HP 40gs User Manual page 239

hp40g+.book Page 57 Friday, December 9, 2005 1:03 AM
LCM
LEGENDRE
PARTFRAC
Computer Algebra System (CAS)
Returns the LCM (Least Common Multiple) of two
polynomials.
Example
Typing:
2
LCM(X + 2·X + 1, X
gives:
2
( ) ⋅ ( )
x + 2x + 1 x 1 –
Returns the polynomial L
n
differential equation:
2
( ) y" ⋅ ⋅ ⋅
x – 1 – 2 x y' n n
where n is a whole number.
Example
Typing:
LEGENDRE(4)
gives:
4 2
⋅ ⋅
35 x – 30 x + 3
----------------------------------------------
8
Returns the partial fraction decomposition of a rational
fraction.
Example
Typing:
5
⎛
X –
⎜ ----------------------------------------------------------- -
ARTFRAC
4 3
⎝
X – 2X +
gives, in real and direct mode:
x 3 – 1 –
----------------- -------------- -
x + + 2 +
2 2x 2 –
2x + 2
and gives, in complex mode:
1 3 i ⋅
– 1 –
----------------- - ----- -
4 2
----------------- - ---------- -
x + + 2 +
x + i x 1 –
2
– 1)
, a non-null solution of the
( ) y ⋅
– + 1 = 0
3
2X + 1
2
2X – 2X + 1
3 i ⋅
1 +
----------------- -
4
------------------
+
x i –
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