Appendix A: Functions and Instructions 885
|
(“with”)
@ Í key H 2 Í key
expression
|
Boolean expression1
[
and Boolean
expression2
]
...
[
and Boolean expressionN
]
The “with” (|) symbol serves as a binary operator.
The operand to the left of | is an expression. The
operand to the right of | specifies one or more
relations that are intended to affect the simplification
of the expression. Multiple relations after | must be
joined by a logical “and”.
The “with” operator provides three basic types of
functionality: substitutions, interval constraints, and
exclusions.
x+1| x=3
¸ 4
x+y| x=sin(y)
¸ sin(y)
+
y
x+y| sin(y)=x
¸ x
+
y
Substitutions are in the form of an equality, such as
x=3
or
y=sin(x)
. To be most effective, the left side
should be a simple variable.
expression
|
variable
=
value
will substitute
value
for every occurrence of
variable
in
expression
.
x^3ì 2x+7! f(x)
¸ Done
f(x)| x=‡(3)
¸ ‡3
+
7
(sin(x))^2+2sin(x)ì 6| sin(x)=d
¸
dñ +2dì 6
Interval constraints take the form of one or more
inequalities joined by logical “and” operators.
Interval constraints also permit simplification that
otherwise might be invalid or not computable.
solve(x^2ì 1=0,x)|x>0 and x<2
¸
x
=
1
‡(x)ù ‡(1/x)|x>0
¸ 1
‡(x)ù ‡(1/x)
¸
1
x
ø x
Exclusions use the “not equals” (/= or
ƒ
) relational
operator to exclude a specific value from
consideration. They are used primarily to exclude an
exact solution when using
cSolve()
,
cZeros()
,
fMax()
,
fMin()
,
solve()
,
zeros()
, etc.
solve(x^2ì 1=0,x)| xƒ1
¸x
=
ë 1
!
(store)
§ key
expression
!
var
list
!
var
matrix
!
var
expression
!
fun_name(parameter1,...)
list
!
fun_name(parameter1,...)
matrix
!
fun_name(parameter1,...)
If variable
var
does not exist, creates
var
and
initializes it to
expression
,
list
, or
matrix
.
If
var
already exists and if it is not locked or
protected, replaces its contents with
expression
,
list
,
or
matrix
.
Hint: If you plan to do symbolic computations using
undefined variables, avoid storing anything into
commonly used, one-letter variables such as a, b, c,
x, y, z, etc.
p/4! myvar
¸
p
4
2cos(x)! Y1(x)
¸ Done
{1,2,3,4}! Lst5
¸ {1 2 3 4}
[1,2,3;4,5,6]! MatG
¸ [
1 2 3
4 5 6
]
"Hello"! str1
¸ "Hello"
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