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Appendix A: Functions and Instructions 431
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 431 of 132
Simultaneous
polynomials
can have extra
variables that have no values, but represent
given numeric values that could be
substituted later.
cZeros({u_
ù
v_
ì
u_
ì
(c_
ù
v_),
v_^2+u_
}
,
{
u_,v_
})
¸
ë
(
1
ì
4
ø
c_+1)
2
4
1
ì
4
ø
c_+1
2
ë
(
1
ì
4
ø
c_
ì
1)
2
4
ë
(
1
ì
4
ø
c_
ì
1)
2
0 0
You can also include unknown variables that
do not appear in the expressions. These
zeros show how families of zeros might
contain arbitrary constants of the form @
k
,
where
k
is an integer suffix from 1 through
255. The suffix resets to 1 when you use
ClrHome
or
ƒ
8:Clear Home
.
For polynomial systems, computation time or
memory exhaustion may depend strongly on
the order in which you list unknowns. If your
initial choice exhausts memory or your
patience, try rearranging the variables in the
expressions and/or
varOrGuess
list.
cZeros({u_
ù
v_
ì
u_
ì
v_,v_^2+u_},
{
u_,v_,w_
})
¸
1/2
ì
3
2
ø
i
1/2 +
3
2
ø
i
@1
1/2 +
3
2
ø
i
1/2
ì
3
2
ø
i
@1
0
0
@1
If you do not include any guesses and if any
expression is non-polynomial in any variable
but all expressions are linear in all
unknowns,
cZeros()
uses Gaussian
elimination to attempt to determine all zeros.
cZeros({u_+v_
ì
e
^(w_),u_
ì
v_
ì
i
},
{
u_,v_
})
¸
e
w_
2
+1/2
ø
i
e
w_
ì
i
2
If a system is neither polynomial in all of its
variables nor linear in its unknowns,
cZeros()
determines at most one zero using an
approximate iterative method. To do so, the
number of unknowns must equal the number
of expressions, and all other variables in the
expressions must simplify to numbers.
cZeros({
e
^(z_)
ì
w_,w_
ì
z_^2},
{
w_,z_
})
¸
[]
.494…
ë
.703…
A non-real guess is often necessary to
determine a non-real zero. For convergence,
a guess might have to be rather close to a
zero.
cZeros({
e
^(z_)
ì
w_,w_
ì
z_^2},
{w_,z_=1+
i
})
¸
[
]
.149…+4.89…
ø
i
1.588…+1.540…
ø
i