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490 Appendix A: Functions and Instructions
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 490 of 132
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:
5
E
ë
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
a
ø
g
ì
c
ø
e
a
ø
f
ì
b
ø
e
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)
x
remain(x,y)
x
ì
y
ù
iPart(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
)
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 L
1
,
l
ist
1
¸
Done
l
ist
1
¸
{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
¸