The text input fields for expressions accept any combination of the following:

**Numbers:**

In decimal format, e.g.**5.317**

See below for information about decimal number format and locale setting,**Constants:****pi**π=3.1416... **e**Euler constant 2.7183... **infty**represents infinity -- commonly used with conditional expressions (see below) to delete part of a graph **Binary Operations:***x***+***y*addition *x***-***y*subtraction *x*******y*multiplication *x***/***y*division *x***^***y*exponentiation ( *x*)^{y}**Unary Operations:****-***x*negation (prefix operator) *x***!**factorial (postfix operator) **Grouping:****(**...**)**parentheses **Operator Precedence:**

Standard rules of arithmetic operator precedence apply. For example, the expression**2*3^4+5**is equivalent to**(2*(3^4))+5**-- exponentiation takes precedence, followed by multiplication, and finally addition. Function notation includes its own parentheses, so grouping is explicit with functions and their precedence is irrelevant. Negation has the same precedence as multiplication. The factorial operator takes higher precedence than exponentiation. Conditional expressions, Boolean relations, and logical connectives take lower precedence than addition.-
**Implied Multiplication:****2pi**number times constant **2x**number times variable **2sin(x)**number times function **2(x+y)**number times parenthesis group *Note:*The first factor in the product*must*be a*number*(in decimal format).

Examples above show what is allowed in the second factor.

Expressions attempting to use implied multiplication between identifiers, such as "**xy**" or "**xsin(x)**," are*in*correct, syntactically. **Variables:**

**x**,**y**,**z**,**r**,**s**,**t**,**u**,**v**,**n**

Availability depends on applet.**Functions:****sin(***x***)**sine function **cos(***x***)**cosine function **tan(***x***)**tangent function **sec(***x***)**secant function **csc(***x***)**cosecant function **cot(***x***)**cotangent function **arcsin(***x***)**arcsine function **arccos(***x***)**arccosine function **arctan(***x***)**arctangent function **arcsec(***x***)**arcsecant function **exp(***x***)**natural exponential function (with base *e*)**ln(***x***)**natural logarithm function (with base *e*)**log(***x***)**common logarithm function (with base 10) **abs(***x***)**absolute value function **sqrt(***x***)**square root function **nrt(***n***,***x***)***n*^{th}root function**int(***x***)**greatest integer function

(returns greatest integer less than or equal to*x*)**alt(***x***)**sign alternation function

(returns 1 if int(*x*) is even, -1 if int(*x*) is odd -- can be used to establish alternation of terms in series without using computationally expensive "(-1)^n" expression)**max(***x***,***y***)**maximum of *x*and*y***min(***x***,***y***)**minimum of *x*and*y***Function Name Aliases:****asin**for **arcsin****acos**for **arccos****atan**for **arctan****Defined Functions:**

In certain applets, when an expression is entered into one field "*f*(*x*)=," the function "**f(x)**" can be used in other expression fields within that applet.**Conditional Expression:***x***?***y***:***z*returns value *y*if*x*>0,*z*otherwise**Boolean Relations:***x***<***y*returns value 1.0 if *x*<*y*, 0.0 otherwise*x***>***y*returns value 1.0 if *x*>*y*, 0.0 otherwise*x***=***y*returns value 1.0 if *x*=*y*, 0.0 otherwise**Logical Connectives:***x***&***y*logical AND connective, returns value 1.0 if *x*>0*and**y*>0, 0.0 otherwise*x***|***y*logical OR connective (inclusive), returns value 1.0 if *x*>0*or**y*>0 (or both), 0.0 otherwise**~***x*logical NOT operator, returns value 1.0 if *not**x*>0, 0.0 otherwise**Indicating Syntax Errors:**

If the expression parser detects a syntax error (incuding use of a variable which is not available to the particular applet), the applet responds by highlighting the entire text within the input field.**Number Format and Applet Locale:**

The decimal number format*is*sensitive to the applet's locale, which can be set using HTML parameters. The separator between the integer part and the fraction part may be either a period ("**.**"), as in American English decimal notation (if the locale is**en_US**), or a comma ("**,**"), as in French notation (if the locale is**fr_FR**). Multiple separators are recognized if they are syntactically correct, as with**12,345.6**in American English notation. However, the parser does*not*recognize a space as a separator, as with**12 345,6**in French notation; the parser does not generate a syntax error in this case, but only returns the number**12,0**, treating the space as the end of the number.