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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_

u_=c_

v_ and

v_^2=

u_,

{

u_,v_

})

u_=

(

c_+1)

and

v_=

c_+1

u_=

(

and

v_=

(

or u_=0 an

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

, where

is an integer suffix from 1

through 255. The suffix resets to 1 when you

use

ClrHome

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_

u_=v_ and

v_^2=

u_,

{

u_,v_,w_

})

u_=1/2 +

and v_=1/2

w_=@

u_=1/2

and v_=1/2 +

w_=@

or u_=0 an

v_=0 an

w_=@

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_=

^(w_) and u_

v_=

, {u_,v_})

u_=

+1/2

and v_=

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(

^(z_)=w_ and w_=z_^2,

{

w_,z_

})

w_=.494… an

z_=

.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(

^(z_)=w_ and w_=z_^2,

{w_,z_=1+

})

w_=.149… + 4.891…

and

z_=1.588… + 1.540…

Display size (HxV)	100 x 160 mm
Memory type	639K FLASH ROM, 188K bytes RAM
Compatible operating systems	Operating System 2.09
Battery type	AAA

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