solve()
Catalog >
You can separate the equations with the
and operator, or you can enter a
SystemOfEqns using a template from the
Catalog. The number of VarOrGuess
arguments must match the number of
equations. Optionally, you can specify an
initial guess for a variable. Each
VarOrGuess must have the form:
variable
– or –
variable = real or non-real number
For example, x is valid and so is x=3.
If all of the equations are polynomials and
if you do NOT specify any initial guesses,
solve() uses the lexical Gröbner/Buchberger
elimination method to attempt to
determine all real solutions.
For example, suppose you have a circle of
radius r at the origin and another circle of
radius r centered where the first circle
crosses the positive x-axis. Use solve() to
find the intersections.
As illustrated by r in the example to the
right, simultaneous polynomial equations
can have extra variables that have no
values, but represent given numeric values
that could be substituted later.
You can also (or instead) include solution
variables that do not appear in the
equations. For example, you can include z
as a solution variable to extend the previous
example to two parallel intersecting
cylinders of radius r.
The cylinder solutions illustrate how
families of solutions might contain arbitrary
constants of the form ck, where k is an
integer suffix from 1 through 255.
To see the entire result, press £ and then
use ¡and¢ to move the cursor.
Alphabetical Listing 169
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