hp40g+.book Page 62 Friday, December 9, 2005 1:03 AM

CAS Functions on the CMDS menu

When you are in the Equation Writer and press , a menu of the full set of CAS functions available to you is displayed. Many of the functions in this menu

match the functions available from the soft-key menus in the Equation Writer; but there are other functions that are only available from this menu. This section describes the additional CAS functions that are available when you

press in the Equation Writer. (See the previous section for other CAS commands.)

ABCUV

This command applies the Bézout identity like EGCD, but

 

the arguments are three polynomials A, B and C. (C must

 

be a multiple of GCD(A,B).)

 

ABCUV(A[X], B[X], C[X]) returns U[X] AND V[X], where U

 

and V satisfy:

 

C[X] = U[X] · A[X] + V[X] · B[X]

 

Example 1

 

Typing:

 

ABCUV(X2 + 2 · X + 1, X2 – 1, X + 1)

 

gives:

 

1

1

 

-

AND –-

 

2

2

CHINREM

Chinese Remainders: CHINREM has two sets of two

 

polynomials as arguments, each separated by AND.

CHINREM((A(X) AND R(X), B(X) AND Q(X)) returns an AND with two polynomials as components: P(X) and S(X). The polynomials P(X) and S(X) satisfy the following relations when GCD(R(X),Q(X)) = 1:

S(X) = R(X) · Q(X),

P(X) = A(X) (modR(X)) and P(X) = B(X) (modQ(X)).

There is always a solution, P(X), if R(X) and Q(X) are mutually primes and all solutions are congruent modulo S(X) = R(X) · Q(X).

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Computer Algebra System (CAS)