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## 9. Mathematical Formulas

They can appear with in the tags listed in table Places of Mathematical Formulas

tag | description | see
f | inline formula | The Formula Tag
dm | displayed formula | Mathematical Paragraph
eq | equation | Mathematical Paragraph Places of Mathematical Formulas

If you view this document mapped to html you will notice that html has no nice way of displaying mathematical formulas.

After a little hand parsing the contents of a mathematical tag looks like:

    <!element  xx       - -
            (((fr|lim|ar|root) |
              (pr|in|sum) |
              (#pcdata|mc|(tu|phr)) |
              (rf|v|fi) |
              (unl|ovl|sup|inf))*)>

The `xx` stands for `f`, `dm` or `eq`. All of them are the same.

Note:

  Because neither Netscape nor Microsoft has seen any need to add mathematical mappings to their browsers (like demanded and defined by w3c), there is no nice way of mapping, or at least displaying the math stuff in html. So if you view the online version, feel free to wonder what nonsense this man is telling here. Might be you should take a glance at the postscript version.

## 9.1 Fraction Tag

    <!element  fr       - - (nu,de) >
    <!element  nu       o o ((%fbutxt;)*) >
    <!element  de       o o ((%fbutxt;)*) >

So what we see from it is, that a fraction consits of a numerator and a denumerator tag, wich again each one can hold a mathematical formula.

I think an example will tell you more:

    <dm><fr><nu/7/<de/13/</fr></dm>

results to:

<DM> <FR><NU>7</NU><DE>13</DE></FR> </DM>

In case we want to to place 1/2 instead of the numerator without cleaning it up, we'll type:

    <dm><fr><nu><fr><nu/1/<de/2/</fr></nu><de/13/</fr></dm>

Which results to:

<DM> <FR><NU><FR><NU>1</NU><DE>2</DE></FR></NU><DE>13</DE></FR> </DM>

## 9.2 Product, Integral and Summation Tag

    <!element  pr       - - (ll,ul,opd?) >
    <!element  in       - - (ll,ul,opd?) >
    <!element  sum      - - (ll,ul,opd?) >

Each of them has a lower limit (`ll` tag), a upper limit (`ul` tag) and a optional operand, where each of them again may consist of a formula. The tags are same in syntax like shown in table Tags with upper-, lower limit and operator.

name | example | result

Product

`<f>y=<pr><ll>i=1<ul>n<opd>x<inf/i/</pr></f>`

y=<PR><LL>i=1</LL>

n

<OPD>xi</OPD></PR>

Integral

`<f>y=<in><ll>a<ul>b<opd>x<sup/2/</in></f>`

y=<INT><LL>a</LL>

b

<OPD>x2</OPD></INT>

Summation

`<f>y=<sum><ll>i=1<ul>n<opd>x<inf/i/</sum></f>`

y=<SUM><LL>i=1</LL>

n

<OPD>xi</OPD></SUM>

Tags with upper-, lower limit and operator

## 9.3 Limited Tag

    <!element  lim      - - (op,ll,ul,opd?) >
    <!element  op       o o (%fcstxt;|rf|%fph;) -(tu) >
    <!element  ll       o o ((%fbutxt;)*) >
    <!element  ul       o o ((%fbutxt;)*) >
    <!element  opd      - o ((%fbutxt;)*) >

You can use that one for operators with upper and lower limits other than products, sums or integrals. The for the other types defined operator is destinied by the `op`tag, wich can contain again a mathematical formula.

<DM> <LIM><OP>B</OP><LL>i=0</LL>

n

<OPD>xi</OPD></LIM> </DM>

## 9.4 Array Tag

    <!element  ar       - - (row, (arr, row)*) >
    <!attlist  ar
        ca     cdata    #required >
    <!element  arr      - o empty >
    <!element  arc      - o empty >
    <!entity   arr "<arr>" >
    <!entity   arc "<arc>" >

Of course a reasonable mathematical document needs a way to describe arrays and matrices. The array (`ar`) is noted down equivalent to a tabular (see section The Tabular Tag). The differences in handling are:

- No `<hline>` tag.
- The `ca` attribute character `|` is not allowd.
- Columns are not separated by `colsep` tag but with the `arc` tag (array collumn).
- Rows are not separated by `rowsep` tag but with the `arr` tag (array row).

Again the characters `|` and `@` are mapped to the adequate separator tag, so you really can note a array same way as a tabular.

    <dm><ar ca="clcr">
    a+b+c | uv    <arc> x-y | 27    @
    a+b   | u+v   | z   | 134   <arr>
    a     | 3u+vw | xyz | 2,978
    </ar></dm>

Is mapped to:

<DM> <AR>a+b+c <ARC>uv <ARC>x-y <ARC>27 <ARR>a+b <ARC>u+v <ARC>z <ARC>134 <ARR>a <ARC>3u+vw <ARC>xyz <ARC>2,978 </AR> </DM>

## 9.5 Root Tag

    <!element  root     - - ((%fbutxt;)*) >
    <!attlist  root
            n cdata "">

The root is noted down by the `root` tag, wich contains a `n` attribute, holding the value for the "n'th" root.

    <dm><root n="3"/x+y/</dm>

is mapped to:

<DM> <ROOT>x+y</ROOT> </DM>

## 9.6 Figure Tag

    <!element  fi  - o (#pcdata) >

With the figure tag you can place mathematical figures. The tagged characters are directly mapped to a mathematical figure. Which character is mapped to which figure you'll find in Mathematical Figures.

## 9.7 Realfont Tag

    <!element  rf  - o (#pcdata) >

This tag is placing a real font within a mathematical formula.

> I'm really not sure about `rf`. What should it be?

No formula is allowed within that tag.

    <dm><rf/Binom:/ (a+b)<sup/2/=a<sup/2/+2ab+b<sup/2/</dm>

is mapped to:

<DM> <RF>Binom:</RF> (a+b)2=a2+2ab+b2 </DM>

## 9.8 Other Mathematical Tags

The remaining tags simply modify the tagged formula, without implying any other tag. The effect is shown in table Mathematical tags without included tags

name | tag | example |  | result
vector | `v` | `<f><v/a/&times;<v/b/=<v/0/</f>` | -> | <V>a</V>×<V>b</V>=<V>0</V>
overline | `ovl` | `<f><ovl/1+1/=<ovl/2/</f>` | -> | <OVL>1+1</OVL>=<OVL>2</OVL>
underline | `unl` | `<f><unl/1+1/=<unl/2/</f>` | -> | <UNL>1+1</UNL>=<UNL>2</UNL>
superior | `sup` | `<f>e=m&times;c<sup/2/</f>` | -> | e=m×c2
inferior | `inf` | `<f>x<inf/i/:=2x<inf/i-1/+3</f>` | -> | xi:=2xi-1+3
Mathematical tags without included tags

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