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:
5Eë14 ùmax(dim(matrix1))
ùrowNorm(matrix1)
Note: See also rref().
ref([ë2,ë2,0,ë6;1,ë1,9,ë9;ë5,
2,4,ë4
])
¸
1 ë2/5 ë4/5 4/5
0 1 4/7 11/7
0 0 1 ë62/71
[a,b,c;e,f,g]!m1 ¸[]
a b c
e f g
ref(m1) ¸
1 f
e g
e
0 1 aøgìcøe
aøfìbøe
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) xìyùiPart(x/y)
remain(7,0) ¸7
remain(7,3) ¸1
remain(ë7,3) ¸ë1
remain(7,ë3) ¸1
remain(ë7,ë3) ¸ë1
remain({12,ë14,16},{9,7,ë5})
¸
{3 0 1}
As a consequence, note that remain(ìx,y)
ìremain(x,y). The result is either zero or it
has the same sign as the first argument.
Note: See also mod().
remain([9,ë7;6,4],[4,3;4,ë3])
¸
[1 ë1
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
¸