Texas Instruments Voyage 200, User Manual

Page: 797 / 1008

Appendix A: Functions and Instructions 799
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 _
(
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))
¸
cSolve(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 _
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 and v_=0
Simultaneous
polynomial
equations can have
extra variables that have no values, but represent
given numeric values that could be substituted
later.
cSolve(u_
ù
v_
ì
u_=c_
ù
v_ and
v_^2=
ë
u_,{u_,v_})
¸
u_=
ë
( 1
ì
4
ø
c_+1)
2
4
and v_=
1
ì
4
ø
c_+1
2
or
u_=
ë
( 1
ì
4
ø
c_
ì
1)
2
4
and v_=
ë
( 1
ì
4
ø
c_
ì
1)
2
or u_=0 and v_=0