Symbolic expression is a rule for computing a single symbolic value represented in the form of character string.
The primary symbolic expression may be a string literal, dummy index, unsubscripted parameter, subscripted parameter, built-in function reference, conditional symbolic expression, or another symbolic expression enclosed in parentheses.
It is also allowed to use a numeric expression as the primary symbolic expression, in which case the resultant value of the numeric expression is automatically converted to the symbolic type.
'May 2003' (string literal) j (dummy index) p (unsubscripted parameter) s['abc',j+1] (subscripted parameter) substr(name[i],k+1,3) (function reference) if i in I then s[i,j] else t[i+1] (conditional expression) ((10 * b[i,j]) & '.bis') (parenthesized expression)
More general symbolic expressions containing two or more primary symbolic expressions may be constructed by using the concatenation operator.
'abc[' & i & ',' & j & ']' "from " & city[i] & " to " & city[j]
The principles of evaluation of symbolic expressions are completely analogous to that ones given for numeric expressions (see above).
In MathProg there are the following built-in functions which may be used in symbolic expressions:
substr(x, y) substring of x starting from position y substr(x, y, z) substring of x starting from position y and having length z time2str(t, f) converting calendar time to character string4
The first argument of
substr must be a symbolic expression while
its second and optional third arguments must be numeric expressions.
The first argument of
time2str must be a numeric expression, and
its second argument must be a symbolic expression.
The resultant value of the symbolic expression, which is a function reference, is the result of applying the function to its arguments.
Currently in MathProg there is the only symbolic operator:
x & y
where x and y are symbolic expressions. This operator means concatenation of its two symbolic operands, which are character strings.
The following list shows the hierarchy of operations in symbolic expressions:
Operation Hierarchy Evaluation of numeric operations 1st-7th Concatenation (&) 8th Conditional evaluation (if $\dots$ then $\dots$ else) 9th
This hierarchy has the same meaning as explained in Section “Numeric expressions”.