MathGene.com^™ is a powerful Mathematics platform that provides a flexible tool for students, scientists, and engineers.

Supported Windows, Mac, Linux browsers:

• Firefox 8+
• Google Chrome 10+
• Apple Safari 5+
• Internet Explorer 10+

Supported Mobile devices:

• Apple iPad 2+
• Android Tablet

MathGene.com^™ is not recommended for use on mobile devices with small screens such as phones.

MathGene.com^™ Arithmetic:

MathGene.com^™ arithmetic is based upon the IEEE754-2008 decimal64 standard as implemented by Javascript in most browsers. This standard provides 16 digits of precision maximum and exponents from -323 to +308 in standard scientific notation. Irrational or infinite repeating decimals are rounded to the nearest 16th digit as are numbers greater than 10¹⁶. The MathGene.com^™ Setup page provides options to limit precision to fewer decimal digits if desired.

PRECEDENCE:Expressions are evaluated from left to right. Math operators have a precedence value that determines which operations are performed first.

Operator precedence from first to last:

1. () → Operations inside parentheses
2. xⁿ → Exponents
3. −x → Negative numbers: −4² = −(4²)
4. xN → Terms such as 2π: 2π/4i = (2π)/(4i)
5. ∠ → angle operator (see complex numbers)
6. / → Divide
7. × → Multiply
8. +− → Add/Subtract

COMPLEX NUMBERS: MathGene.com^™ has full support for complex and imaginary numbers and their operations. By default, complex numbers are represented in rectangular form a+bi, where i is the imaginary constant. Polar forms are also supported using the notation A∠B where A is the magnitude and B is the angle. The Settings menu selects which form is displayed by default as a calculation result. Angles can be represented in Radians (default), Degrees, or Gradians which are also selected in the Settings menu. Expressions can be entered using either rectangular or polar form and they can be mixed together. The result will be converted to form selected in the Settings menu. This allows easy conversions between rectangular and polar forms.

ROUNDING: Different operations are rounded to different precision based upon the accumulated errors in computation inevitable on any computing platform.

• (+−×/^) → real or imaginary numbers rounded to 16 decimals
• trig functions → all numbers rounded to 10 decimals
• complex numbers → both components rounded to 6 decimals
• complex numbers → if one component is less than 10^-6 of the other, it is assumed to be a rounding error and is set to 0

MathGene.com^™ Symbolic Math:

The following MathGene functions compute symbolic math:

• Expression reduction/evaluation - reduces the expression to simplest form, evaluates all calculus, limits, summations, reduces fractions, etc.
• Solve for variable - solve the equation for the specified variable
• Substitute - substitute a variable with an expression
• Factor - factor symbolically
• Expand - inverse of Factor
• Trig to Exp - converts trig and hyperbolic functions to exponential equivalents
• Exp to Trig - converts exponential equivalents to trig and hyperbolic functions
• Analysis - returns range of expression
• Series - returns Taylor series of expression

Conventions:

• negative exponents 'x^(-n)' are simplified to '1/x^n'
• x^(1/2) and x^(1/3) are simplified to square and cube roots
• (-x)/y is simplified to -(x/y)
• (x+y)/z is simplified to x/z+y/z

LaTeX is a standardized representational code format for use in mathematics publishing. MathGene supports a subset of LaTeX which can be used for both output rendering and computations.

LaTeX references can be found at these links:

https://en.wikibooks.org/wiki/LaTeX/Mathematics

https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols

These exceptions apply to MathGene LaTeX:

• MathGene does not support LaTeX sizing features such as 'big'
• '\usepackage' is not supported
• All matrix formats are converted to '{bmatrix}' at output
• {array} element is not supported
• Newline '\\' is currently not supported except in the matrix object
• all braces '{}' must be closed and terminated
• '/' slash divide symbol is always interpreted as equivalent to '\frac'

MathGene LaTeX follows these conventions:

• 'e' is interpreted as Euler's number (2.718...)
• '\pi' is interpreted as Archimedes constant (3.14...)
• '\imath' is interpreted as the imaginary constant 'i'
• d is interpreted as a differential when followed by a variable as in 'dx' or as in 'd/dx'
• some functions like arctanh(x), erf(x), etc. lack LaTeX equivalents so they are handled as if they do: \arctanh \erf
• all plain variables are italicized

MathGene has the unique ability to render pure HTML math output and export for use in web publishing. This has many advantages over the conventional image-based approach or MathML for web mathematics publishing:

Advantages:

• no image or font download, instant rendering using built-in HTML extended ASCII characters
• fast rendering on mobile devices
• fully scalable math rendering without pixelation, math stays razor sharp after zooming
• easy insertion into HTML documents
• simple and compact markup language compared to MathML
• compatible with all modern browsers and mobile devices
• Released under GPL. No fees or licensing!

BROWSER CONFIGURATION:

Javascript must be ENABLED.

COOKIES REQUIRED:Cookies must be enabled on all of the above devices and browsers for memory, setup, and recall functions to operate properly. This also means that deleting cookies via the browser "Clear Cache" menu will result in the loss of calculator configurations and data! Set the browser to accept and retain cookies. (This is default on most modern browsers.)

About the Author:

MathGene.com^™ Web App and MathGene Open-Source Math Library were designed by George J. Paulos, a US-based Software Engineer and "JavaScript Junkie" who has a keen interest in mathematics and math education. The MathGene project was initially just a hobby calculator project intended to learn Javascript and mobile web programming while brushing up on college math. Over several years the project evolved into a full-function mathematics processing system.