HP 40gs User Manual page 245

hp40g+.book Page 63 Friday, December 9, 2005 1:03 AM
CYCLOTOMIC
EXP2HYP
Computer Algebra System (CAS)
Example
Find the solutions P(X) of:
2
P(X) = X (mod X + 1)
2
P(X) = X – 1 (mod X
Typing:
CHINREM((X) AND (X
gives:
2 4
x – 2x + 1 x –
------------------------- - ------------- -
– AND
2 2
That is:
2
x – 2x + 1
P X [ ]
------------------------- -
= –
2
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) = X
Example 2
Typing:
CYCLOTOMIC(20)
gives:
8 6 4 2
x – x + x – x + 1
EXP2HYP has an expression enclosing exponentials as an
argument. It transforms that expression with the relation:
exp(a) = sinh(a) + cosh(a).
– 1)
2 2
+ 1), (X – 1) AND (X
1
4
x – 1
⎛ ⎞
------------- -
mod –
⎝ ⎠
2
– 1))
2
+ 1.
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