The lagrange function, The lcm function – HP 48gII User Manual
Page 192
Page 5-21
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
1
,x
2
, …, x
n
] [y
1
, y
2
, …,
y
n
]]. Application of the function LAGRANGE produces the polynomial
expanded from
.
)
(
)
(
)
(
1
,
1
,
1
1
j
n
j
n
j
k
k
k
j
n
j
k
k
k
n
y
x
x
x
x
x
p
⋅
−
−
=
∑
∏
∏
=
≠
=
≠
=
−
For example, for n = 2, we will write:
2
1
2
1
1
2
2
1
2
1
2
1
1
2
1
2
1
)
(
)
(
)
(
x
x
x
y
x
y
x
y
y
y
x
x
x
x
y
x
x
x
x
x
p
−
⋅
−
⋅
+
⋅
−
=
⋅
−
−
+
⋅
−
−
=
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)’