
- x
- t
-
-
-
+
+ g
+
+
+ x
+
+
+=
+
+
+ lim
+
+ t
+ →
+ T
+
+
+
+
+ f
+
+
+ x
+ t
+
+
+
\end{lstlisting}
And, the expression
@@ -1287,23 +1288,23 @@ \subsection{Markup of limits and the derivative}
\end{equation}
shall be marked up as
\begin{lstlisting}[language=HTML]
-
-
- lim
-
- x
- →
- 0
-
-
-
-
- 1
- x
-
-
- =
- ∞
+
+
+ lim
+
+ x
+ →
+ 0
+
+
+
+
+ 1
+ x
+
+
+ =
+ ∞
\end{lstlisting}
\end{examples}
@@ -1322,20 +1323,20 @@ \subsubsection{The \emph{Lagrange notation}}
When we want to write the derivative of a function using \emph{Lagrange's notation}, as in $f'(x)$, the required markup is
\begin{lstlisting}[language=HTML]
-
-
-
+
+
+
[a single greek letter
or
a single letter in the reqions a-z or A-Z]
-
- ′
-
-
-
+
+ ′
+
+
+
[markup of one or more arguments]
-
-
+
+
\end{lstlisting}
\listofdemands{
@@ -1359,52 +1360,52 @@ \subsubsection{The \emph{Lagrange notation}}
\end{equation}
The correct markup of this expression is
\begin{lstlisting}[language=HTML]
-
-
- f
- ′
-
-
-
- x
-
-
-=
-
-
- lim
-
- h
- →
- 0
-
-
-
-
-
-
- f
-
-
-
- x
- +
- h
-
-
-
- -
-
- f
-
-
- h
-
-
-
- h
-
-
+
+
+ f
+ ′
+
+
+
+ x
+
+
+=
+
+
+ lim
+
+ h
+ →
+ 0
+
+
+
+
+
+
+ f
+
+
+
+ x
+ +
+ h
+
+
+
+ -
+
+ f
+
+
+ h
+
+
+
+ h
+
+
\end{lstlisting}
And
\begin{equation}
@@ -1412,36 +1413,36 @@ \subsubsection{The \emph{Lagrange notation}}
\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
-
- f
- ″
-
-
-
- x
-
-
-=
-
-
- f
- ′
-
-
-
-
-
- f
- ′
-
-
-
- x
-
-
-
-
+
+
+ f
+ ″
+
+
+
+ x
+
+
+=
+
+
+ f
+ ′
+
+
+
+
+
+ f
+ ′
+
+
+
+ x
+
+
+
+
\end{lstlisting}
\end{examples}
@@ -1450,12 +1451,12 @@ \subsubsection{The \emph{Lagrange notation}}
When we want to write the derivative of a named function using \emph{Lagrange's notation}, as in $(\sin x)'$, the required markup is
\begin{lstlisting}[language=HTML]
-
-
+
+
[markup representing the function]
-
- ′
-
+
+ ′
+
\end{lstlisting}
\listofdemands{
@@ -1475,43 +1476,43 @@ \subsubsection{The \emph{Lagrange notation}}
\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
-
-
- 3
-
- a
-
-
- x
- 3
-
-
-
- ″
-
-=
-
-
-
- 9
-
- a
-
-
- x
- 2
-
-
-
- ′
-
-=
-18
-
-a
-
-x
+
+
+
+ 3
+
+ a
+
+
+ x
+ 3
+
+
+
+ ″
+
+=
+
+
+
+ 9
+
+ a
+
+
+ x
+ 2
+
+
+
+ ′
+
+=
+18
+
+a
+
+x
\end{lstlisting}
@@ -1525,18 +1526,18 @@ \subsubsection{The \emph{Leibniz notation}}
the required markup is
\begin{lstlisting}[language=HTML]
-
-
- ⅆ
+
+
+ ⅆ
[markup required to represent the function]
-
-
- ⅆ
-
+
+
+ ⅆ
+
[a letter in the region a-z]
-
-
-
+
+
+
\end{lstlisting}
\listofdemands{
@@ -1560,60 +1561,60 @@ \subsubsection{The \emph{Leibniz notation}}
\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
-
- f
- ′
-
-
-
- x
-
-
-=
-
-
- ⅆ
-
- f
-
-
- x
-
-
-
-
- ⅆ
- x
-
-
+
+
+ f
+ ′
+
+
+
+ x
+
+
+=
+
+
+ ⅆ
+
+ f
+
+
+ x
+
+
+
+
+ ⅆ
+ x
+
+
\end{lstlisting}
\end{examples}
Markup of higher order derivatives of a function, based on \emph{Leibniz's notation}, is just an extension of the markup of the first derivative:
\begin{lstlisting}[language=HTML]
-
-
-
- ⅆ
-
+
+
+
+ ⅆ
+
[order of differentiation]
-
-
+
+
[markup required to represent the function]
-
-
- ⅅ
-
-
+
+
+ ⅅ
+
+
[a letter in the region a-z]
-
-
+
+
[order of differentiation]
-
-
-
-
+
+
+
+
\end{lstlisting}
\listofdemands{
@@ -1645,37 +1646,37 @@ \subsubsection{The \emph{Leibniz notation}}
\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
-
- g
- ″
-
-
-
- x
-
-
-=
-
-
-
- ⅆ
- 2
-
-
- sin
-
- x
-
-
-
- ⅆ
-
- x
- 2
-
-
-
+
+
+ g
+ ″
+
+
+
+ x
+
+
+=
+
+
+
+ ⅆ
+ 2
+
+
+ sin
+
+ x
+
+
+
+ ⅆ
+
+ x
+ 2
+
+
+
\end{lstlisting}
\end{examples}
@@ -1701,36 +1702,36 @@ \subsection{Markup of the integral}
For the \emph{indefinite integral}, with a very simple argument, such as $\int f = g +C$ and $T = \oint f$ and even $a(x) = \iint \cos x$, the following markup will be sufficient:
\begin{lstlisting}[language=HTML]
-∫
-f
-=
-g
-+
-C
+∫
+f
+=
+g
++
+C
\end{lstlisting}
and
\begin{lstlisting}[language=HTML]
-T
-=
-∮
-g
+T
+=
+∮
+g
\end{lstlisting}
and
\begin{lstlisting}[language=HTML]
-
- a
-
-
- x
-
-
-=
-∬
-
- cos
-
- x
-
+
+ a
+
+
+ x
+
+
+=
+∬
+
+ cos
+
+ x
+
\end{lstlisting}
respectively.
@@ -1741,12 +1742,12 @@ \subsection{Markup of the integral}
\end{equation}
will require a very specific markup:
\begin{lstlisting}[language=HTML]
-∫
+∫
[markup of function to be integrated
-
- ⅅ
- [integration variable]
-
+
+ ⅅ
+ [integration variable]
+
\end{lstlisting}
Note that the \entity{\#8747} entity in the first \element{mo} element could just as well be any of the other integral entities listed \vpageref{integraltegn}.
@@ -1756,40 +1757,40 @@ \subsection{Markup of the integral}
\end{equation}
would be
\begin{lstlisting}[language=HTML]
-
- C
-
-
- z
-
-
-=
-∫
-
- 1
- z
-
-
- ⅅ
- z
-
+
+ C
+
+
+ z
+
+
+=
+∫
+
+ 1
+ z
+
+
+ ⅅ
+ z
+
\end{lstlisting}
\bigskip
For \emph{definite integrals}, where the interval of the integration is specified, there are further requirements to the markup.
\begin{lstlisting}[language=HTML]
-
-
- [integration sign]
+
+
+ [integration sign]
[upper limit]
[lower limit]
-
+
[any markup representing the expression to be integrated]
-
- ⅅ
- [a letter in the region a-z]
-
-
+
+ ⅅ
+ [a letter in the region a-z]
+
+
\end{lstlisting}
%
@@ -1819,40 +1820,40 @@ \subsection{Markup of the integral}
\end{equation}
must be marked up as
\begin{lstlisting}[language=HTML]
-
- F
-
-
- x
-
-
-=
-
-
- ∫
-
- t
- =
- a
-
-
- t
- =
- x
-
-
-
- f
-
-
- t
-
-
-
- ⅅ
- t
-
-
+
+ F
+
+
+ x
+
+
+=
+
+
+ ∫
+
+ t
+ =
+ a
+
+
+ t
+ =
+ x
+
+
+
+ f
+
+
+ t
+
+
+
+ ⅅ
+ t
+
+
\end{lstlisting}
Another example:
@@ -1861,55 +1862,55 @@ \subsection{Markup of the integral}
\end{equation}
must be represented by the following markup:
\begin{lstlisting}[language=HTML]
-∮
-
- 1
- z
-
-
- ⅅ
- z
-
-=
-
-
- ∫
- 0
-
- 2
-
- π
-
-
-
-
- 1
-
- e
-
- i
-
- t
-
-
-
-
- i
-
-
- e
-
- i
-
- t
-
-
-
-
- ⅅ
- t
-
-
+∮
+
+ 1
+ z
+
+
+ ⅅ
+ z
+
+=
+
+
+ ∫
+ 0
+
+ 2
+
+ π
+
+
+
+
+ 1
+
+ e
+
+ i
+
+ t
+
+
+
+
+ i
+
+
+ e
+
+ i
+
+ t
+
+
+
+
+ ⅅ
+ t
+
+
\end{lstlisting}
\end{examples}
@@ -1927,27 +1928,27 @@ \subsection{Markup of matrices}
\end{equation}
\begin{lstlisting}[language=HTML]
-
-
-
-
- 1
- 0
- 0
-
-
- 0
- 1
- 0
-
-
- 0
- 0
- 1
-
-
-
-
+
+
+
+
+ 1
+ 0
+ 0
+
+
+ 0
+ 1
+ 0
+
+
+ 0
+ 0
+ 1
+
+
+
+
\end{lstlisting}
\end{examples}
@@ -1961,18 +1962,18 @@ \subsection{Markup of set delimiters}
\end{equation}
\begin{lstlisting}[language=HTML]
-
-
-
- x
- +
- y
- +
- z
-
- ⏟
-
-
+
+
+
+ x
+ +
+ y
+ +
+ z
+
+ ⏟
+
+
\end{lstlisting}
@@ -1983,18 +1984,18 @@ \subsection{Markup of set delimiters}
\end{equation}
\begin{lstlisting}[language=HTML]
-
-
-
- x
- +
- y
- +
- z
-
- ⏞
-
-
+
+
+
+ x
+ +
+ y
+ +
+ z
+
+ ⏞
+
+
\end{lstlisting}
\end{examples}
@@ -2017,64 +2018,64 @@ \subsection{Markup of chemistry}\label{chemistry}
The markup would be as follows:
\begin{lstlisting}[language=HTML]
-
-
- 6
-
- C
-
- O
- 2
-
-
-
- +
-
- 6
-
-
- H
- 2
-
- O
-
-
- +
- light
- →
-
-
-
- C
- 6
-
-
-
-
- H
- 12
-
-
-
-
- O
- 6
-
-
-
- +
-
- 6
-
- O
- 2
-
-
-
+
+ 6
+
+ C
+
+ O
+ 2
+
+
+
+ +
+
+ 6
+
+
+ H
+ 2
+
+ O
+
+
+ +
+ light
+ →
+
+
+
+ C
+ 6
+
+
+
+
+ H
+ 12
+
+
+
+
+ O
+ 6
+
+
+
+ +
+
+ 6
+
+ O
+ 2
+
+
+
\end{lstlisting}
\end{examples}
@@ -2085,11 +2086,11 @@ \subsubsection{Superscript in upper left to denote isotope}\label{chemistry-isot
\ce{^{14}C}
\end{equation}
\begin{lstlisting}[language=HTML]
-
-
- 14
-
- C
+
+
+ 14
+
+ C
\end{lstlisting}
Where \entity{\#32} represents a blank space.
\end{examples}
@@ -2103,13 +2104,13 @@ \subsection{Markup of physics}\label{physics}
\begin{examples}
The markup would be as follows:
\begin{lstlisting}[language=HTML]
-
...
-
+
\end{lstlisting}
\end{examples}
@@ -2122,13 +2123,13 @@ \subsection{Markup of math elements within code blocks}
\begin{examples}
The markup would be as follows:
\begin{lstlisting}[language=HTML]
-
...
-
+
\end{lstlisting}
\end{examples}
@@ -2148,31 +2149,31 @@ \subsection{Dividing obvious words into single letters}
\end{equation}
\begin{lstlisting}[language=HTML, caption={\textbf{Invalid markup}}]
-
- index
-
- m
- e
- a
- n
-
-
+
+ index
+
+ m
+ e
+ a
+ n
+
+
\end{lstlisting}
\begin{lstlisting}[language=HTML, caption={Valid markup 1}]
-
- index
- mean
-
+
+ index
+ mean
+
\end{lstlisting}
\begin{lstlisting}[language=HTML, caption={Valid markup 2}]
-
- index
-
- mean
-
-
+
+ index
+
+ mean
+
+
\end{lstlisting}
\end{examples}
@@ -2195,17 +2196,17 @@ \subsection{Decimals}
20,0
\end{equation}
\begin{lstlisting}[language=HTML, caption={\textbf{Invalid markup}}]
- 20
- ,
- 0
+ 20
+ ,
+ 0
\end{lstlisting}
This will cause the TTS to divide the expression into two numbers: 20 and 0, which is not good. Thus should this be avoided one of the following ways:
\begin{lstlisting}[language=HTML, caption={Valid markup 1}]
- 20,0
+ 20,0
\end{lstlisting}
\begin{lstlisting}[language=HTML, caption={Valid markup 2}]
- 20.0
+ 20.0
\end{lstlisting}
\end{examples}
@@ -2216,14 +2217,14 @@ \subsection{Thousand separator}
\begin{examples}
\textsc{164 000}
\begin{lstlisting}[language=HTML, caption={\textbf{Invalid markup}}]
- 164
-
- 000
+ 164
+
+ 000
\end{lstlisting}
This will cause the TTS to divide the expression into two numbers: 164 and 0, which is not good. Thus should this be avoided the following way:
\begin{lstlisting}[language=HTML, caption={Valid markup}]
- 164000
+ 164000
\end{lstlisting}
\end{examples}
@@ -2236,11 +2237,11 @@ \subsection{Union}
A \cup B
\end{equation}
\begin{lstlisting}[language=HTML]
-
- A
- ∪
- B
-
+
+ A
+ ∪
+ B
+
\end{lstlisting}
\end{examples}
@@ -2253,11 +2254,11 @@ \subsection{Intersection}
A \cap B
\end{equation}
\begin{lstlisting}[language=HTML]
-
- A
- ⋂
- B
-
+
+ A
+ ⋂
+ B
+
\end{lstlisting}
\end{examples}
@@ -2272,10 +2273,10 @@ \subsection{Tables}
|
- ...
+
|
- ...
+
|
@@ -2285,18 +2286,18 @@ \subsection{Tables}
\subsection{Identifiers and texts}
-Identifiers will always be marked up as \element{} whilst texts \element{}. The general rule here is that all the identifiers represented in the strings parameter in this file: \url{https://github.com/nlbdev/service-stem/blob/master/conversions/data/text-identifiers.json} are identifiers and should be marked up with \element{}, in addition to this there's function and expression related identifiers, such as \element{x}, \element{f} or \element{g}. The rest, is to be marked up with \element{}.
+Identifiers will always be marked up as \element{} whilst texts \element{}. The general rule here is that all the identifiers represented in the strings parameter in this file: \url{https://github.com/nlbdev/service-stem/blob/master/conversions/data/text-identifiers.json} are identifiers and should be marked up with \element{}, in addition to this there's function and expression related identifiers, such as \element{x}, \element{f} or \element{g}. The rest, is to be marked up with \element{}.
\begin{examples}
\begin{equation}
x * \text{All the values of A}
\end{equation}
\begin{lstlisting}[language=HTML]
-
- x
- *
- All the values of A
-
+
+ x
+ *
+ All the values of A
+
\end{lstlisting}
\end{examples}