hp40g+.book Page 57 Friday, December 9, 2005 1:03 AM

LCM

Returns the LCM (Least Common Multiple) of two

 

polynomials.

 

 

 

 

 

 

 

 

Example

 

 

 

 

 

 

 

 

 

Typing:

 

 

 

 

 

 

 

 

 

LCM(X2 + 2·X + 1, X2 – 1)

 

gives:

 

 

 

 

 

 

 

 

 

(x2 + 2x + 1) ⋅ (x – 1)

 

 

LEGENDRE

Returns the polynomial Ln, a non-null solution of the

 

differential equation:

 

 

 

 

(x2 – 1) ⋅ y″ – 2 ⋅ x ⋅ y′ – n(n + 1) ⋅ y = 0

 

where n is a whole number.

 

 

Example

 

 

 

 

 

 

 

 

 

Typing:

 

 

 

 

 

 

 

 

 

LEGENDRE(4)

 

 

 

 

 

 

gives:

 

 

 

 

 

 

 

 

 

35 ⋅ x4 – 30 ⋅ x2

+ 3

 

 

 

----------------------------------------------

 

 

 

 

8

 

 

 

 

 

 

PARTFRAC

Returns the partial fraction decomposition of a rational

 

fraction.

 

 

 

 

 

 

 

 

 

Example

 

 

 

 

 

 

 

 

 

Typing:

 

 

 

 

 

 

 

 

 

 

 

⎛

 

 

X5 – 2X3 + 1

 

ARTFRAC⎜----------------------------------------------------------

 

 

 

-

 

 

 

⎝X4 – 2X3 + 2X2 – 2X + 1

 

gives, in real and direct mode:

 

x + 2 +

-----------------x– 3 + --------------

–1

 

 

 

 

2x

2

+ 2

 

2x – 2

 

 

 

 

 

 

 

 

 

 

 

and gives, in complex mode:

 

 

1 – 3 ⋅ i

 

 

–1

 

1 + 3 ⋅ i

 

 

-----------------

 

 

 

-----

 

-----------------

 

x + 2 +

-----------------

4

+

----------2-

+

-----------------4-

 

 

x + i

 

 

x – 1

 

x – i

Computer Algebra System (CAS)

14-57