﻿ Graphmatica Help - Operator Table

OPERATORS

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 `+` addition `-` subtraction `*, ×, ·` multiplication `/, ÷` division `%` or `mod` modulo (remainder after integer division) `^` or `**` or ⁰¹²³⁴⁵⁶⁷⁸⁹ Exponentiation | | 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.

 Function Meaning `abs` absolute value (same as | | operator) `acos, asec` arc cosine (inverse cosine), arc secant `asin, acsc` arc sine, arc cosecant `atan, acot` arc tangent, arc cotangent `ceiling` least integer greater than the argument `cos` cosine `cosh` hyperbolic cosine `cot` cotangent (1/tan x) `csc` cosecant (1/sin x) `cubert, ∛` cube root `exp` Euler's number to the given power `fourthrt, ∜` fourth root `floor` synonym for int (greatest integer less than or equal to the argument) `gamma, Γ` The statistical function Γ, defined by the recurrence relation Γ(x+1) = x Γ(x) `gammaln, Γln` 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. `int` greatest integer ([x] notation not supported) `ln, log` natural logarithm, logarithm base 10 `max(a,b)` maximum (greater of the two arguments) `min(a,b)` minimum (lesser of the two arguments) `rand` pseudo-random (time-based) number between 0 and `arg` `sin` sine `sinh` hyperbolic sine `sec` secant (1/cos x) `sign` -1 for x < 0, 0 for x = 0, 1 for x > 0 `sqrt (sqr, √)` square root `step` Heaviside step function: step(x) = 0, for x < 0, 1/2 for x = 0, 1 for x > 0 `sum, Σ` Perform summation of a sequence or convergent infinite series. Detailed description and examples. `tan` tangent `tanh` hyperbolic tangent `truncate` 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.

 Variables Usage `x, y` rectangular coordinates `r, t (θ)` r and θ in polar coordinates `x, y, t` x and y as functions of t in parametric form `t, x, dx` dif-eq mode, solves first order ODE* `x, y, dy ` (alternate notation) `d2x,` `d3x`... or higher order ODEs** `t,x,y,z,w,dx`...`dw` systems of ODEs `t,x1`...`x4,dx1`...`dx4 ` (alternate notation) `t,x₁`...`x₄,dx₁`...`dx₄ ` (using proper subscripts) `a, b, c, j, k` user-settable free variables

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

 Constant Value `d, °` converts degrees to radians = π/180 `e` Euler'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:

• `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.

kSoft, Inc. ksoft@graphmatica.com Last updated: Sun 11 Jun 2017