One advantage to using the symbolic equal sign discussed in the last section is that it is “live,” just like the numerical processing in Mathcad. That is, Mathcad checks all the variables and functions making up the expression being evaluated to see if they’ve been defined earlier in the worksheet. If Mathcad does find a definition, it uses it. Any other variables and functions are evaluated symbolically. Later on, whenever you make a change to the worksheet, the results automatically update. This is useful when the
symbolic and numerical equations in the worksheet are tied together.There may be times, however, when a symbolic calculation is quite separate from the rest of your worksheet and does not need to be tied to any previous definitions. In these cases, you can use commands from the Symbolic menu. These commands are not live:you apply them on a case by case basis to selected expressions, they do not “know” about previous definitions, and they do not automatically update.The basic steps for using the Symbolic menu are the same for all the menu commands:
• Place whatever math expression you want to evaluate between the two editing lines or, for some commands, click on a variable in the expression.
• Choose the appropriate command from the Symbolic menu.
• Mathcad will place the evaluated expression into your document.
For example, to evaluate an expression symbolically using the Symbolic menu, follow these steps:
• Enter the expression you want to evaluate.
• Surround the expression with the editing lines.
• Choose Evaluate⇒Symbolically from the Symbolic menu.
Mathcad will place the evaluated expression into your worksheet. The location of the result in relation to the original expression depends on the Evaluation Style you’ve selected, as described below:
Displaying symbolic results
If you’re using the symbolic equal sign, “→”, the result of a symbolic transformation will always go to the right of the “→”. However, when you use the Symbolic menu, you can tell Mathcad to place the symbolic results in one of the following ways:
• The symbolic result can go below the original expression.
• The symbolic result can go to the right of the original expression.
• The symbolic result can simply replace the original expression.
In addition, you can also choose whether or not you want Mathcad to generate text describing what had to be done to get from the original expression to the symbolic result. This text will go between the original expression and the symbolic result, in effect creating a narrative for the symbolic evaluation. These text regions are referred to as “evaluation comments.”
To control both the placement of the symbolic result and the presence of narrative text,
choose Evaluation Style from the Symbolics menu to bring up the “Evaluation Style”
dialog box. The check box at the top of the dialog box shows whether Mathcad will automatically generate evaluation comments at each step of the evaluation. Click in this box to toggle these comments on or off.
The three option buttons control where symbolic results are placed. These options do he following:
• “Show evaluation steps vertically, inserting lines” is useful when you expect lengthy intermediate results and you want to reserve an entire line for them.
• “Show evaluation steps vertically, without inserting lines” is useful when you want to show two parallel derivations side by side. In this mode, you can position expressions arbitrarily. New answers may, however, overwrite old ones.
• “Show evaluation steps horizontally” is useful if you want to place the symbolic result to the right of the expression being transformed.
Sometimes you don’t care about saving the steps of a derivation. You may just want to transform an expression in place, for example to make a substitution, or to factor the numerator of a fraction. In this case, choose Evaluation Style from the Symbolic menu and click in the check box for “Evaluate in Place.” This tells Mathcad to replace the old expression with the new one. In this mode, evaluation comments are inappropriate and therefore omitted altogether.