836 Appendix A: Functions and Instructions
ref() MATH/Matrix menu
ref(
matrix1
[
,
tol
]
) ⇒
matrix
Returns the row echelon form of
matrix1
.
Optionally, any matrix element is treated as zero if
its absolute value is less than
tol
. This tolerance is
used only if the matrix has floating-point entries and
does not contain any symbolic variables that have
not been assigned a value. Otherwise,
tol
is ignored.
•
If you use
¥¸
or set the mode to
Exact/Approx=APPROXIMATE
, computations
are done using floating-point arithmetic.
•
If
tol
is omitted or not used, the default tolerance
is calculated as:
5Eë 14 ù max(dim(
matrix1
)) ù rowNorm(
matrix1
)
Note: See also
rref().
ref([ë 2,ë 2,0,ë 6;1,ë 1,9,ë 9;ë 5,
2,4,ë 4])
¸
1 ë 2/5 ë 4/5 4/5
0 1 4/7 11/7
0 0 1 ë 62/71
[a,b,c;e,f,g]!m1 ¸
a b c
e f g
ref(m1) ¸
1
f
e
g
e
0 1
aøgì cøe
aøfì bøe
remain() MATH/Number menu
remain(
expression1
,
expression2
) ⇒
expression
remain(
list1
,
list2
) ⇒
list
remain(
matrix1
,
matrix2
) ⇒
matrix
Returns the remainder of the first argument with
respect to the second argument as defined by the
identities:
remain(x,0) r x
remain(x,y) r xì yùiPart(x/y)
remain(7,0)
¸ 7
remain(7,3)
¸ 1
remain(ë 7,3)
¸ ë 1
remain(7,ë 3)
¸ 1
remain(ë 7,ë 3)
¸ ë 1
remain({12,ë 14,16},{9,7,ë 5})
¸
{3 0 1}
As a consequence, note that
remain(ì x,y)
r
ì
remain(x,y)
. The result is either zero or it has the
same sign as the first argument.
Note: See also
mod()
.
remain([9,ë 7;6,4],[4,3;4,ë 3])
¸
[
1 ë 1
2 1
]
Rename CATALOG
Rename
oldVarName
,
newVarName
Renames the variable
oldVarName
as
newVarName
.
{1,2,3,4}! L1
¸ {1,2,3,4}
Rename L1, list1
¸ Done
list1
¸ {1,2,3,4}
Request CATALOG
Request
promptString
,
var
If
Request
is inside a
Dialog
...
EndDlog
construct,
it creates an input box for the user to type in data. If
it is a stand-alone instruction, it creates a dialog box
for this input. In either case, if
var
contains a string,
it is displayed and highlighted in the input box as a
default choice.
promptString
must be
{
20
characters.
This instruction can be stand-alone or part of a
dialog construct.
Request "Enter Your Name",str1
¸
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