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Graphmatica supports the following operators, functions, and variables in your equations and user-defined functions. You can use the Special Characters tool window (Special Characters in the Edit menu) to enter characters that don't appear on your keyboard.
|less than or equal, greater than or equal|
|modulo (remainder after integer division)|
|| |||Absolute value of expression between "|" characters|
|Separate halves of a parametric equation or clauses in a piecewise-defined function|
|Make rest of the equation a comment|
|Specify domain exclusive of m and inclusive of n|
1 parentheses may be nested to any extent, and you can alternate between ( and [ to aid you in balancing your expressions, but the parser will not differentiate between ( and [.
m is the start of the domain and
n is the end. Either end may be left open by omitting an operand.
|absolute value (same as | | operator)|
|arc cosine (inverse cosine), arc secant|
|arc sine, arc cosecant|
|arc tangent, arc cotangent|
|least integer greater than the argument|
|cotangent (1/tan x)|
|cosecant (1/sin x)|
|Euler's number to the given power|
|synonym for int (greatest integer less than or equal to the argument)|
|The statistical function Γ, defined by the recurrence relation Γ(x+1) = x Γ(x)|
|The natural logarithm of the gamma function. This may be used to prevent overflow when the desired expression is actually something like gamma(x)/e^x.|
|greatest integer ([x] notation not supported)|
|natural logarithm, logarithm base 10|
|maximum (greater of the two arguments)|
|minimum (lesser of the two arguments)|
|pseudo-random (time-based) number between 0 and
|secant (1/cos x)|
|-1 for x < 0, 0 for x = 0, 1 for x > 0|
|Heaviside step function: step(x) = 0, for x < 0, 1/2 for x = 0, 1 for x > 0|
|Perform summation of a sequence or convergent infinite series. Detailed description and examples.|
|truncate towards zero (ceiling for x < 0, floor for x >= 0)|
Note that you may also define your own single-variable functions or constants using the Functions and Constants item in the Tools menu. You may reference these functions and constants in the same way as the built-in ones.
|r and θ in polar coordinates|
|x and y as functions of t in parametric form|
|dif-eq mode, solves first order ODE*|
|or higher order ODEs**|
|systems of ODEs|
|(using proper subscripts)|
|user-settable free variables|
*dx is actually dx/dt in dx/dt = f(x,t)
**d2x is d²x/dt²
|converts degrees to radians = π/180|
|Euler's number = 2.718...|
|π = 3.14159...|
Note: by default, all trig functions work in radians, not degrees. You can convert using the degrees symbol or the constant d:
sin (45°)= sin (π/4)
cos (x*d)= cosine of x, in degrees
You will need to change the range of x to 0 to 360 to get the full graph.