Texas Instruments PLUS TI-89 - Manual (Page 448)

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_ùv_мu_м(c_ùv_),
v_^2+u_},{u_,v_}) ¸




л ( 1м 4шc_+1) 2
4
1м 4шc_+1
2
л ( 1м 4шc_м 1) 2
4
л ( 1м 4шc_м 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 м
3
2
шi 1/2 +
3
2
øi @1
1/2 +
3
2
øi 1/2 м
3
2
шi @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
+1/2øi
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…øi 1.588…+1.540…øi