hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM

In real mode, the result is:

(x2 + 2 ⋅ x + 1) ⋅ (x2 – 2 ⋅ x + 1)

 

In complex mode (using CFG), the result is:

 

1

 

 

----- ⋅ (2x + (1 + i) ⋅ 2) ⋅ (2x–(1 + i) ⋅ 2) ⋅ (2x + (1 – i) ⋅ 2)

 

16

 

 

⋅ (2x–(1 – i) ⋅

2)

PARTFRAC

Partial fraction expansion

 

PARTFRAC has a rational fraction as an argument.

 

PARTFRAC returns the partial fraction decomposition of

 

this rational fraction.

 

Example

 

 

To perform a partial fraction decomposition of a rational

 

function, such as:

 

 

x5 – 2 ⋅ x3 + 1

 

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

 

x4

– 2 ⋅ x3 + 2 ⋅ x2 – (2 ⋅ x + 1)

you use the PARTFRAC command.

 

In real and direct mode, this produces:

 

 

 

x + 2 +

---------------------x– 3

+

 

–1

 

 

 

2 ⋅ x

2

 

2------------------⋅x – 2

 

 

 

 

 

 

+ 2

 

 

 

 

In complex mode, this produces:

 

 

 

 

 

 

 

1 – 3i

 

–1

 

 

1 + 3i

 

 

 

 

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

 

 

-----

 

 

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

 

 

 

x + 2 +

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

4

 

+

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

+ -------------

4

 

 

 

 

 

x + i

 

 

x – 1

 

x – i

QUOTE

Quoted expression

 

 

 

 

 

 

 

 

 

QUOTE(expression) is used to prevent an expression

 

from being evaluated or simplified.

 

 

Example 1

 

 

 

 

 

 

 

 

 

Typing:

 

 

 

 

 

 

 

 

 

 

 

m

⎛

QUOTE((2X – 1) ⋅

 

 

1

– 1 ), X = +∞

 

⎝

EXP(---

 

 

 

 

 

 

 

 

 

X

 

gives: +∞

Computer Algebra System (CAS)

14-13