Appendix A: Functions and Instructions 869
You can also (or instead) include unknowns that do
not appear in the expressions. For example, you
can include z as an unknown to extend the previous
example to two parallel intersecting cylinders of
radius r. The cylinder zeros illustrate how families of
zeros might contain arbitrary constants in 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
.
zeros({x^2+y^2ì r^2,
(xì r)^2+y^2ì r^2},{x,y,z})
¸
r
2
3ør
2
@1
r
2
ë
3ør
2
@1
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
list.
If you do not include any guesses and if any
expression is non-polynomial in any variable but all
expressions are linear in the unknowns,
zeros()
uses Gaussian elimination to attempt to determine
all real zeros.
zeros({x+
e
^(z)ù yì 1,xì yì sin(z)
},{x,y}) ¸
e
z
øsin(z)+1
e
z
+1
ë (sin(z)ì 1)
e
z
+1
If a system is neither polynomial in all of its
variables nor linear in its unknowns,
zeros()
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.
Each unknown starts at its guessed value if there is
one; otherwise, it starts at 0.0.
zeros({
e
^(z)ùyì1,ëyìsin(z)},
{y,z}) ¸
[]
.041… 3.183…
Use guesses to seek additional zeros one by one.
For convergence, a guess may have to be rather
close to a zero.
zeros({
e
^(z)ù yì 1,ë yì sin(z)},
{y,z=2p}) ¸
[]
.001… 6.281…
ZoomBox CATALOG
ZoomBox
Displays the Graph screen, lets you draw a box that
defines a new viewing window, and updates the
window.
In function graphing mode:
1.25xù cos(x)! y1(x)
¸ Done
ZoomStd:ZoomBox
¸
The display after defining
ZoomBox
by pressing
¸
the second time.
1st corner
2nd corner
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