Expression Syntax

An expression combines any number of numbers, strings, variables, and functions with operators. An expression evaluates to a numeric or string value. The general, recursive definition of an expression is

[EXPRESSION] = [sign] [ATOMIC] [op] [ATOMIC] [op] [ATOMIC] ... [op] [ATOMIC]

where

• [sign] is an optional leading sign of + or -
• [op] are operators that determine how the [ATOMIC]'s are combined. The options are:
  • + for addition
  • - for subtraction
  • * for multiplication
  • / for division
  • ^ for raising to a power
  • & for string concatenation
  When there are multiple operators, the operations are combined with the usual operator precedence of ^ followed by * and / followed by + and -. When there are multiple operators of the same precedence, they are evaluated left to right.
• [ATOMIC] are the elements that are combined. The possible atomics are:
  • An unsigned number (23, 2.234, 3e2, 4.56e-3, ...)
  • A variable (such as #varname, #x[2], #z[#i][#j], etc.) and the value of the variable is used. The variable must have been previously defined.
  • Text in quotes ("some text") and the value is the text after the quotes are removed.
  • Unquoted text and the value is all the text between the operators after all spaces have been removed. To include spaces in text [ATOMIC]'s, the text must be quoted.
  • Another expression in parenthesis or ([EXPRESSION]) and the value of the [ATOMIC] is the value of the included expression.
  • A function of an expression (such as sin([EXPRESSION])) and the value of the [ATOMIC] is the value of the function applied to the value of the expression. The allowed functions are:
    • sin() - sine of argument in radians
    • cos() - cosine of argument in radians
    • tan() - tangent of argument in radians
    • asin() - inverse sine with result in radians
    • acos() - inverse cosine with result in radians
    • atan() - inverse tangent with result in radians
    • exp() - exponential
    • log() - natural log
    • log10() - log base 10
    • sqrt() - square root
    • abs() - absolute value
    • sinh() - hyperbolic sine
    • cosh() - hyperbolic cosine
    • tanh() - hyperbolic tangent
    • int() - integer part
    • sign() - 1 if argument is positive or 0 if it is negative
    • rand() - a random number between 0 and the argument.
    • erf() - error function.
    • erfc() - error function complement.
    • length() - number of characters in a string.
    • words() - number of words in a string.
    • firstWord() - first word in a string.
    • lastWord() - last word in a string.
    • removeFirstWord() - string with first word removed.
    • removeLastWord() - string with last word removed.
    • chars(c1\c2\string) - returns characters c1 to c2 of string (the first character is character 1). c1 defaults to 1 if omitted (or less than 0) and c2 defaults to length of string (if omitted or larger). Thus char(c1\string) gets character 1 to the end and char(\c2\string) gets character 1 through c2.
    • word(w1\string) - returns word w1 of string. If w1 is less than 1 or greater then number of words in string, an empty string is returned.
    • offset(s1\c1\string) - returns offset of string s1 in string at or after character c1 (the first character is character 1) or returns 0 if string s1 is not found. c1 can be omitted to find s1 any place in string. The search is case insensitive.
    • replace(s1\s2\string) - returns string where all occurrences of string s1 in string are replaced with string s2. s2 may be omitted to delete all occurrences of string s1.
    • upperCase() - convert string to upper case.
    • lowerCase() - convert string to lower case.
    • titleCase() - convert to string with capitalized words.
  • <a name="atexpr"></a>An "at" expression beginning in an @ sign and containing specific items separated by periods, such as "@key.TopLeft.x" to evaluate to the x value of the keypoint named "TopLeft":
    • The available "at" expressions are defined elsewhere (see <a href="keypoint.html">Keypoint</a> and <a href="path.html">Path</a> commands, for example).
    • Any of the period-delimited items can be a variable (such as @key.#kname.x) and the contents of #kname will replace that item in the expression.
    • Variables used as items can only be a single variable and not an expression. They also cannot be an array variable with a variable index (e.g., it can be #n[3] but not #n[#i]). Hint: if you need to index an array, you can define simple variable first (e.g., #ni=#n[#i]) and then use that in an expression (e.g., @key.#ni.y).

Notes

1. An assignment command can be combined with an operator as in

   #x [op] = [EXPRESSION]
   

   which is equivalent to

   #x = #x [op] ([EXPRESSION])
   

   provided the variable is already a defined variable. It is an error if the variable has not previously been defined.