Texas Instruments TI-89 - Page 443

426 Appendix A: Functions and Instructions
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 426 of 132
cSolve()
starts with exact symbolic methods.
Except in
EXACT
mode,
cSolve()
also uses
iterative approximate complex polynomial
factoring, if necessary.
Note: See also
cZeros()
,
solve()
, and
zeros()
.
Note: If
equation
is non-polynomial with
functions such as
abs()
,
angle()
,
conj()
,
real()
,
or
imag()
, you should place an underscore _
(
TI-89:
¥ 
TI-92 Plus:
2 
) at the end
of
var
. By default, a variable is treated as a
real value.
Display
Digits
mode in
Fix 2
:
exact(cSolve(x^5+4x^4+5x
^3
ì
6x
ì
3=0,x))
¸
cSo
l
ve
(
ans
(1)
,x
)
¸
If you use
var
_ , the variable is treated as
complex.
You should also use
var
_ for any other
variables in
equation
that might have unreal
values. Otherwise, you may receive
unexpected results.
z is treated as real:
cSolve(conj(z)=1+
i
,z)
¸
z=1+
i
z_ is treated as complex:
cSolve(conj(z_)=1+
i
,z_)
¸
z_=1
−
i
cSolve(equation1 and equation2
[
and …
]
,
{varOrGuess1, varOrGuess2
[
, …
]
})
⇒
Boolean expression
Returns candidate complex solutions to the
simultaneous algebraic equations, where
each
varOrGuess
specifies a variable that you
want to solve for.
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+
i.
If all of the equations are polynomials and if
you do NOT specify any initial guesses,
cSolve()
uses the lexical Gröbner/Buchberger
elimination method to attempt to determine
all complex solutions.
Note: The following examples use an
underscore _ (
TI-89:
¥ 
TI-92 Plus:
2 
) so that the variables
will be treated as complex.
Complex solutions can include both real and
non-real solutions, as in the example to the
right.
cSolve(u_
ù
v_
ì
u_=v_ and
v_^2=
ë
u_,
{
u_,v_
})
¸
u_=1/2 +
3
2
ø
i
and v_=1/2
ì
3
2
ø
i
or u_=1/2
ì
3
2
ø
i
and v_=1/2 +
3
2
ø
i
or u_=0 an
d
v_=0