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
^3ì6xì3=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_ùv_ìu_=v_ and
v_^2=ëu_,
{
u_,v_
})
¸
u_=1/2 + 3
2øi and v_=1/2 ì3
2øi
or u_=1/2 ì3
2øi and v_=1/2 + 3
2øi
or u_=0 an
d
v_=0