# Propfrac; Ptayl; Quot - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Description:
Given an integer, finds the closest prime number smaller than the integer. Like ISPRIME?, it
uses a pseudoprime check for large numbers.
Arithmetic, !Þ
Access:
Input:
An integer or an expression that evaluates to an integer.
Output:
The closest prime number smaller than the integer.
Example:
Find the closest, smaller prime number to 145.
Command:
PREVPRIME(145)
Result:
139
ISPRIME?, NEXTPRIME

## PROPFRAC

Type:
Command
Description:
Toggles between an improper fraction and its corresponding integer and fractional part.
P
Access:
ARITH
Input:
An improper fraction, or an object that evaluates to an improper fraction. It must not contain
real numbers. Alternately, the input may be an integer part plus a proper fraction.
Output:
An integer part plus a proper fraction; or alternately, if the input was an integer part plus a
proper fraction, an improper fraction.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Express the following as a proper fraction:
3
x
+
4
------------- -
2
x
Command:
PROPFRAC((X^3+4)/X^2))
Result:
X+(4/X^2)

### PTAYL

Type:
Function
Description:
Returns the Taylor polynomial at x = a for a specified polynomial.
Arithmetic, !Þ
Access:
Input:
Level 2/Argument 1: A polynomial, P.
Level 1/Argument 2: A number, a.
Output:
A polynomial, Q such that Q(x – a)=P(x).
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the polynomial Q(x) such that
Q(x-2)=x
Command:
PTAYL(X^2+3*X+2, 2)
Result:
X^2+7*X+12

### QUOT

Type:
Function
L
INTEGER
or Arithmetic, !ÞL
POLYNOMIAL
+3x+2.
2
LL
Computer Algebra Commands 4-59