Xorpic Catalog; Zeros Math/Algebra Menu - Texas Instruments TITANIUM TI-89 User Manual

XorPic
CATALOG
picVar
XorPic [,
Displays the picture stored in
Graph screen.
Uses
xor
positions that are exclusive to either the screen or
the picture are turned on. This instruction turns
off pixels that are turned on in both images.
picVar must contain a pic data type.
row and
coordinates for the upper left corner of the
picture. Defaults are (0, 0).
zeros()
MATH/Algebra menu
expression
zeros(
Returns a list of candidate real values of
make
expression
computing
For some purposes, the result form for
more convenient than that of
the result form of
solutions, solutions that require inequalities, or
solutions that do not involve
Note: See also
expression1
zeros({
varOrGuess2
Returns candidate real zeros of the simultaneous
algebraic
specifies an unknown whose value you seek.
Optionally, you can specify an initial guess for a
variable. Each
variable
– or –
variable
For example,
If all of the expressions are polynomials and if
you do NOT specify any initial guesses,
uses the lexical Gröbner/Buchberger elimination
method to attempt to determine all real zeros.
For example, suppose you have a circle of radius r
at the origin and another circle of radius r
centered where the first circle crosses the positive
x-axis. Use
As illustrated by r in the example to the right,
simultaneous
extra variables that have no values, but represent
given numeric values that could be substituted
later.
Each row of the resulting matrix represents an
alternate zero, with the components ordered the
same as the
index the matrix by [
Appendix A: Functions and Instructions
row column
] [, ]
picVar
logic for each pixel. Only those pixel
column , if included, specify the pixel
) ⇒ ⇒ ⇒ ⇒
var list
,
=0. does this by
zeros()
exp8 8 8 8 list(solve( expression
solve()
cannot express implicit
zeros()
.
var
,
cSolve() cZeros()
expression2 varOrGuess1
, }, {
}) ⇒ ⇒ ⇒ ⇒
... matrix
[ , ]
, where each
expressions
varOrGuess must have the form:
= -
real or non real number
is valid and so is
x x=3
to find the intersections.
zeros()
polynomial
expressions can have
list. To extract a row,
varOrGuess
].
row
on the current
zeros(a ù x^2+b ù x+c,x) ¸
that
var
ë ( b ñ- 4 ø a ø c - +b)
=0, .
var ,var
) )
a ù x^2+b ù x+c|x=ans(1)[2] ¸
exact(zeros(a ù (
is
zeros()
. However,
(sign (x) ì 1),x)) ¸
exact(solve(a ù (
(sign (x) ì 1)=0,x)) ¸
, and .
solve()
,
varOrGuess
.
zeros()
zeros({x^2+y^2 ì r^2,
(x ì r)^2+y^2 ì r^2},{x,y}) ¸
Extract row 2:
b ñ- 4 ø a ø c - b
2 ø a 2 ø a
^(x)+x)
e
^(x)+x)
e
x + x = 0 or x>0 or a = 0
e




0
{}
r ø r

3

2 2

r ø r
ë 3

2 2
895