Symbolic Mode
-------------

Calculations are normally performed numerically wherever possible.
For example, the `calc-sqrt' command, or `sqrt' function in an
algebraic expression, produces a numeric answer if the argument is a
number or a symbolic expression if the argument is an expression: `2
Q' pushes 1.4142 but `' x+1 RET Q' pushes `sqrt(x+1)'.

In "symbolic mode", controlled by the `m s' (`calc-symbolic-mode')
command, functions which would produce inexact, irrational results are
left in symbolic form.  Thus `16 Q' pushes 4, but `2 Q' pushes
`sqrt(2)'.

The shift-`N' (`calc-eval-num') command evaluates numerically the
expression at the top of the stack, by temporarily disabling
`calc-symbolic-mode' and executing `=' (`calc-evaluate').  Given a
numeric prefix argument, it also sets the floating-point precision to
the specified value for the duration of the command.

To evaluate a formula numerically without expanding the variables it
contains, you can use the key sequence `m s a v m s' (this uses
`calc-alg-evaluate', which resimplifies but doesn't evaluate
variables.)