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Në gjuhë tjera: [[En:Help:Formula|en]], [[De:Wikipedia:TeX|de]], [[Fi:Wikipedia:TeX-opas|fi]] [[Fr:Wikipédia:Formules TeX|fr]], [[hu: Wikip%C3%A9dia:Formula_le%C3%ADr%C3%B3nyelv|Magyarul (Hungarian)]], [[Ia:Wikipedia:Formulas mathematic|ia]], [[Ja:Wikipedia:TeX markup|ja]], [[Sv:Wikipedia:AttAnvändaTeX|sv]], [[Zh:Wikipedia:数学公式|zh]], [[Ru:Википедия:Как_отображать_формулы|ru]]
==TeX==
[[MediaWiki]] për formulat nga matematika përdorë '''[[:en:TeX|TeX]] markup'''(anglisht). Ky program ndihmon për krijimin e figurave të formatit [[:en:PNG|PNG]](anglisht) si dhe dizajnin e thjeshtë të [[HTML]], varësisht nga rekomandimet (parapëlqimet) që ju keni përgatitur për përdorimin e fletave të Wikipedias. Në të ardhmen do të jetë e mundshme që të shënohen formula edhe më komplekse si p.sh:[[:en:MathML|MathML]](anglisht).
Figurat e formatit PNG, janë bardhë e zi dhe nuk janë transparente. Ngjyrat dhe dizajni i figurave varret shumë nga shfletuesi që ju përdorni. shpesh do të ndodhë që dizajni i përpiluar do nuk do të jetë ai që ju keni pritur sikurse tel HTML.
==Funksionet, simbolet, shenjat e veçanta==
(shiko në anglisht [[:en:Help:Special characters]])
<table border="1">
<tr>
<th>Tema</th>
<th>Sintaksa</th>
<th>Si duket e lëmuar</th>
</tr>
<tr>
<td>Funksione (drejtë)</td>
<td>\sin x + \ln y +\operatorname{sgn} z</td>
<td><math>\sin x + \ln y +\operatorname{sgn} z</math></td>
</tr>
<tr>
<td>Funksione (gabim)</td>
<td>sin x + ln y + sgn z</td>
<td><math>sin x + ln y + sgn z\,</math></td>
</tr>
<tr>
<td>Module arit.</td>
<td>s_k \equiv 0 \pmod{m}</td>
<td><math>s_k \equiv 0 \pmod{m}</math></td>
</tr>
<tr>
<td>Derivate</td>
<td>\nabla \partial x dx \dot x \ddot y</td>
<td><math>\nabla \ \partial x \ dx \ \dot x\ \ddot y</math></td>
</tr>
<tr>
<td>Bashkësi</td>
<td>\forall x \not\in \varnothing \subseteq A \cap \bigcap B \cup \bigcup \exists \{x,y\}
\times C</td>
<td><math>\forall x \not\in \varnothing \subseteq A \cap \bigcap B \cup \bigcup \exists \{x,y\}
\times C</math></td>
</tr>
<tr>
<td>Logjikë</td>
<td>p \land \bar{q} \to p\lor \lnot q</td>
<td><math>p \land \bar{q} \to p\lor \lnot q</math></td>
</tr>
<tr>
<td rowspan="2">Rrënjë</td>
<td>\sqrt{2}\approx 1.4</td>
<td><math>\sqrt{2}\approx 1.4</math></td>
</tr>
<tr>
<td>\sqrt[n]{x}</td>
<td><math>\sqrt[n]{x}</math></td>
</tr>
<tr>
<td>Relacione</td>
<td>\sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne \propto</td>
<td><math> \sim \ \simeq \ \cong \ \le \ \ge \ \equiv \ \not\equiv \ \approx \ \ne \ \propto</math></td>
</tr>
<tr>
<td>Gjeometri</td>
<td>\triangle \angle \perp \| 45^\circ</td>
<td><math>\triangle \ \angle \perp \| \ 45^\circ</math></td>
</tr>
<tr>
<td rowspan="2">Shigjeta</td>
<td>
\leftarrow \rightarrow \leftrightarrow<br/>
\longleftarrow \longrightarrow<br/>
\mapsto \longmapsto<br/>
\nearrow \searrow \swarrow \nwarrow<br/>
\uparrow \downarrow \updownarrow<br/>
</td>
<td>
<math>\leftarrow\ \rightarrow\ \leftrightarrow</math>
<math>\longleftarrow\ \longrightarrow</math>
<math>\mapsto\ \longmapsto</math>
<math>\nearrow\ \searrow\ \swarrow\ \nwarrow</math>
<math>\uparrow\ \downarrow\ \updownarrow</math>
</td>
</tr>
<tr>
<td>
\Leftarrow \Rightarrow \Leftrightarrow<br/>
\Longleftarrow \Longrightarrow \Longleftrightarrow<br/>
\Uparrow \Downarrow \Updownarrow
</td>
<td>
<math>\Leftarrow\ \Rightarrow\ \Leftrightarrow</math>
<math>\Longleftarrow\ \Longrightarrow\ \Longleftrightarrow</math>
<math>\Uparrow\ \Downarrow\ \Updownarrow</math>
</td>
</tr>
<tr>
<td>Të veçanta</td>
<td>\div \oplus \otimes \pm \mp \hbar \wr \dagger \ddagger \star * \ldots \circ \cdot \times
\bullet \infty \vdash \models</td>
<td><math>\div \oplus \otimes \pm \mp \hbar \wr \dagger \ddagger \star * \ldots</math>
<math>\circ \cdot \times \bullet\ \infty \ \vdash \ \models</math></td>
</tr>
<tr>
<td>Të posaçme</td>
<td>\mathcal {45abcdenpqstuvwx}</td>
<td><math>\mathcal {45abcdenpqstuvwx}</math>
</td>
</tr>
</table>
== Fuqizimet, indekset, integralet ==
<table border="1">
<tr>
<th>Tema</th>
<th>Sintaksa</th>
<th>Si duket e lëmuar</th>
</tr>
<tr>
<td>Fuqizimi</td>
<td>a^2</td>
<td><math>a^2</math></td>
<td><math>a^2 \,\!</math></td>
</tr>
<tr>
<td>Indeksi</td>
<td>a_2</td>
<td><math>a_2</math></td>
<td><math>a_2 \,\!</math></td>
</tr>
<tr>
<td rowspan="2">Grupimi</td>
<td>a^{2+2}</td>
<td><math>a^{2+2}</math></td>
<td><math>a^{2+2} \,\!</math></td>
</tr>
<tr>
<td>a_{i,j}</td>
<td><math>a_{i,j}</math></td>
<td><math>a_{i,j} \,\!</math></td>
</tr>
<tr>
<td>Kombinim i fuqizimit dhe indeksit</td>
<td>x_2^3</td>
<td colspan="2"><math>x_2^3</math></td>
</tr>
<tr>
<td>Derivate (drejtë)</td>
<td>x'</td>
<td><math>x'</math></td>
<td><math>x' \,\!</math></td>
</tr>
<tr>
<td>Derivate (gabim në HTML)</td>
<td>x^\prime</td>
<td><math>x^\prime</math></td>
<td><math>x^\prime \,\!</math></td>
</tr>
<tr>
<td>Derivate (gabim në PNG)</td>
<td>x\prime</td>
<td><math>x\prime</math></td>
<td><math>x\prime \,\!</math></td>
</tr>
<tr>
<td>Derivate (pikësimi)</td>
<td>\dot{x}, \ddot{x}</td>
<td colspan="2"><math>\dot{x}, \ddot{x}</math></td>
</tr>
<tr>
<td>Shënimi mbi dhe nën</td>
<td>\hat a \bar b \vec c \widehat {d e f} \overline {g h i} \underline {j k l} </td>
<td colspan="2"><math>\hat a \ \bar b \ \vec c \ \widehat {d e f} \ \overline {g h i} \ \underline {j k l}</math></td>
</tr>
<tr>
<td>Shuma</td>
<td>\sum_{k=1}^N k^2</td>
<td colspan="2"><math>\sum_{k=1}^N k^2</math></td>
</tr>
<tr>
<td>Produkti</td>
<td>\prod_{i=1}^N x_i</td>
<td colspan="2"><math>\prod_{i=1}^N x_i</math></td>
</tr>
<tr>
<td>Limiti</td>
<td>\lim_{n \to \infty}x_n</td>
<td colspan="2"><math>\lim_{n \to \infty}x_n</math></td>
</tr>
<tr>
<td>Integrali</td>
<td>\int_{-N}^{N} e^x\, dx</td>
<td colspan="2"><math>\int_{-N}^{N} e^x\, dx</math></td>
</tr>
<tr>
<td>Integrali i vijëzuar</td>
<td>\oint_{C} x^3\, dx + 4y^2\, dy</td>
<td colspan="2"><math>\oint_{C} x^3\, dx + 4y^2\, dy</math></td>
</tr>
</table>
== Thyesat, matricat, dhënia e funksioni ==
<table border="1">
<tr>
<th>Tema</th>
<th>Sintaksa</th>
<th>Si duket gjate perdorikit te zakonshem </th>
</tr>
<tr>
<td>Thyesa</td>
<td>\frac{2}{4} or {2 \over 4}</td>
<td><math>\frac{2}{4}</math></td>
</tr>
<tr>
<td>Koeficienti binomial</td>
<td>{n \choose k}</td>
<td><math>{n \choose k}</math></td>
</tr>
<tr>
<td>Thyesa (të vogla)</td>
<td>\begin{matrix} \frac{2}{4} \end{matrix}</td>
<td><math>\begin{matrix} \frac{2}{4} \end{matrix}</math></td>
</tr>
<tr>
<td rowspan="6">Matrica</td>
<td>\begin{matrix} x & y \\ z & v \end{matrix}</td>
<td><math>\begin{matrix} x & y \\ z & v
\end{matrix}</math></td>
</tr>
<tr>
<td>\begin{vmatrix} x & y \\ z & v \end{vmatrix}</td>
<td><math>\begin{vmatrix} x & y \\ z & v
\end{vmatrix}</math></td>
</tr>
<tr>
<td>\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}</td>
<td><math>\begin{Vmatrix} x & y \\ z & v
\end{Vmatrix}</math></td>
</tr>
<tr>
<td>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots &
\ddots & \vdots \\ 0 & \cdots &
0\end{bmatrix}</td>
<td><math>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots
& \ddots & \vdots \\ 0 & \cdots &
0\end{bmatrix} </math></td>
</tr>
<tr>
<td>\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}</td>
<td><math>\begin{Bmatrix} x & y \\ z & v
\end{Bmatrix}</math></td>
</tr>
<tr>
<td>\begin{pmatrix} x & y \\ z & v \end{pmatrix}</td>
<td><math>\begin{pmatrix} x & y \\ z & v
\end{pmatrix}</math></td>
</tr>
<tr>
<td>Diskutimi i funksionit</td>
<td>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}</td>
<td><math>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} </math></td>
</tr>
<tr>
<td>Ekuacioni i shumëishtë</td>
<td>\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ &
= & n^2 + 2n + 1 \end{matrix}</td>
<td><math>\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}</math></td>
</tr>
<tr>
<td>Ekuacioni (shënim tjetër-tabelarë) </td>
<td><pre>
<nowiki>
{|
|-
|<math>f(n+1)</math>
|<math>=(n+1)^2</math>
|-
|
|<math>=n^2 + 2n + 1</math>
|}
</nowiki>
</pre>
</td>
<td>
{|
|-
|<math>f(n+1) \,\!</math>
|<math>=(n+1)^2 \,\!</math>
|-
|
|<math>=n^2 + 2n + 1 \,\!</math>
|}
</td>
</tr>
</table>
== Dekorimi i shkronjave ==
<table border="1">
<tr>
<th>Tema</th>
<th>Sintaksa</th>
<th>Si duket e lëmuar</th>
</tr>
<tr>
<td>[[:en:Greek alphabet|ABC-greke (ang.)]]</td>
<td>\alpha \beta \gamma \Gamma \phi \Phi \Psi\ \tau \Omega</td>
<td colspan="2"><math>\alpha\ \beta\ \gamma\ \Gamma\ \phi\ \Phi\ \Psi\ \tau\ \Omega</math></td>
</tr>
<tr>
<td>[[:en:Blackboard bold|Të trasha (ang.)]]</td>
<td>x\in\mathbb{R}\sub\mathbb{C}</td>
<td colspan="2"><math>x\in\mathbb{R}\subset\mathbb{C}</math></td>
</tr>
<tr>
<td>[[:en:boldface|Të trasha (ang.)]] (vektorët)</td>
<td>\mathbf{x}\cdot\mathbf{y} = 0</td>
<td colspan="2"><math>\mathbf{x}\cdot\mathbf{y} = 0</math></td>
</tr>
<tr>
<td>Të trasha (greke)</td>
<td>\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}</td>
<td colspan="2"><math>\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}</math></td>
</tr>
<tr>
<td>[[:en:Fraktur typeface|ABC-Fraktur (ang.)]]</td>
<td>\mathfrak{a} \mathfrak{B}</td>
<td colspan="2"><math>\mathfrak{a} \mathfrak{B}</math></td>
</tr>
<tr>
<td>ABC-Script</td>
<td>\mathcal{ABC}</td>
<td colspan="2"><math>\mathcal{ABC}</math></td>
</tr>
<tr>
<td>[[:en:Hebrew alphabet|ABC-hebrese (ang.)]]</td>
<td>\aleph \beth \gimel \daleth</td>
<td colspan="2"><math>\aleph\ \beth\ \gimel\ \daleth</math></td>
</tr>
<tr>
<td>karakteret jo të pjerrëta</td>
<td>\mbox{abc}</td>
<td><math>\mbox{abc}</math></td>
<td><math>\mbox{abc} \,\!</math></td>
</tr>
<tr>
<td>Të përziera (gabim)</td>
<td>\mbox{if} n \mbox{is even}</td>
<td><math>\mbox{if} n \mbox{is even}</math></td>
<td><math>\mbox{if} n \mbox{is even} \,\!</math></td>
</tr>
<tr>
<td>Të përziera (drejtë)</td>
<td>\mbox{if }n\mbox{ is even}</td>
<td><math>\mbox{if }n\mbox{ is even}</math></td>
<td><math>\mbox{if }n\mbox{ is even} \,\!</math></td>
</tr>
</table>
== Thyesat komplekse, kllapa, zbrastirat ==
<table border="1">
<tr>
<th>Tema</th>
<th>Sintaksa</th>
<th>Si duket e lëmuar</th>
</tr>
<tr>
<td>Gabim</td>
<td>( \frac{1}{2} )</td>
<td><math>( \frac{1}{2} )</math></td>
</tr>
<tr>
<td>Drejtë</td>
<td>\left ( \frac{1}{2} \right )</td>
<td><math>\left ( \frac{1}{2} \right )</math></td>
</tr>
</table>
Mund të përdorni edhe \left and \right:
<table border="1">
<tr>
<th>Tema</th>
<th>Sintaksa</th>
<th>Si duket e lëmuar</th>
</tr>
<tr>
<td>Kllapa të zakonshme</td>
<td>\left ( A \right )</td>
<td><math>\left ( A \right )</math></td>
</tr>
<tr>
<td>Kllapa këndore</td>
<td>\left [ A \right ]</td>
<td><math>\left [ A \right ]</math></td>
</tr>
<tr>
<td>Kllapa gjarpërore</td>
<td>\left \{ A \right \}</td>
<td><math>\left \{ A \right \}</math></td>
</tr>
<tr>
<td>Kllapa shijetore</td>
<td>\left \langle A \right \rangle</td>
<td><math>\left \langle A \right \rangle</math></td>
</tr>
<tr>
<td>Vlera absolute</td>
<td>\left | A \right | and \left \| B \right \|</td>
<td><math>\left | A \right | and \left \| B \right \|</math></td>
</tr>
<tr>
<td>
Përzierja e kllapave<br/> përderisa '''\left''' dhe '''\right''' ekuilibrohen
</td>
<td>
\left [ 0,1 \right )<br/>\left \langle \psi \right |
</td>
<td>
<math>\left [ 0,1 \right )</math><br/><math>\left \langle \psi \right |</math>
</td>
</tr>
<tr>
<td>Përdorimi i '''\left.''' me pikë, dhe '''\right.'''me pikë, në raste<br/>të panevojshme:</td>
<td>\left . \frac{A}{B} \right \} \to X</td>
<td><math>\left . \frac{A}{B} \right \} \to X</math></td>
</tr>
</table>
== Fushat dhe hapësirat boshe (zbrazëta) ==
Zakonist që programi TeX krijon fushat vetëvetiu, por nganjëherë ju nevojitet diçka më shumë kontrollë mbi hapsirat në mes të karaktereve.
<table border="1">
<tr>
<th>Tema</th>
<th>Sintaksa</th>
<th>Si duket e lëmuar</th>
</tr>
<tr>
<td>Fusha boshe e dyfishë</td>
<td>a \qquad b</td>
<td><math>a \qquad b</math></td>
</tr>
<tr>
<td>Fusha boshe</td>
<td>a \quad b</td>
<td><math>a \quad b</math></td>
</tr>
<tr>
<td>Hapësira e tekstit</td>
<td>a\ b</td>
<td><math>a\ b</math></td>
</tr>
<tr>
<td>Hapësira e tekstit të pa lëmuar nga PNG-ja</td>
<td>a \mbox{ } b</td>
<td><math>a \mbox{ } b</math></td>
</tr>
<tr>
<td>Hapësira të gjëra</td>
<td>a\;b</td>
<td><math>a\;b</math></td>
</tr>
<tr>
<td>Hapësira të mesme</td>
<td>a\>b</td>
<td>[not supported]</td>
</tr>
<tr>
<td>Hapësira të ngushta</td>
<td>a\,b</td>
<td><math>a\,b</math></td>
</tr>
<tr>
<td>Pa hapësirë</td>
<td>ab</td>
<td><math>ab\,</math></td>
</tr>
<tr>
<td>Hapësira negative</td>
<td>a\!b</td>
<td><math>a\!b</math></td>
</tr>
</table>
== Align with normal text flow ==
Nëse dëshironi të fusni në tekstë diçka të tilë si kjo: <font style="vertical-align:-100%;"><math>\int_{-N}^{N} e^x\, dx</math></font> mund të shkruani në HTML <tt><font></tt> ''tag''-un për ''vertical alignment'':
: ''<nowiki><font style="vertical-align:-100%;"><math>...</math></font></nowiki>''
== Lëmimi i forcua i PNG-së ==
<!--
If you must, it is possible to force the formula to render as PNG, without affecting the display of the formula, by adding <tt>\,</tt> (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in [[Special:Preferences|Preferences]]).
You can also use <tt>\,\!</tt> (small space and negative space, which cancel out) anywhere inside the math tags. This ''does'' force PNG in "HTML if possible" mode, unlike <tt>\,</tt>.
This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).
-->
Për shembull:
<table border="1">
<tr>
<th>Sintaksa</th>
<th>Si duket e lëmuar</th>
</tr>
<tr>
<td>a^{2+2}</td>
<td><math>a^{2+2}</math></td>
</tr>
<tr>
<td>a^{2+2} \,</td>
<td><math>a^{2+2} \,</math></td>
</tr>
<tr>
<td>a^{\,\!2+2}</td>
<td><math>a^{\,\!2+2}</math></td>
</tr>
<tr>
<td>\int_{-N}^{N} e^x\, dx</td>
<td><math>\int_{-N}^{N} e^x\, dx</math></td>
</tr>
<tr>
<td>\int_{-N}^{N} e^x\, dx \,</td>
<td><math>\int_{-N}^{N} e^x\, dx \,</math></td>
</tr>
<tr>
<td>\int_{-N}^{N} e^x\, dx \,\!</td>
<td><math>\int_{-N}^{N} e^x\, dx \,\!</math></td>
</tr>
</table>
<!--This has been tested with most of the formulae on this page, and seems to work perfectly.
You might want to include a comment in the HTML so people don't "correct" the formula by removing it:-->
:''<nowiki><!-- Shenjat \,\! jan pë të mbajtur formulat të lëmuara si PNG në vend të HTML. Ju lutem mos i hiqni.--></nowiki>''
== Shembuj ==
<center>
<math>x_{1,2} = {{ - b \pm \sqrt {b^2 - 4ac} } \over {2a}}</math>
<math>\frac{4}{3-x} = \frac{3}{2-x}</math>
<math>\left(3-x\right) \times \left( \frac{2}{3-x} \right) = \left(3-x\right) \times \left( \frac{3}{2-x} \right)</math>
<math>2 = \left(3-x\right) \times \left( \frac{3}{2-x} \right)</math>
<math>2 = \left( \frac{\left(3-x\right) \times 3}{2-x} \right)</math>
<math>2 = \left( \frac{9-3x}{2-x} \right)</math>
<math>2 \times \left(2-x\right) = \left(2-x\right) \times \left( \frac{9-3x}{2-x} \right)</math>
<math>2 \times \left(2-x\right) = \frac{\left(2-x\right) \times \left(9-3x\right)}{2-x}</math>
<math>2 \times \left(2-x\right) = 9-3x \!</math>
<math>4-2x = 9-3x \!</math>
<math>-2x+3x = 9-4 \!</math>
<math>x = 5 \!</math>
</center>
==Shiko dhe këtë==
* Proposed [[:en:GNU LilyPond support]]
== Lidhje të jashtme ==
* Mësime nga '''LaTeX''' http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
* A [[en:Portable Document Format|PDF]] document introducing TeX -- see page 39 onwards for a good introduction to the maths side of things: http://www.ctan.org/tex-archive/info/gentle/gentle.pdf
* A PDF document introducing LaTeX -- skip to page 59 for the math section. See page 72 for a complete reference list of symbols included in LaTeX and AMS-LaTeX. http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf
* TeX reference card: http://www.csit.fsu.edu/~mimi/tex/tex-refcard-letter.pdf
* Can't remember but I put it here so it must be ok ;-) http://www.ams.org/tex/amslatex.html
* A set of public domain fixed-size math symbol bitmaps: http://us.metamath.org/symbols/symbols.html
[[en:Help:Formula]]
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