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Appendix A: Functions and Instructions 427
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 427 of 132
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 an
d
v_=0
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
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 solution variables.
If your initial choice exhausts memory or
your patience, try rearranging the variables in
the equations and/or
varOrGuess
list.
cSolve(u_
ù
v_
ì
u_=v_ and
v_^2=
ë
u_,
{
u_,v_,w_
})
¸
u_=1/2 +
3
2
ø
i
and v_=1/2
ì
3
2
ø
i
an
d
w_=@
1
or
u_=1/2
ì
3
2
ø
i
and v_=1/2 +
3
2
ø
i
an
d
w_=@
1
or u_=0 an
d
v_=0 an
d
w_=@
1
If you do not include any guesses and if any
equation is non-polynomial in any variable
but all equations are linear in all solution
variables,
cSolve()
uses Gaussian elimination
to attempt to determine all solutions.
cSolve(u_+v_=
e
^(w_) and u_
ì
v_=
i
, {u_,v_})
¸
u_=
e
w_
2
+1/2
ø
i
and v_=
e
w_
ì
i
2
If a system is neither polynomial in all of its
variables nor linear in its solution variables,
cSolve()
determines at most one solution
using an approximate iterative method. To do
so, the number of solution variables must
equal the number of equations, and all other
variables in the equations must simplify to
numbers.
cSolve(
e
^(z_)=w_ and w_=z_^2,
{
w_,z_
})
¸
w_=.494… an
d
z_=
ë
.703…
A non-real guess is often necessary to
determine a non-real solution. For
convergence, a guess might have to be rather
close to a solution.
cSolve(
e
^(z_)=w_ and w_=z_^2,
{w_,z_=1+
i
})
¸
w_=.149… + 4.891…
ø
i
and
z_=1.588… + 1.540…
ø
i