hp40g+.book Page 63 Friday, December 9, 2005 1:03 AM

 

Example

 

 

 

 

 

Find the solutions P(X) of:

 

 

 

P(X) = X (mod X2 + 1)

 

 

 

P(X) = X – 1 (mod X2 – 1)

 

 

Typing:

 

 

 

 

 

CHINREM((X) AND (X2 + 1), (X – 1) AND (X2 – 1))

 

gives:

 

 

 

 

 

x2 – 2x + 1

x4

– 1

 

 

 

–-------------------------

AND -------------

 

 

 

2

2

 

 

 

That is:

 

 

 

 

 

x2

– 2x + 1

⎛

x4 – 1⎞

 

P[X] = –--------------------------

⎝

mod–-------------

⎠

 

 

2

2

CYCLOTOMIC

Returns the cyclotomic polynomial of order n. This is a

 

polynomial having the nth primitive roots of unity as

 

zeros.

 

 

 

 

 

CYCLOTOMIC has an integer n as its argument.

 

Example 1

 

 

 

 

 

When n = 4 the fourth roots of unity are {1, i, –1, –i}.

 

Among them, the primitive roots are: {i, –i}. Therefore, the

 

cyclotomic polynomial of order 4 is (X – i).(X + i) = X2 + 1.

 

Example 2

 

 

 

 

 

Typing:

 

 

 

 

 

CYCLOTOMIC(20)

 

 

 

 

gives:

 

 

 

 

 

x8 – x6 + x4 – x2 + 1

 

 

 

EXP2HYP

EXP2HYP has an expression enclosing exponentials as an

 

argument. It transforms that expression with the relation:

exp(a) = sinh(a) + cosh(a).

Computer Algebra System (CAS)

14-63