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10. Miscelaneous

10.1 Mathematical Formulas

They can appear with in the following tags:
tagdescriptionsee finline formula The Formula Tag dmdisplayed formula Mathematical Paragraph eqequatuion Mathematical Paragraph

After a little handparsing 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.

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 thing an example will tell you more:

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

results to:

713

In case we wanto 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>

Wich results to:

1213

Product, Integral and Summation Tag


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

These tags are same in syntax. 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.


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

xi Integral<f>y=<in><ll>a<ul>b<opd>x<sup/2/</in></f>y=ax2 Summation<f>y=<sum><ll>i=1<ul>n<opd>x<inf/i/</sum></f>y=i=1xi

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 optag, wich can contain again a mathematical formula.

Bi=0

xi

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 decsribe arrays and matrices. The array (ar) is noted down aequivalent to a tabular (see section The Tabular Tag). The differences in handling are: 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:

a+b+c uv x-y 27 a+b u+v z 134 a 3u+vw xyz 2,978

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:

x+y

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. Wich character is mappt to wich figure you'll find int Mathematical Figures.

Realfont Tag


<!element  rf  - o (#pcdata) >

This tag is placing a real font within a mathematical formular.
I'm really not shure 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:

Binom: (a+b)2=a2+2ab+b2

Other Mathematcal Tags

The remaining tags simply modify the tagged formula, without implying any other tag.


nametagtyped results vectorv<f><v/a/&times;<v/b/=<v/0/</f>->a×b=0 overlineovl<f><ovl/1+1/=<ovl/2/</f>->1+1=2 underlineunl<f><unl/1+1/=<unl/2/</f>->1+1=2 superiorsup<f>e=m&times;c<sup/2/</f>->e=m×c2 inferiorinf<f>x<inf/i/:=2x<inf/i-1/+3</f>->xi:=2xi-1+3


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