GNU Emacs Calc 2.02 Manual
11.6 Solving Equations
The a S (calc-solve-for) [solve] command rearranges
an equation to solve for a specific variable. An equation is an
expression of the form L = R. For example, the command a S x
will rearrange y = 3x + 6 to the form, x = y/3 - 2. If the
input is not an equation, it is treated like an equation of the
form X = 0.
This command also works for inequalities, as in y < 3x + 6.
Some inequalities cannot be solved where the analogous equation could
be; for example, solving
a < b c for b is impossible
without knowing the sign of c. In this case, a S will
produce the result
b != a/c (using the not-equal-to operator)
to signify that the direction of the inequality is now unknown. The
inequality
a <= b c is not even partially solved.
See section 7.6 Declarations, for a way to tell Calc that the signs of the
variables in a formula are in fact known.
Two useful commands for working with the result of a S are
a . (see section 11.10 Logical Operations), which converts x = y/3 - 2
to y/3 - 2, and s l (see section 13.4 The Let Command) which evaluates
another formula with x set equal to y/3 - 2.
