HP 40gs - Manual (Page 245)

Computer Algebra System (CAS) 14-63
Example
Find the solutions P(X) of:
P(X) = X (mod X 2 + 1)
P(X) = X – 1 (mod X 2 – 1)
Typing:
CHINREM((X) AND (X 2 + 1), (X – 1) AND (X 2 – 1))
gives:
That is:
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) = X
2 + 1.
Example 2
Typing:
CYCLOTOMIC(20)
gives:
EXP2HYP EXP2HYP has an expression enclosing exponentials as an
argument. It transforms that expression with the relation:
exp(a) = sinh(a) + cosh(a).
x
2
2x – 1 +
2
-------------------------- – AND
x
4
1 –
2
--------------
P X [ ]
x
2
2x – 1 +
2
-------------------------- mod
x
4
1 –
2
-------------- –
⎝ ⎠
⎛ ⎞
– =
x
8
x
6
– x
4
x
2
– 1 + +
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