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

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
See also: 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