Texas Instruments PLUS TI-89 - Manual (Page 507)

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 л 14 щ max(dim( matrix1 ))
ù rowNorm( matrix1 )
Note: See also rref().
ref([л 2,л 2,0,л 6;1,л 1,9,л 9;л 5,
2,4,л 4]) ¸





 1 л 2/5 л 4/5 4/5
0 1 4/7 11/7
0 0 1 л 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)  x
remain(x,y)  x ì y ù iPart(x/y)
remain(7,0) ¸ 7
remain(7,3) ¸ 1
remain(л 7,3) ¸ л 1
remain(7,ë 3) ¸ 1
remain(л 7,л 3) ¸ л 1
remain({12,л 14,16},{9,7,л 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,л 7;6,4],[4,3;4,л 3])
¸
[
1 л 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
¸