Added description and examples.

EXAMPLES.md

@@ -0,0 +1,173 @@
+# MathRender Examples
+
+## Square of sums
+```LaTeX
+(a_1 + a_2)^2 = a_1^2 + 2a_1a_2 + a_2^2
+```
+
+![Square Formula](img/square.png)
+
+## Quadratic Formula
+```LaTeX
+x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
+```
+
+![Quadratic Formula](img/quadratic.png)
+
+## Standard Deviation
+```LaTeX
+\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^N (x_i - \mu)^2}
+```
+![Standard Deviation](img/standard.png)
+
+## De Morgan's laws
+```LaTeX
+\neg(P\land Q) \iff (\neg P)\lor(\neg Q)
+```
+
+![De Morgan](img/demorgan.png)
+
+## Log Change of Base
+```LaTeX
+\log_b(x) = \frac{\log_a(x)}{\log_a(b)}
+```
+
+![Log Base Change](img/log.png)
+
+## Cosine addition
+```LaTeX
+\cos(\theta + \varphi) = \cos(\theta)\cos(\varphi) - \sin(\theta)\sin(\varphi)
+```
+
+![Cos Sum](img/trig.png)
+
+## Limit e^k
+```LaTeX
+\lim_{x\to\infty}\left(1 + \frac{k}{x}\right)^x = e^k
+```
+
+![Limit](img/limit.png)
+
+## Calculus
+```LaTeX
+f(x) = \int\limits_{-\infty}^\infty\!\hat f(\xi)\,e^{2 \pi i \xi x}\,\mathrm{d}\xi
+```
+
+![Calculus](img/calculus.png)
+
+## Stirling Numbers of the Second Kind
+```LaTeX
+{n \brace k} = \frac{1}{k!}\sum_{j=0}^k (-1)^{k-j}\binom{k}{j}(k-j)^n
+```
+
+![Stirling Numbers](img/stirling.png)
+
+## Gaussian Integral
+```LaTeX
+\int_{-\infty}^{\infty} \! e^{-x^2} dx = \sqrt{\pi}
+```
+
+![Gauss Integral](img/gaussintegral.png)
+
+## Arithmetic mean, geometric mean inequality
+```LaTeX
+\frac{1}{n}\sum_{i=1}^{n}x_i \geq \sqrt[n]{\prod_{i=1}^{n}x_i}
+```
+
+![AM-GM](img/amgm.png)
+
+## Cauchy-Schwarz inequality
+```LaTeX
+\left(\sum_{k=1}^n a_k b_k \right)^2 \le \left(\sum_{k=1}^n a_k^2\right)\left(\sum_{k=1}^n b_k^2\right)
+```
+![Cauchy Schwarz](img/cauchyschwarz.png)
+
+## Cauchy integral formula
+```LaTeX
+f^{(n)}(z_0) = \frac{n!}{2\pi i}\oint_\gamma\frac{f(z)}{(z-z_0)^{n+1}}dz
+```
+
+![Cauchy Integral](img/cauchyintegral.png)
+## Schroedinger's Equation
+```LaTeX
+i\hbar\frac{\partial}{\partial t}\mathbf\Psi(\mathbf{x},t) = -\frac{\hbar}{2m}\nabla^2\mathbf\Psi(\mathbf{x},t)
++ V(\mathbf{x})\mathbf\Psi(\mathbf{x},t)
+```
+
+![Schroedinger](img/schroedinger.png)
+
+## Lorentz Equations
+Use the `gather` or `displaylines` environments to center multiple
+equations.
+```LaTeX
+\begin{gather}
+\dot{x} = \sigma(y-x) \\
+\dot{y} = \rho x - y - xz \\
+\dot{z} = -\beta z + xy"
+\end{gather}
+```
+
+![Lorentz](img/lorentz.png)
+
+## Cross product
+```LaTeX
+\vec \bf V_1 \times \vec \bf V_2 =  \begin{vmatrix}
+\hat \imath &\hat \jmath &\hat k \\
+\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
+\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
+\end{vmatrix}
+```
+
+![Cross Product](img/cross.png)
+
+## Maxwell's Equations
+Use the `aligned`, `eqalign` or `split` environments to align
+multiple equations.
+```LaTeX
+\begin{eqalign}
+\nabla \cdot \vec{\bf E} & = \frac {\rho} {\varepsilon_0} \\
+\nabla \cdot \vec{\bf B} & = 0 \\
+\nabla \times \vec{\bf E} &= - \frac{\partial\vec{\bf B}}{\partial t} \\
+\nabla \times \vec{\bf B} & = \mu_0\vec{\bf J} + \mu_0\varepsilon_0 \frac{\partial\vec{\bf E}}{\partial t}
+\end{eqalign}
+```
+
+![Maxwell's Equations](img/maxwell.png)
+
+## Matrix multiplication
+Supported matrix environments: `matrix`, `pmatrix`, `bmatrix`, `Bmatrix`,
+`vmatrix`, `Vmatrix`.
+```LaTeX
+\begin{pmatrix}
+a & b\\ c & d
+\end{pmatrix}
+\begin{pmatrix}
+\alpha & \beta \\ \gamma & \delta
+\end{pmatrix} = 
+\begin{pmatrix}
+a\alpha + b\gamma & a\beta + b \delta \\
+c\alpha + d\gamma & c\beta + d \delta 
+\end{pmatrix}
+```
+
+![Matrix Multiplication](img/matrixmult.png)
+
+## Cases
+```LaTeX
+f(x) = \begin{cases}
+\frac{e^x}{2} & x \geq 0 \\
+1 & x < 0
+\end{cases}
+```
+
+![Cases](img/cases.png)
+
+## Splitting long equations
+```LaTeX
+\frak Q(\lambda,\hat{\lambda}) =
+-\frac{1}{2} \mathbb P(O \mid \lambda ) \sum_s \sum_m \sum_t \gamma_m^{(s)} (t) +\\
+\quad \left( \log(2 \pi ) + \log \left| \cal C_m^{(s)} \right| +
+\left( o_t - \hat{\mu}_m^{(s)} \right) ^T \cal C_m^{(s)-1} \right) 
+```
+
+![Long equation](img/long.png)

README.md

@@ -1,3 +1,258 @@
 # SwiftMath
 
-A description of this package.
+`SwiftMath` provides a full Swift implementation of [iosMath](https://travis-ci.org/kostub/iosMath) 
+for displaying beautifully rendered math equations in iOS and MacOS applications. It typesets formulae written 
+using LaTeX in a `UILabel` equivalent class. It uses the same typesetting rules as LaTeX and
+so the equations are rendered exactly as LaTeX would render them. 
+
+`SwiftMath` prepackages everything needed for direct access via the Swift Package Manager.
+No need for complicated alien pods that never seem to work quite right.
+
+It is similar to [MathJax](https://www.mathjax.org) or
+[KaTeX](https://github.com/Khan/KaTeX) for the web but for native iOS or MacOS
+applications without having to use a `UIWebView` and Javascript. More
+importantly, it is significantly faster than using a `UIWebView`.
+
+## Examples
+Here are screenshots of some formulae that were rendered with this library:
+
+![Quadratic Formula](img/quadratic.png) 
+
+![Calculus](img/calculus.png)
+
+![AM-GM](img/amgm.png)
+
+![Ramanujan Identity](img/ramanujan.png)
+
+More examples are included in [EXAMPLES](EXAMPLES.md)
+ 
+## Requirements
+`SwiftMath` works on iOS 6+ or MacOS 10.8+ and requires ARC to build. It depends
+on the following Apple frameworks:
+
+* Foundation.framework
+* CoreGraphics.framework
+* QuartzCore.framework
+* CoreText.framework
+
+Additionally for iOS it requires:
+* UIKit.framework
+
+Additionally for MacOS it requires:
+* AppKit.framework
+
+## Installation
+
+### Swift Package
+
+`SwiftMath` is available from [SwiftMath](https://github.com/mgriebling/SwiftMath.git). 
+To use it in your code, just add the https://github.com/mgriebling/SwiftMath.git path to
+XCode's package manager.
+
+## Usage
+
+The library provides a class `MTMathUILabel` which is a `UIView` that
+supports rendering math equations. To display an equation simply create
+an `MTMathUILabel` as follows:
+
+```swift
+
+import SwiftMath
+
+let label = MTMathUILabel()
+label.latex = "x = \\frac{-b \\pm \\sqrt{b^2-4ac}}{2a}"
+
+```
+Adding `MTMathUILabel` as a sub-view of your `UIView` will render the
+quadratic formula example shown above.
+
+The following code creates a SwiftUI component called `MathView` encapsulating the MTMathUILabel:
+
+```swift
+import SwiftUI
+import SwiftMath
+
+struct MathView: UIViewRepresentable {
+
+    @Binding var equation: String
+    @Binding var fontSize: CGFloat
+    
+    func makeUIView(context: Context) -> MTMathUILabel {
+        let view = MTMathUILabel()
+        return view
+    }
+    
+    func updateUIView(_ uiView: MTMathUILabel, context: Context) {
+        uiView.latex = equation
+        uiView.fontSize = fontSize
+        uiView.font = MTFontManager().termesFont(withSize: fontSize)
+        uiView.textAlignment = .right
+        uiView.labelMode = .text
+    }
+}
+```
+
+If you need code that works with SwiftUI running natively under MacOS you'll need the following:
+
+```swift
+import SwiftUI
+import SwiftMath
+
+struct MathView: NSViewRepresentable {
+    
+    @Binding var equation: String
+    @Binding var fontSize: CGFloat
+    
+    func makeNSView(context: Context) -> MTMathUILabel {
+        let view = MTMathUILabel()
+        return view
+    }
+    
+    func updateNSView(_ view: MTMathUILabel, context: Context) {
+        view.latex = equation
+        view.fontSize = fontSize
+        view.font = MTFontManager().termesFont(withSize: fontSize)
+        view.textColor = .textColor
+        view.textAlignment = .center
+        view.labelMode = .display
+    }
+}
+```
+
+### Included Features
+This is a list of formula types that the library currently supports:
+
+* Simple algebraic equations
+* Fractions and continued fractions
+* Exponents and subscripts
+* Trigonometric formulae
+* Square roots and n-th roots
+* Calculus symbos - limits, derivatives, integrals
+* Big operators (e.g. product, sum)
+* Big delimiters (using \\left and \\right)
+* Greek alphabet
+* Combinatorics (\\binom, \\choose etc.)
+* Geometry symbols (e.g. angle, congruence etc.)
+* Ratios, proportions, percents
+* Math spacing
+* Overline and underline
+* Math accents
+* Matrices
+* Equation alignment
+* Change bold, roman, caligraphic and other font styles (\\bf, \\text, etc.)
+* Most commonly used math symbols
+* Colors
+
+### Example
+
+The [SwiftMathDemo](https://github.com/mgriebling/SwiftMathDemo) is a Swift version
+of the Objective-C demo included in `iosMath` that uses `SwiftMath` as a Swift package dependency.
+
+### Advanced configuration
+
+`MTMathUILabel` supports some advanced configuration options:
+
+##### Math mode
+
+You can change the mode of the `MTMathUILabel` between Display Mode
+(equivalent to `$$` or `\[` in LaTeX) and Text Mode (equivalent to `$`
+or `\(` in LaTeX). The default style is Display. To switch to Text
+simply:
+
+```swift
+label.labelMode = .text
+```
+
+##### Text Alignment
+The default alignment of the equations is left. This can be changed to
+center or right as follows:
+
+```swift
+label.textAlignment = .center
+```
+
+##### Font size
+The default font-size is 25pt. You can change it as follows:
+
+```swift
+label.fontSize = 30
+```
+##### Font
+The default font is *Latin Modern Math*. This can be changed as:
+
+```swift
+label.font = MTFontManager().termesFont(withSize:20)
+```
+
+This project has 3 fonts bundled with it, but you can use any OTF math
+font.  Note: I couldn't get the `iosMath` Python script to work.  If
+you do manage to get it working, please let me know.
+
+##### Color
+The default color of the rendered equation is black. You can change
+it to any other color as follows:
+
+```swift
+label.textColor = .red
+```
+
+It is also possible to set different colors for different parts of the
+equation. Just access the `displayList` field and set the `textColor`
+on the underlying displays that you want to change the color of. 
+
+##### Custom Commands
+You can define your own commands that are not already predefined. This is
+similar to macros is LaTeX. To define your own command use:
+
+```swift
+MTMathAtomFactory.addLatexSymbol("lcm", value: MTMathAtomFactory.operator(withName: "lcm", limits: false))
+```
+
+This creates an `\lcm` command that can be used in the LaTeX.
+
+##### Content Insets
+The `MTMathUILabel` has `contentInsets` for finer control of placement of the
+equation in relation to the view.
+
+If you need to set it you can do as follows:
+
+```swift
+label.contentInsets = UIEdgeInsets(top: 0, left: 10, bottom: 0, right: 20)
+```
+
+##### Error handling
+
+If the LaTeX text given to `MTMathUILabel` is
+invalid or if it contains commands that aren't currently supported then
+an error message will be displayed instead of the label.
+
+This error can be programmatically retrieved as `label.error`. If you
+prefer not to display anything then set:
+
+```swift
+label.displayErrorInline = true
+```
+
+## Future Enhancements
+
+Note this is not a complete implementation of LaTeX math mode. There are
+some important pieces that are missing and will be included in future
+updates. This includes:
+
+* Support for explicit big delimiters (bigl, bigr etc.)
+* Addition of missing plain TeX commands 
+
+## License
+
+`SwiftMath` is available under the MIT license. See the [LICENSE](./LICENSE)
+file for more info.
+
+### Fonts
+This distribution contains the following fonts. These fonts are
+licensed as follows:
+* Latin Modern Math: 
+    [GUST Font License](GUST-FONT-LICENSE.txt)
+* Tex Gyre Termes:
+    [GUST Font License](GUST-FONT-LICENSE.txt)
+* [XITS Math](https://github.com/khaledhosny/xits-math):
+    [Open Font License](OFL.txt)

Sources/SwiftMath/mathFonts.bundle/GUST-FONT-LICENSE.txt

@@ -0,0 +1,30 @@
+% This is a preliminary version (2006-09-30), barring acceptance from
+% the LaTeX Project Team and other feedback, of the GUST Font License.
+% (GUST is the Polish TeX Users Group, http://www.gust.org.pl)
+%
+% For the most recent version of this license see
+% http://www.gust.org.pl/fonts/licenses/GUST-FONT-LICENSE.txt
+% or
+% http://tug.org/fonts/licenses/GUST-FONT-LICENSE.txt
+%
+% This work may be distributed and/or modified under the conditions
+% of the LaTeX Project Public License, either version 1.3c of this
+% license or (at your option) any later version.
+% 
+% Please also observe the following clause:
+% 1) it is requested, but not legally required, that derived works be
+%    distributed only after changing the names of the fonts comprising this
+%    work and given in an accompanying "manifest", and that the
+%    files comprising the Work, as listed in the manifest, also be given
+%    new names. Any exceptions to this request are also given in the
+%    manifest.
+%    
+%    We recommend the manifest be given in a separate file named
+%    MANIFEST-<fontid>.txt, where <fontid> is some unique identification
+%    of the font family. If a separate "readme" file accompanies the Work, 
+%    we recommend a name of the form README-<fontid>.txt.
+%
+% The latest version of the LaTeX Project Public License is in
+% http://www.latex-project.org/lppl.txt and version 1.3c or later
+% is part of all distributions of LaTeX version 2006/05/20 or later.
+

Sources/SwiftMath/mathFonts.bundle/LICENSE

@@ -0,0 +1,21 @@
+The MIT License (MIT)
+
+Copyright (c) 2013 MathChat
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

Sources/SwiftMath/mathFonts.bundle/OFL.txt

@@ -0,0 +1,103 @@
+STIX Font License
+
+24 May 2010
+
+Copyright (c) 2001-2010 by the STI Pub Companies, consisting of the American
+Institute of Physics, the American Chemical Society, the American Mathematical
+Society, the American Physical Society, Elsevier, Inc., and The Institute of
+Electrical and Electronic Engineers, Inc. (www.stixfonts.org), with Reserved
+Font Name STIX Fonts, STIX Fonts (TM) is a  trademark of The Institute of
+Electrical and Electronics Engineers, Inc.
+
+Portions copyright (c) 1998-2003 by MicroPress, Inc. (www.micropress-inc.com),
+with Reserved Font Name TM Math. To obtain additional mathematical fonts, please
+contact MicroPress, Inc., 68-30 Harrow Street, Forest Hills, NY 11375, USA,
+Phone: (718) 575-1816.
+
+Portions copyright (c) 1990 by Elsevier, Inc.
+
+This Font Software is licensed under the SIL Open Font License, Version 1.1.
+This license is copied below, and is also available with a FAQ at:
+http://scripts.sil.org/OFL
+
+---------------------------------------------------------------------------
+SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
+---------------------------------------------------------------------------
+
+PREAMBLE
+
+The goals of the Open Font License (OFL) are to stimulate worldwide development
+of collaborative font projects, to support the font creation efforts of academic
+and linguistic communities, and to provide a free and open framework in which
+fonts may be shared and improved in partnership with others.
+
+The OFL allows the licensed fonts to be used, studied, modified and redistributed
+freely as long as they are not sold by themselves. The fonts, including any
+derivative works, can be bundled, embedded, redistributed and/or sold with any
+software provided that any reserved names are not used by derivative works. The
+fonts and derivatives, however, cannot be released under any other type of license.
+The requirement for fonts to remain under this license does not apply to any
+document created using the fonts or their derivatives.
+
+DEFINITIONS
+
+"Font Software" refers to the set of files released by the Copyright Holder(s) under
+this license and clearly marked as such. This may include source files, build
+scripts and documentation.
+
+"Reserved Font Name" refers to any names specified as such after the copyright
+statement(s).
+
+"Original Version" refers to the collection of Font Software components as
+distributed by the Copyright Holder(s).
+
+"Modified Version" refers to any derivative made by adding to, deleting, or
+substituting -- in part or in whole -- any of the components of the Original Version,
+by changing formats or by porting the Font Software to a new environment.
+
+"Author" refers to any designer, engineer, programmer, technical writer or other
+person who contributed to the Font Software.
+
+PERMISSION & CONDITIONS
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of the
+Font Software, to use, study, copy, merge, embed, modify, redistribute, and sell
+modified and unmodified copies of the Font Software, subject to the following
+conditions:
+
+1) Neither the Font Software nor any of its individual components, in Original or
+Modified Versions, may be sold by itself.
+
+2) Original or Modified Versions of the Font Software may be bundled, redistributed
+and/or sold with any software, provided that each copy contains the above copyright
+notice and this license. These can be included either as stand-alone text files,
+human-readable headers or in the appropriate machine-readable metadata fields within
+text or binary files as long as those fields can be easily viewed by the user.
+
+3) No Modified Version of the Font Software may use the Reserved Font Name(s) unless
+explicit written permission is granted by the corresponding Copyright Holder. This
+restriction only applies to the primary font name as presented to the users.
+
+4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font Software shall
+not be used to promote, endorse or advertise any Modified Version, except to
+acknowledge the contribution(s) of the Copyright Holder(s) and the Author(s) or with
+their explicit written permission.
+
+5) The Font Software, modified or unmodified, in part or in whole, must be distributed
+entirely under this license, and must not be distributed under any other license. The
+requirement for fonts to remain under this license does not apply to any document
+created using the Font Software.
+
+TERMINATION
+
+This license becomes null and void if any of the above conditions are not met.
+
+DISCLAIMER
+
+THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
+INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
+PARTICULAR PURPOSE AND NONINFRINGEMENT OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER
+RIGHT. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES,
+WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF THE USE OR
+INABILITY TO USE THE FONT SOFTWARE OR FROM OTHER DEALINGS IN THE FONT SOFTWARE.