Texas Instruments TI-89 Titanium User Manual page 780

You should also use
that might have unreal values. Otherwise,
equation
you may receive unexpected results.
equation1
cSolve(
{ varOrGuess1
⇒
Boolean expression
Returns candidate complex solutions to the
simultaneous algebraic equations, where each
varOrGuess
solve for.
Optionally, you can specify an initial guess for a
variable. Each
variable
– or –
=
variable
For example,
If all of the equations are polynomials and if you do
NOT specify any initial guesses,
lexical Gröbner/Buchberger elimination method to
attempt to determine all complex solutions.
Complex solutions can include both real and non-
real solutions, as 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 include solution variables that do not
appear in the equations. These solutions show how
families of solutions might contain arbitrary
constants of the form @ k , where
suffix from 1 through 255. The suffix resets to 1
when you use
For polynomial systems, computation time or
memory exhaustion may depend strongly on the
order in which you list solution variables. If your
initial choice exhausts memory or your patience, try
rearranging the variables in the equations and/or
varOrGuess
Appendix A: Functions and Instructions
_ for any other variables in
var
equation2 ...
and [and ],
, varOrGuess2 [ , ... ] })
specifies a variable that you want to
must have the form:
varOrGuess
-
real or non real number
is valid and so is
x x=3+
cSolve()
is an integer
k
or ƒ
ClrHome 8:Clear Home
list.
cSolve(conj(z)=1+
z_ is treated as complex:
cSolve(conj(z_)=1+
i .
Note: The following examples use an
uses the underscore _
@
¥
H
2
treated as complex.
cSolve(u_ù v_ì u_=v_ and
v_^2=ë u_,{u_,v_}) ¸
u_=1/2 +
or u_=1/2 ì
cSolve(u_ù v_ì u_=c_ù v_ and
v_^2=ë u_,{u_,v_}) ¸
ë( 1ì4øc_+1)
u_=
or
ë( 1ì4øc_ì1)
u_=
cSolve(u_ù v_ì u_=v_ and
v_^2=ë u_,{u_,v_,w_}) ¸
u_=1/2 +
.
or
u_=1/2 ì
or u_=0 and v_=0 and w_=@1
,z) ¸
i
i ,z_) ¸
z_=1−
so that the variables will be
3
ø i and v_=1/2 ì
2
3
ø
i and v_=1/2 +
2
or u_=0 and v_=0
2
and v_= 1ì4øc_+1
4
ë( 1ì4øc_ì1)
2
and v_=
4 2
or u_=0 and v_=0
3
ø and v_=1/2 ì
i
2
and w_=@1
3
ø i
and v_=1/2 +
2
and w_=@1
i
z=1+
i
3
ø i
2
3
ø
i
2
2
3
ø
i
2
3
ø i
2
777