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zeros()
MATH/Algebra menu
expression
zeros(
Returns a list of candidate real values of
make
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
) ⇒ ⇒ ⇒ ⇒
var
list
,
=0.
does this by
expression
zeros()
exp8 8 8 8 list(solve(
expression
cannot express implicit
zeros()
,
cSolve()
cZeros()
expression2
varOrGuess1
,
}, {
}) ⇒ ⇒ ⇒ ⇒
...
matrix
[
,
]
, where each
expressions
must have the form:
varOrGuess
=
-
real or non
real number
is valid and so is
x
to find the intersections.
zeros()
polynomial
expressions can have
varOrGuess
list. To extract a row,
].
row
that
var
=0,
.
var
,var
)
)
is
zeros()
. However,
solve()
.
var
, and
.
solve()
,
varOrGuess
.
x=3
zeros()
zeros({x^2+y^2 ì r^2,
(x ì r)^2+y^2 ì r^2},{x,y}) ¸
ans(1)[2] ¸
zeros(a ù x^2+b ù x+c,x) ¸
ë( bñ-4øaøc-+b)
bñ-4øaøc-b
2øa
a ù x^2+b ù x+c|x=ans(1)[2] ¸
exact(zeros(a ù (
^(x)+x)
e
(sign (x) ì 1),x)) ¸
exact(solve(a ù (
^(x)+x)
e
(sign (x) ì 1)=0,x)) ¸
x
+ x = 0 or x>0 or a = 0
e
Extract row 2:
2øa
0
{}
r
ø r
3
2
2
r
ø r
ë
3
2
2
r
ø r
ë
3
2
2
895
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