Horner; Iabcuv; Ibasis - HP 48gII Advanced User's Reference Manual

1 1
1 -- - -- -
2 3
1 1 1
-- - -- - -- -
2 3 4
1 1 1
-- - -- - -- -
3 4 5
Result:
See also: CON, IDN, RANM, VANDERMONDE

HORNER

Type: Command
Description: Executes a Horner scheme on a polynomial. That is, for a given polynomial P, and a number
r, HORNER returns QUOT(P/(x–r)), r and also P(r)
Arithmetic, !Þ
Access:
Input: Level 2/Argument 1: A polynomial, P.
Level 1/Argument 2: A number, r.
Output: Level 3/Item 1: QUOT(P/(x–r))
Level 2/Item 2: r
Level 1/Item 3: P(r), the remainder of the division process.
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: For r = 3, find the result of executing a Horner scheme on the following polynomial:
2
x + + x
Command:
HORNER(X^2+X+1,3)
Results:
(X+4,3,13)

IABCUV

Type: Command
Description: Returns a solution in integers u and v of au + bv = c, where a, b, and c are integers.
Arithmetic, !Þ
Access:
Input: Level 3/Argument 1: the value of a.
Level 2/Argument 2: the value of b.
Level 1/Argument 3: the value of c.
Output: Level 2/Item 1: The value for u.
Level 1/Item 2: The value for v.
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 a solution in integers of the equation:
6a + 11b = 3
Command:
IABCUV(6,11,3)
Result:
{6,-3}
See also: ABCUV, IEGCD

IBASIS

Type: Command
4-38 Computer Algebra Commands
L
POLY
1
INTEGER