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They can appear with in the tags listed in table
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.
<!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:
713
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:
1213
<!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=i=1xi |
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 |
Tags with upper-, lower limit and operator
|
<!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.
Bi=0xi
<!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:
a+b+c uv x-y 27 a+b u+v z 134 a 3u+vw xyz 2,978
<!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
<!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.
<!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:
Binom: (a+b)2=a2+2ab+b2
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/×<v/b/=<v/0/</f> | -> | a×b=0 |
overline | ovl | <f><ovl/1+1/=<ovl/2/</f> | -> | 1+1=2 |
underline | unl | <f><unl/1+1/=<unl/2/</f> | -> | 1+1=2 |
superior | sup | <f>e=m×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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