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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.

Operator Meaning
=equals sign
< >strict inequality
<= (≤), >= (≥)less than or equal, greater than or equal
*, ×, ·multiplication
/, ÷division
% or modmodulo (remainder after integer division)
^ or ** or ⁰¹²³⁴⁵⁶⁷⁸⁹Exponentiation
| |Absolute value of expression between "|" characters
[( )]Parentheses1
; (semicolon)Separate halves of a parametric equation or clauses in a piecewise-defined function
' (single quote)Make rest of the equation a comment
{m, n}Specify domain2
{(m, n]}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 [.
2 m is the start of the domain and n is the end. Either end may be left open by omitting an operand.

absabsolute value (same as | | operator)
acos, asecarc cosine (inverse cosine), arc secant
asin, acscarc sine, arc cosecant
atan, acotarc tangent, arc cotangent
ceilingleast integer greater than the argument
coshhyperbolic cosine
cotcotangent (1/tan x)
csccosecant (1/sin x)
cubert, ∛cube root
expEuler's number to the given power
fourthrt, ∜fourth root
floorsynonym for int (greatest integer less than or equal to the argument)
gamma, ΓThe statistical function Γ, defined by the recurrence relation Γ(x+1) = x Γ(x)
gammaln, ΓlnThe 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.
intgreatest integer ([x] notation not supported)
ln, lognatural logarithm, logarithm base 10
max(a,b)maximum (greater of the two arguments)
min(a,b)minimum (lesser of the two arguments)
randpseudo-random (time-based) number between 0 and arg
sinhhyperbolic sine
secsecant (1/cos x)
sign-1 for x < 0, 0 for x = 0, 1 for x > 0
sqrt (sqr, √)square root
stepHeaviside step function: step(x) = 0, for x < 0, 1/2 for x = 0, 1 for x > 0
sum, ΣPerform summation of a sequence or convergent infinite series. Detailed description and examples.
tanhhyperbolic tangent
truncatetruncate 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.

x, yrectangular coordinates
r, t (θ)r and θ in polar coordinates
x, y, tx and y as functions of t in parametric form
t, x, dxdif-eq mode, solves first order ODE*
x, y, dy (alternate notation)
d2x, d3x...or higher order ODEs**
t,x,y,z,w,dx...dwsystems of ODEs
t,x1...x4,dx1...dx4 (alternate notation)
t,x₁...x₄,dx₁...dx₄ (using proper subscripts)
a, b, c, j, kuser-settable free variables

*dx is actually dx/dt in dx/dt = f(x,t)
**d2x is d²x/dt²

d, °converts degrees to radians = π/180
eEuler's number = 2.718...
pi (or p)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:

You will need to change the range of x to 0 to 360 to get the full graph.

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kSoft, Inc. Last updated: Sun 11 Jun 2017