Calculator User Manual
856  Appendix A: Functions and Instructions 
propFrac()  MATH/Algebra menu 
propFrac(
expression1
[, 
var
])  ⇒
⇒⇒
⇒ 
expression
propFrac(
rational_number
) returns 
rational_number
as the sum of an integer and a fraction having the 
same sign and a greater denominator magnitude 
than numerator magnitude. 
propFrac(4/3) ¸  1 + 1/3 
propFrac(
ë 4/3) ¸  ë 1ì 1/3 
propFrac(
rational_expression,var
) returns the sum 
of proper ratios and a polynomial with respect to 
var
. The degree of 
var
 in the denominator exceeds 
the degree of 
var
 in the numerator in each proper 
ratio. Similar powers of 
var
 are collected. The 
terms and their factors are sorted with 
var
 as the 
main variable. 
If 
var
 is omitted, a proper fraction expansion is 
done with respect to the most main variable. The 
coefficients of the polynomial part are then made 
proper with respect to their most main variable 
first and so on. 
For rational expressions, 
propFrac() is a faster 
but less extreme alternative to 
expand(). 
propFrac((x^2+x+1)/(x+1)+ 
(y^2+y+1)/(y+1),x)
 ¸ 
propFrac(ans(1)) 
PtChg  CATALOG 
PtChg 
x
, 
y
PtChg 
xList
, 
yList
Displays the Graph screen and reverses the screen 
pixel nearest to window coordinates 
(
x
, 
y
). 
Note: 
PtChg through PtText show continuing 
similar examples. 
PtChg 2,4 ¸ 
PtOff  CATALOG 
PtOff 
x
, 
y
PtOff 
xList
, 
yList
Displays the Graph screen and turns off the 
screen pixel nearest to window coordinates 
(
x
, 
y
). 
PtOff 2,4 ¸ 
PtOn  CATALOG 
PtOn 
x
, 
y
PtOn 
xList
, 
yList
Displays the Graph screen and turns on the screen 
pixel nearest to window coordinates 
(
x
, 
y
). 
PtOn 3,5 ¸ 
ptTest()  CATALOG 
ptTest (
x
, 
y
)  ⇒
⇒⇒
⇒ 
Boolean constant expression
ptTest (
xList
, 
yList
)  ⇒
⇒⇒
⇒ 
Boolean constant expression
Returns true or false. Returns true only if the 
screen pixel nearest to window coordinates (
x
, 
y
) 
is on. 
ptTest(3,5) ¸ true 










