# The Lagrange Function; The Lcm Function - HP F2226A - 48GII Graphic Calculator User Manual

Graphing calculator.

## The LAGRANGE function

The function LAGRANGE requires as input a matrix having two rows and n
columns. The matrix stores data points of the form [[x
y
]]. Application of the function LAGRANGE produces the polynomial
n
expanded from
p
For example, for n = 2, we will write:
x
x
p
(
x
)
2
y
1
1
x
x
1
2
Check this result with your calculator:
LAGRANGE([[ x1,x2],[y1,y2]]) = '((y1-y2)*X+(y2*x1-y1*x2))/(x1-x2)'.
Other examples: LAGRANGE([[1, 2, 3][2, 8, 15]]) = '(X^2+9*X-6)/2'
LAGRANGE([[0.5,1.5,2.5,3.5,4.5][12.2,13.5,19.2,27.3,32.5]]) =
'-(.1375*X^4+ -.7666666666667*X^3+ - .74375*X^2 =
1.991666666667*X-12.92265625)'.
Note: Matrices are introduced in Chapter 10.

### The LCM function

The function LCM (Least Common Multiple) obtains the least common multiple
of two polynomials or of lists of polynomials of the same length. Examples:
LCM('2*X^2+4*X+2' ,'X^2-1' ) = '(2*X^2+4*X+2)*(X-1)'.
LCM('X^3-1','X^2+2*X') = '(X^3-1)*( X^2+2*X)'
n
(
x
x
n
k
=
, 1
k
j
(
x
)
=
n
1
n
j
=
1
(
x
j
k
=
, 1
k
j
x
x
(
y
1
y
1
2
x
x
2
1
,x
, ..., x
] [y
, y
1
2
n
1
)
k
y
.
j
x
)
k
y
)
x
(
y
x
y
x
2
2
1
1
x
x
1
2
Page 5-21
, ...,
2
)
2