Texas Instruments TITANIUM TI-89 User Manual page 804

Optionally, you can specify an initial guess for a
variable. Each
variable
– or –
variable
For example,
If all of the expressions are polynomials and you
do NOT specify any initial guesses,
the lexical Gröbner/Buchberger elimination
method to attempt to determine all complex
zeros.
Complex zeros can include both real and non-real
zeros, as in the example to the right.
Each row of the resulting matrix represents an
alternate zero, with the components ordered the
same as the
index the matrix by [
Simultaneous
variables that have no values, but represent given
numeric values that could be substituted later.
You can also include unknown variables that do
not appear in the expressions. These zeros show
how families of zeros might contain arbitrary
constants of the form @
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 unknowns. If your initial
choice exhausts memory or your patience, try
rearranging the variables in the expressions
and/or
varOrGuess
If you do not include any guesses and if any
expression is non-polynomial in any variable but
all expressions are linear in all unknowns,
cZeros()
determine all zeros.
If a system is neither polynomial in all of its
variables nor linear in its unknowns,
determines at most one zero using an
approximate iterative method. To do so, the
number of unknowns must equal the number of
expressions, and all other variables in the
expressions must simplify to numbers.
804
must have the form:
varOrGuess
=
real or non-real number
is valid and so is
x x=3+
list. To extract a row,
varOrGuess
].
row
polynomials
can have extra
k , where
or ƒ
ClrHome 8:Clear Home
list.
uses Gaussian elimination to attempt to
.
i
Note: The following examples use an
underscore _ ( ¥ ) so that the variables will
uses
cZeros()
be treated as complex.
cZeros({u_ùv_ìu_ìv_,v_^2+u_},
{u_,v_}) ¸
Extract row 2:
ans(1)[2] ¸
cZeros({u_ùv_ìu_ì(c_ùv_),
v_^2+u_},{u_,v_}) ¸

ë ( 1ì 4øc_+1)

ë ( 1ì 4øc_ì 1)


0
cZeros({u_ùv_ìu_ìv_,v_^2+u_},
{u_,v_,w_}) ¸
k is an integer
.
cZeros({u_+v_ì
{u_,v_}) ¸
cZeros({
¸
cZeros()
Appendix A: Functions and Instructions

3
i
1/2 ì 1/2 +
ø
2

3
i
1/2 + 1/2 ì
ø

2
0 0

3
i
1/2 + 1/2 ì
ø

2
2
1ì 4øc_+1
4 2
ë ( 1ì 4øc_ì 1)
2
4 2
0

3
i
1/2 ì 1/2 +
ø
2

3
i
1/2 + 1/2 ì
ø
 2
0 0
^(w_),u_ìv_ì
e i
e
w_

+1/2ø

2
^(z_)ìw_,w_ìz_^2}, {w_,z_})
e
[
.494...

3
i
ø
2

3
i
ø

2

3
i
ø

2





3
i
@1
ø
2

3
i
@1
ø
2 
@1
},
e ì i
w_

i

2
]
ë.703...