Texas Instruments TI-89 Manual Book page 537

zeros({expression1, expression2}, {varOrGuess1,
varOrGuess2 [, ... ]})
Returns candidate real zeros of the
simultaneous algebraic
each
varOrGuess
value you seek.
Optionally, you can specify an initial guess
for a variable. Each
form:
variable
– or –
=
variable
For example,
If all of the expressions are polynomials and
if you do NOT specify any initial guesses,
uses the lexical Gröbner/Buchberger
zeros()
elimination method to attempt to determine
all real zeros.
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
the intersections.
As illustrated by r in the example to the right,
simultaneous polynomial expressions can
have extra variables that have no values, but
represent given numeric values that could be
substituted later.
Each row of the resulting matrix represents
an alternate zero, with the components
ordered the same as the
extract a row, index the matrix by [
You can also (or instead) include unknowns
that do not appear in the expressions. For
example, you can include z as an unknown to
extend the previous example to two parallel
intersecting cylinders of radius r. The
cylinder zeros illustrate how families of zeros
might contain arbitrary constants in the form
@k, where k is an integer suffix from 1
through 255. The suffix resets to 1 when you
use
ClrHome
520 Appendix A: Functions and Instructions
matrix
expressions
specifies an unknown whose
must have the
varOrGuess
-
real or non real number
is valid and so is
x x=3
zeros()
varOrGuess
or ƒ
.
8:Clear Home
, where
.
to find
zeros({x^2+y^2ì r^2,
(xì r)^2+y^2ì r^2},{x,y}) ¸
list. To
Extract row 2:
].
row
ans(1)[2] ¸
zeros({x^2+y^2ì r^2,
(xì r)^2+y^2ì r^2},{x,y,z}) ¸
ør
3
r
2 2
ë ør
3
r
2 2
ë ør
3
r
2 2
ør
3
r
@1
2 2
ë ør
3
r
@1
2 2