diff --git a/Nordic MathML Guidelines.md b/Nordic MathML Guidelines.md
index 90e00af..f04d3d8 100644
--- a/Nordic MathML Guidelines.md
+++ b/Nordic MathML Guidelines.md
@@ -10,28 +10,28 @@ The basis of this document is the [MathML Core specification](https://www.w3.org
## When To Use MathML
-In general, all mathematics should be marked up with MathML. Even simple arithmetic expressions such as 4 − 1 = 3, should be in MathML. Sometimes a mathematical expression is additional information, and the expression is placed inside parentheses. For consistency, always include the parentheses inside the MathML markup. For example, in the sentence “the price for three pairs of jeans was 90 euros (30 € × 3), and he paid for them in cash”, include the parentheses in the MathML markup.
+In general, all mathematics should be marked up with MathML. Even simple arithmetic expressions such as $4 − 1 = 3$, should be in MathML. Sometimes a mathematical expression is additional information, and the expression is placed inside parentheses. For consistency, always include the parentheses inside the MathML markup. For example, in the sentence “the price for three pairs of jeans was 90 euros $(30 € × 3)$, and he paid for them in cash”, include the parentheses in the MathML markup.
### Numbers and Numbers with Units
-Non-negative numbers, like 3 and 5.2, should be in plain text. If a number has a minus, like −4 or −3.1, it should be in MathML. If a number is part of a mathematical expression, it should be in MathML.
+Non-negative numbers, like 3 and 5.2, should be in plain text. If a number has a minus, like $−4$ or $−3.1$, it should be in MathML. If a number is part of a mathematical expression, it should be in MathML.
-Units should be in plain text, except if there is an exponent, division or Greek letter in it. For example, "10 m" should be in plain text, while "10 m/s2" should be in MathML.
+Units should be in plain text, except if there is an exponent, division or Greek letter in it. For example, 10 m should be in plain text, while $10 \hspace{0.25em} \text{m}/\text{s}^2$ should be in MathML.
### Variables, Parameters and Greek Letters
Variables and parameters should always be marked up with MathML.
-In STEM books Greek letters should always be in MathML. In these books they are variables and parameters. In non-STEM books isolated Greek letters should be in plain text. However, if they are part of an expression, like Δx, the whole expression should be marked up with MathML.
+In STEM books Greek letters should always be in MathML. In these books they are variables and parameters. In non-STEM books isolated Greek letters should be in plain text. However, if they are part of an expression, like $Δx$, the whole expression should be marked up with MathML.
-Variables, Greek letters etc. with a sign above, like $\bar{x}$ or $\hat{y}$, or with indexes, like β1 or ℇ0, should always be marked up with MathML, using “mover” and “msub” respectively. Note that there are distinct characters like ŷ (U+0177), but these are not intended for mathematics and should not be used.
+Variables, Greek letters etc. with a sign above, like $\bar{x}$ or $\hat{y}$, or with indexes, like $β_1$ or $ε_0$, should always be marked up with MathML, using “mover” and “msub” respectively. Note that there are distinct characters like ŷ (U+0177), but these are not intended for mathematics and should not be used.
### Some Things That Should Be In Plain Text
Things that are not mathematics should not be marked up with MathML. Below is a list with some examples. If it is unclear whether something is mathematics or not, please ask the Ordering Agency.
- Years: “The 1950s” (English), “1950-årene” (Norwegian)
-- Dates: “23.10.2013”, “23/10 - 13”
+- Dates: “23.10.2013”, “2013-10-23”
- Time periods: “1840–1845”, “June 1–June 4”
- Intervals like “7–8 children” (7 to 8 children), “90–95% of the participants voted yes”
- Numbers on journals etc: “Vi menn 1/2025”
@@ -45,7 +45,7 @@ Things that are not mathematics should not be marked up with MathML. Below is a
### Chemistry
-MathML markup is required to be used for all chemistry content in general. However, if the source material contains occasional occurrences of chemical substances written like CO2 or H2O, and no other type of chemistry notation, these can be captured using standard HTML. If MathML is used for other types of chemistry notation, then MathML must be used for all chemistry content in order to ensure a consistent output for the reader. How to mark up chemistry using MathML is explained here: [Chemistry](#chemistry-in-mathml).
+MathML markup is required to be used for all chemistry content in general. However, if the source material contains occasional occurrences of chemical substances written like $\text{C}\text{O}_2$ or $\text{H}_2\text{O}$, and no other type of chemistry notation, these can be captured using standard HTML. If MathML is used for other types of chemistry notation, then MathML must be used for all chemistry content in order to ensure a consistent output for the reader. How to mark up chemistry using MathML is explained here: [Chemistry](#chemistry-in-mathml).
## MathML Fundamentals
@@ -79,7 +79,7 @@ The Ordering Agency may decide if the `alttext` and `altimg` attributes should b
#### Block vs Inline
-Mathematical expressions can occur in three different ways:
+Mathematical expressions can occur in three different ways:
- as part of a sentence or paragraph as an inline element
- as part of a sentence or paragraph as a block element
@@ -87,7 +87,7 @@ Mathematical expressions can occur in three different ways:
The way in which a math expression is visually rendered is controlled by the `display` attribute of the `
```
+
The example will be rendered as follows:
Here is an inline equation: $x = 5.$
-**Note:** Make sure to have space between the normal text and the MathML markup.
+**Note:** Make sure to have space between the normal text and the MathML markup.
-It is common in STEM books for a mathematical expression to be part of a sentence or paragraph, yet displayed as a separate block element. In such examples it is important to place the `
```
-The example will be rendered as follows:
+
+The example will be rendered as follows:
To find the mean of a set of observations, add the values and divide by the number of observations:
-``` math
-\bar{x} = \frac{x_1 + x_2 + … + x_n}{n}
-```
-This can be written in more compact form:
-``` math
+
+$$
+\bar{x} = \frac{x_1 + x_2 + … + x_n}{n}.
+$$
+
+This can be written in more compact form:
+
+$$
\bar{x} = \frac{1}{n}∑x_i.
-```
+$$
-Other times the mathematical expression is a stand-alone element, not part of an ongoing sentence or paragraph. In such examples it is important to place the `` element inside a `` element or something similar. Here is an example:
+Other times the mathematical expression is a stand-alone element, not part of an ongoing sentence or paragraph. In such examples it is important to place the `` element inside a `` element or something similar. Here is an example:
```html
Text preceding a stand-alone block of math content.
@@ -161,14 +166,16 @@ Other times the mathematical expression is a stand-alone element, not part of an
```
+
The example will be rendered as follows:
Text preceding a stand-alone block of math content.
-``` math
+
+$$
a + b = c.
-```
+$$
-Sometimes a mathematical expression consists of multiple mathematical expressions, and they all appear on the same line. Examples are functions where the domain is a restricted interval, or a differential equation with an intial value. In such cases, all the expressions should be captured in the same `` element separated by ``. Here is an example:
+Sometimes a mathematical expression consists of multiple mathematical expressions, and they all appear on the same line. Examples are functions where the domain is a restricted interval, or a differential equation with an intial value. In such cases, all the expressions should be captured in the same `` element separated by ``. Here is an example:
```html
The curve is represented by the equation
@@ -185,11 +192,12 @@ Sometimes a mathematical expression consists of multiple mathematical expression
```
-The example will be rendered as follows:
-``` math
+The example will be rendered as follows:
+
+$$
r = \sqrt{|\text{sin}(nθ)|}, \hspace{1em} 0 ≤ θ ≤ 2π.
-```
+$$
### Semantics and Annotations
@@ -234,6 +242,7 @@ The `` element is used to mark up all kinds of numeric characters. This also
There are different ways to mark up the decimal and thousand separators based on the publication. Follow the mark up of the publication unless specifically told otherwise by the Ordering Agency.
Examples of decimal and thousand separator markup includes
+
- comma as a decimal separator: `3,14`
- non-breaking space as a thousand separator: `89 000`
- period as a decimal separator: `2.74`
@@ -241,7 +250,7 @@ Examples of decimal and thousand separator markup includes
#### `` for operators, fences, separators or accents
-The `` element is used to denote operators. The definition of an operator is loose and it can mean the actual mathematical operators plus (+), minus (−), times (·) and divided by (/).
+The `` element is used to denote operators. The definition of an operator is loose and it can mean the actual mathematical operators plus (+), minus (−), times (⋅) and divided by (/).
In MathML it also means different parentheses. For example the parenthesis `(` and curly bracket `{`. Please note that the element `` is deprecated and may not be used!
@@ -249,7 +258,8 @@ The percent sign is a `` element. For example 50 percent should be written a
The same character can be used in a different meaning based on the context. For example, the comma can be part of a number but in a sequence the comma is an operator.
-The sequence {1,2,3,…} written in MathML:
+The sequence {1, 2, 3, …} written in MathML:
+
```html
{
@@ -258,6 +268,7 @@ The sequence {1,2,3,…} written in MathML:
2
,
3
+ ,
…
}
@@ -282,7 +293,7 @@ The `` element is used to denote functions, variables, units, and other iden
Functions and function names are identifiers: `tan`, `sin` or `log`.
-Units are identifiers. For example meter `m` or second `s`. When units are written using multiple letters, they should be marked up as a single element: `Nm`. Depending on the layout of the unit, you have to use other MathML elements to mark up a single unit such as metre per second squared:
+Units are identifiers. For example meter `m` or second `s`. When units are written using multiple letters, they should be marked up as a single element: `Nm`. Depending on the layout of the unit, you have to use other MathML elements to mark up a single unit such as meter per second squared:
```html
@@ -296,7 +307,7 @@ Units are identifiers. For example meter `m` or se
```
-Which renders as $\frac{\text{m}}{\text{s}^2}$.
+Which renders as $\frac{\text{m}}{\text{s}^2}$.
Note that the attribute mathvariant="normal" is necessary for a single-letter unit not to be in italic.
The ellipsis or three dots … is also an identifier `…`.
@@ -319,7 +330,7 @@ The explanatory text in between the math expressions should be regular text and
After this lemma [mathematical expression] we can see that this holds for [more mathematical expression] and it happens so.
```
-`` should only be used in places where the visual rendering requires it.
+`` should only be used in places where the visual rendering requires it.
Examples of this are in tabular math, such as equation solving, and what is often seen in text books: $\frac{\text{numerator}}{\text{denominator}}$.
@@ -461,6 +472,7 @@ Exampe of rendering a determinant when the `` hasn't been used at all:
The element `` is used for fractions, but also for other mathematical expressions that have the same visual layout such as the binomial.
Example mark up for a fraction:
+
```html
@@ -472,8 +484,8 @@ Example mark up for a fraction:
The fraction rendered: $\frac{5}{2}$.
-
Example mark up for a binomial:
+
```html
(
@@ -526,12 +538,13 @@ This would render: $\sqrt[3]{8} = 2$
`` is used to visually render space around an element. `` is used to visually render space between elements.
-Both of the elements accept attributes that can be used to modify the width, height and depth of the expressions. Only use relative units for these attributes such as em or rem unless specified otherwise by the Ordering Agency.
+Both of the elements accept attributes that can be used to modify the width, height and depth of the expressions. Only use relative units for these attributes such as em or en unless specified otherwise by the Ordering Agency.
#### Visual alignment of expressions
-Expressions should be marked up to display as similar to the source as possible. This means that sometimes the alignment of terms in e.g. a fraction or a system of equations needs to be adjusted. `` should be used for this purpose. For example, the fraction
-
+Expressions should be marked up to display as similar to the source as possible. This means that sometimes the alignment of terms in e.g. a fraction or a system of equations needs to be adjusted. `` should be used for this purpose. For example, the fraction
+
+
is marked up as follows:
@@ -560,7 +573,6 @@ is marked up as follows:
### Script and Limit Schemata
-
#### Subscripts and Superscripts, ``, ``, ``
Superscript notation is marked up using ``. The first child element is the base, and the second child element is the superscript. For example, $x^2$ is marked up as follows:
@@ -634,7 +646,7 @@ The same principle applies for ``. Note also that the base can be group
```
-Or $\int_a^b$:
+Or $\int_a^b f(x) \hspace{0.25em} dx$:
```html
@@ -652,6 +664,7 @@ Or $\int_a^b$:
x
```
+
Note the markup of the space between the integrand $f(x)$, and $dx$. Mark up $dx$ in two separate `` elements. It is also possible to use `` for integrals. Use the markup that matches the original source.
#### Underscripts and Overscripts, ``, ``, ``
@@ -674,7 +687,8 @@ Underscript notation is marked up using the element ``. The first child
Sometimes it is necessary to nest multiple `` elements. For example when you want to mark up text that is underneath an expression:

-Mark up for this expression is as follows
+Markup for this expression is as follows
+
```html
@@ -736,7 +750,7 @@ When both an underscript and overscript are needed, the element `` i
```
-Note that `` can be used to group together base, underscript or overscript respectively, as explained in [Subscripts and Superscripts](#Subscripts-and-Superscripts,-``,-``,-``).
+Note that `` can be used to group together base, underscript or overscript respectively, as explained in [Subscripts and Superscripts](#subscripts-and-superscripts-msub-msup-msubsup).
#### Prescripts and Postscripts, ``
@@ -759,7 +773,8 @@ Sometimes multiple prescripts and postscripts are attached to the same base, e.g
```
-In the example, A is the base. `` marks where the prescripts begin.
+In the example, A is the base. `` marks where the prescripts begin.
+
- `A` is the base element.
- `m` is a postscript subscript.
- `n` and `p` are postscript superscripts.
@@ -847,6 +862,7 @@ If there is mathematical notation that cannot be achieved with an HTML ``
Any mathematical notation that spans multiple lines should be marked up with the MathML ``.
Some use cases for tabular math include:
+
- matrices
- determinants
- piecewise functions
@@ -942,6 +958,7 @@ Example of a piecewise function. It is important that the different expressions
```
Some notation might look like tabular math, but is not. Some possibilities for confusion:
+
- absolute value $|x+2|$
- intervals $[5,15]$.
@@ -954,6 +971,7 @@ If the rows and columns need to be spanned across multiple cells, use the `rowsp
Note that `columnspan` is written this way due to backwards compatability for MathML 3.
### Labeling and referencing equations
+
It is common to label equations and then reference these equations later on in mathematical text. In MathML the `` element is used to mark up labeled equations.
For labeled equations that are part of a paragraph, place the `` element inside a `` element, and place the id for the equation on the `` element.
@@ -979,11 +997,12 @@ For labeled equations that are part of a paragraph, place the `` element i
```
-To reference the equation, use the anchor tag and the href attribute. For example:
+To reference the equation, use the anchor tag and the href attribute. For example:
-```html
+```html
From equation (1.1) we can see that...
```
+
Place the id for the equation on the `` element if the `` element is the only element inside the `` element.
```html
@@ -1006,7 +1025,6 @@ Place the id for the equation on the `
` element if the `` element is th
```
-