"Matematiksel formüller" sayfasının sürümleri arasındaki fark

13:39, 19 Şubat 2014 tarihindeki hâli

MediaWiki yazılımı matematiksel ifadelerin biçimlendirilmesinde LaTeX ve AMSLaTeX yazılımlarını içeren TeX yazılımını kullanmaktadır. Bazı matematiksel formüller kişisel tercihlere bağlı olarak PNG, bazıları ise HTML olarak gözükebilir.

UNIQ0bd346bf6e656e70-item-541--QINU

Kodlama

Matematiksel kodlar UNIQ0bd346bf6e656e70-code-0000021E-QINU kodları arasına yazılır. Math markup goes inside UNIQ0bd346bf6e656e70-code-0000021F-QINU. The edit toolbar has a button for this.

UNIQ0bd346bf6e656e70-item-544--QINU Tex kodları doğru yazılmadıkları zaman hata uyarısı verirler. Bu nedenle kodları doğru yazdığınızdan emin olmalısınız.

UNIQ0bd346bf6e656e70-item-545--QINU

Sunum

UNIQ0bd346bf6e656e70-item-546--QINU It should be pointed out that most of these shortcomings have been addressed by Maynard Handley, but have not been released yet.

The UNIQ0bd346bf6e656e70-code-00000223-QINU attribute of the PNG images (the text that is displayed if your browser can't display images; Internet Explorer shows it up in the hover box) is the wikitext that produced them, excluding the UNIQ0bd346bf6e656e70-code-00000224-QINU and UNIQ0bd346bf6e656e70-code-00000225-QINU.

Apart from function and operator names, as is customary in mathematics for variables, letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use UNIQ0bd346bf6e656e70-code-00000226-QINU or UNIQ0bd346bf6e656e70-code-00000227-QINU. For example, UNIQ0bd346bf6e656e70-code-00000228-QINU gives $ \mbox{abc} $.

TeX ve HTML

Before introducing TeX markup for producing special characters, it should be noted that, as this comparison table shows, sometimes similar results can be achieved in HTML (see Help:Special characters).

UNIQ0bd346bf6e656e70-item-559--QINUas follows.

HTML'nin avantajları

1. HTML ile yazılan formüller her zaman yazının bütünü gibi durur.
2. HTML ile yazılan formüllerde, sayfanın arka planı, font türü, internet sunucusunun ayarları aktif olarak çalışır.
3. HTML kullanarak yazılan formüller sayfa açılım hızını arttırır.

TeX kullanımının avantajları

1. Tex kalite bakımından HTML'den ileri bir yazılımdır.
2. Tex yazılımında "UNIQ0bd346bf6e656e70-code-00000230-QINU" kodlaması matematiksel değişken anlamına gelir. Fakat HTML'de "UNIQ0bd346bf6e656e70-code-00000231-QINU" kodlaması herhangi bir anlama gelebilir. Bu yüzden bilgiler daha kolay kaybolabilir.
3. TeX yazılımı özellikle formül yazımı için tasarlanmıştır. Bu nedenle daha kolay ve daha işlevseldir.
4. One consequence of point 1 is that TeX can be transformed into HTML, but not vice-versa. This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It's true that the current situation is not ideal, but that's not a good reason to drop information/contents. It's more a reason to help improve the situation.
5. Diğer önemli husus TeX MathML kodlamasına, bu kodlamayı destekleyen sunucular tarafından çevirlebilmektedir.
6. TeX komutlarını kullanırken sunucu desteğine ya da diğer teknik desteklere ihtiyaç duymazsınız. Bu kodlamanın işlevselliğini serverler sağlamaktadır. Bu nedenle her türlü sunucuda, rahatlıkla yazıp kullanabileceğiniz bir kodlama türüdür.

Fonksiyonlar, semboller, özel karakterler

UNIQ0bd346bf6e656e70-item-562--QINU{| class="wikitable"

Aksanlar/Vurgular

|- |UNIQ0bd346bf6e656e70-code-00000233-QINU |$ \acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000234-QINU |$ \check{a} \bar{a} \ddot{a} \dot{a}\,\! $ |- ! colspan="2" |

Standart fonksiyonlar

|- |UNIQ0bd346bf6e656e70-code-00000235-QINU |$ \sin a \cos b \tan c\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000236-QINU |$ \sec d \csc e \cot f\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000237-QINU |$ \arcsin h \arccos i \arctan j\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000238-QINU |$ \sinh k \cosh l \tanh m \coth n\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000239-QINU |$ \operatorname{sh}o \operatorname{ch}p \operatorname{th}q\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023A-QINU |$ \operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023B-QINU |$ \lim u \limsup v \liminf w \min x \max y\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023C-QINU |$ \inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023D-QINU |$ \deg h \gcd i \Pr j \det k \hom l \arg m \dim n\,\! $ |-

Modüler aritmatik

|- |UNIQ0bd346bf6e656e70-code-0000023E-QINU |$ s_k \equiv 0 \pmod{m} a \bmod b\,\! $ |- ! colspan="2" |

Türevsel karakterler

|- |UNIQ0bd346bf6e656e70-code-0000023F-QINU |$ \nabla \partial x dx \dot x \ddot y\,\! $ |- ! colspan="2" |

Kümeler

|- |UNIQ0bd346bf6e656e70-code-00000240-QINU |$ \forall \exists \empty \emptyset \varnothing\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000241-QINU |$ \in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000242-QINU |$ \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000243-QINU |$ \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\! $ |- ! colspan="2" |

Operatör işaretler

|- |UNIQ0bd346bf6e656e70-code-00000244-QINU |$ + \oplus \bigoplus \pm \mp - \,\! $ |- |UNIQ0bd346bf6e656e70-code-00000245-QINU |$ \times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000246-QINU |$ \star * / \div \frac{1}{2}\,\! $ |- ! colspan="2" |

Mantıksal ifadeler

|- |UNIQ0bd346bf6e656e70-code-00000247-QINU |$ \land \wedge \bigwedge \bar{q} \to p\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000248-QINU |$ \lor \vee \bigvee \lnot \neg q \And\,\! $ |- ! colspan="2" |

Kök alma

|- |UNIQ0bd346bf6e656e70-code-00000249-QINU |$ \sqrt{2} \sqrt[n]{x}\,\! $ |- ! colspan="2" |

Eşitlik/Denklik/Benzerlik işaretleri

|- |UNIQ0bd346bf6e656e70-code-0000024A-QINU |$ \sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000024B-QINU |$ \le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,\! $ |- ! colspan="2" |

Geometrik

|- |UNIQ0bd346bf6e656e70-code-0000024C-QINU |$ \Diamond \, \Box \, \triangle \, \angle \perp \, \mid \; \nmid \, \| 45^\circ\,\! $ |- ! colspan="2" |

Oklar/Bildiri ifadeleri

|- |UNIQ0bd346bf6e656e70-code-0000024D-QINU |$ \leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000024E-QINU |$ \mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000024F-QINU |$ \uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000250-QINU |$ \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000251-QINU |$ \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\! $ |- |UNIQ0bd346bf6e656e70-code-00000252-QINU |$ \leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000253-QINU |$ \curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000254-QINU |$ \nLeftrightarrow \longleftrightarrow\,\! $ |-

Özel

|- |UNIQ0bd346bf6e656e70-code-00000255-QINU |$ \eth \S \P \% \dagger \ddagger \ldots \cdots\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000256-QINU |$ \smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000257-QINU |$ \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000258-QINU |$ \ell \mho \Finv \Re \Im \wp \complement \diamondsuit\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000259-QINU |$ \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\! $ |- ! colspan="2" |

Unsorted (new stuff)

|- |UNIQ0bd346bf6e656e70-code-0000025A-QINU |$ \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown $ |- |UNIQ0bd346bf6e656e70-code-0000025B-QINU |$ \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge $ |- |UNIQ0bd346bf6e656e70-code-0000025C-QINU |$ \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes $ |- |UNIQ0bd346bf6e656e70-code-0000025D-QINU |$ \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant $ |- |UNIQ0bd346bf6e656e70-code-0000025E-QINU |$ \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq $ |- |UNIQ0bd346bf6e656e70-code-0000025F-QINU |$ \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft $ |- |UNIQ0bd346bf6e656e70-code-00000260-QINU |$ \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot $ |- |UNIQ0bd346bf6e656e70-code-00000261-QINU |$ \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq $ |- |UNIQ0bd346bf6e656e70-code-00000262-QINU |$ \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork $ |- |UNIQ0bd346bf6e656e70-code-00000263-QINU |$ \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq $ |- |UNIQ0bd346bf6e656e70-code-00000264-QINU |$ \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid $ |- |UNIQ0bd346bf6e656e70-code-00000265-QINU |$ \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr $ |- |UNIQ0bd346bf6e656e70-code-00000266-QINU |$ \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq $ |- |UNIQ0bd346bf6e656e70-code-00000267-QINU |$ \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq $ |- |UNIQ0bd346bf6e656e70-code-00000268-QINU |$ \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq $ |- |UNIQ0bd346bf6e656e70-code-00000269-QINU |$ \jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000026A-QINU |$ \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000026B-QINU |$ \dashv \asymp \doteq \parallel\,\! $ |}

Üslü ifadeler, toplam-çarpım sembolleri, türev, integral

Fractions, matrices, multilines

Alphabets and typefaces

Parenthesizing big expressions, brackets, bars

You can use various delimiters with \left and \right:

Spacing

Note that TeX handles most spacing automatically, but you may sometimes want manual control.

Align with normal text flow

Due to the default css

UNIQ0bd346bf6e656e70-pre-000002F1-QINU

an inline expression like $ \int_{-N}^{N} e^x\, dx = 2 \sinh N $ should look good.

If you need to align it otherwise, use UNIQ0bd346bf6e656e70-code-000002F2-QINU and play with the UNIQ0bd346bf6e656e70-code-000002F3-QINU argument until you get it right; however, how it looks may depend on the browser and the browser settings.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

Forced PNG rendering

To force the formula to render as PNG, add UNIQ0bd346bf6e656e70-code-000002F4-QINU (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 preferences).

You can also use UNIQ0bd346bf6e656e70-code-000002F5-QINU (small space and negative space, which cancel out) anywhere inside the math tags. This does force PNG even in "HTML if possible" mode, unlike UNIQ0bd346bf6e656e70-code-000002F6-QINU.

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).

For instance:

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:

UNIQ0bd346bf6e656e70-nowiki-000002F7-QINU

Color

Equations can use color:

• UNIQ0bd346bf6e656e70-code-000002F8-QINU

  $ {\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1} $

• UNIQ0bd346bf6e656e70-code-000002F9-QINU

  $ x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a} $

See here for all named colours supported by LaTeX.

Note that color should not be used as the only way to identify something because color blind people may not be able to distinguish between the two colors. See en:Wikipedia:Manual of Style#Formatting issues.

Examples

$ ax^2 + bx + c = 0 $

UNIQ0bd346bf6e656e70-nowiki-000002FA-QINU

$ ax^2 + bx + c = 0\,\! $

UNIQ0bd346bf6e656e70-nowiki-000002FB-QINU

$ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} $

UNIQ0bd346bf6e656e70-nowiki-000002FC-QINU

$ 2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right) $

UNIQ0bd346bf6e656e70-nowiki-000002FD-QINU

$ S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2} $

UNIQ0bd346bf6e656e70-nowiki-000002FE-QINU

$ \int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy $

UNIQ0bd346bf6e656e70-nowiki-000002FF-QINU

$ \sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)} $

UNIQ0bd346bf6e656e70-nowiki-00000300-QINU

$ u'' + p(x)u' + q(x)u=f(x),\quad x>a $

UNIQ0bd346bf6e656e70-nowiki-00000301-QINU

$ |\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z) $

UNIQ0bd346bf6e656e70-nowiki-00000302-QINU

$ \lim_{z\rightarrow z_0} f(z)=f(z_0) $

UNIQ0bd346bf6e656e70-nowiki-00000303-QINU

$ \phi_n(\kappa)  = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R}  \frac{\partial}{\partial R}  \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR $

UNIQ0bd346bf6e656e70-nowiki-00000304-QINU

$ \phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0} $

UNIQ0bd346bf6e656e70-nowiki-00000305-QINU

$ f(x) = \begin{cases}1 & -1 \le x < 0 \\  \frac{1}{2} & x = 0 \\ 1 - x^2 & 0 < x \le 1\end{cases} $

UNIQ0bd346bf6e656e70-nowiki-00000306-QINU

$ {}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!} $

UNIQ0bd346bf6e656e70-nowiki-00000307-QINU

Bug reports

Discussions, bug reports and feature requests should go to the Wikitech-l mailing list. These can also be filed on Mediazilla under MediaWiki extensions.

See also

• Typesetting of mathematical formulas
• Proposed m:GNU LilyPond support
• Table of mathematical symbols
• m:Blahtex, or blahtex: a LaTeX to MathML converter for Wikipedia
• General help for editing a Wiki page
• Mimetex alternative for an another way to display mathematics using Mimetex.cgi

External links

• A LaTeX tutorial. http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
• A 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/docs/tex/tex-refcard-letter.pdf
• http://www.ams.org/tex/amslatex.html
• A set of public domain fixed-size math symbol bitmaps: http://us.metamath.org/symbols/symbols.html
• MathML - A product of the W3C Math working group, is a low-level specification for describing mathematics as a basis for machine to machine communication. http://www.w3.org/Math/Wikipedia:TeX