Graphmatica accepts equations written in a format similar to many spreadsheets and graphing calculators, but reviewing the rules below may help you avoid having your equations rejected due to parsing errors.

Most equations **must** include: *

- exactly one dependent variable (
`y`

,`x`

, or`r`

). As a special case, you can also start your equation with "f(x)=" instead of "y=", although the parser will not make that substitution on the right-hand side or for more complicated expressions in the left-hand side of your equation. - exactly one equality or inequality operator (
`=`

,`<`

,`<=`

,`>`

,or`>=`

) - some sort of expression on each side of the equals sign

The rest is up to you. You can also include:

- as many instances of the independent variable (
`x`

or`t`

) as you like, or none. - special free variables
`a`

,`b`

,`c`

,`j`

, and`k`

- constants (decimal numbers,
`pi`

,`d`

,`e`

are pre-defined, but you can also define your own) - basic math operations (
`+`

,`-`

,`*`

,`/`

for division,`^`

for exponents). You can also use the Special Characters pane to enter Unicode multiplication and division symbols (×, ·, ÷). Or leave out the multiplication operator in cases where it can be implied. - nested parentheses to any extent
- trigonometric, exponential, and other functions.
- a domain, which may be open or closed on both sides
- a comment, so you can make notes to yourself or others

(* Parametric equations, because they are inherently different from most others, have different requirements which are explained in detail in Parametric Graphing. Also, note that many implicit Cartesian functions can be graphed even though they contain multiple references to both x and y.)

For a complete list of the supported operators, variables, and functions see the Operator Table.

The order of operations is the standard algebraic left to right of:

- Functions
- Parentheses
- Exponents
- Unary minus (-)
- Multiplication and division
- Addition and subtraction

- You do not have to surround arguments to functions with parentheses in most cases. If you choose not to use them,
the first term following the function name (i.e. up to the first + or - sign) will be taken as the argument.
For example,
`y=cos 2x + 3`

is equivalent to`y=cos(2x)+3`

- To use a complex expression as the parameter of the function, surround that expression with
parentheses:
`y=cos(x^2+pi/2)`

. - As a special case, when the parameter is a single-letter variable, you can even omit the space after the function
name and run it together with the parameter:
`y=cosx+1`

. - To express powers of functions, you can either surround the entire function call in parentheses as the base of the exponent
[e.g.
`y=(cos x)^2`

] or place simple exponents with a constant power directly after the function name [e.g.`y=cos^2 x`

or`y=sin²x`

].

**IMPLIED MULTIPLICATION**

In order to simplify your expressions, Graphmatica supports implied multiplication, as in `3x`

or `5(2x+3)`

.
It will handle constants followed by identifiers without a space in between, but you must separate alphabetic identifiers
with a space, paren, or an arithmetic operator (except for the single special case "`xy`

").
In addition, numbers which follow a variable or function must be separated from it by an operator or space, in order to support variables
and functions with numerals in their names (currently only d2x, d3x, etc.)--`x3`

would have to be expressed as
`x*3`

or `x 3`

.

For brief or in-depth information about each of the types of graphs Graphmatica supports, read the Overview of Graphing Techniques.

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