HP 40gs Manuel d'utilisateur télécharger pdf (Page 244)

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101

14-62 Computer Algebra System (CAS)

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(X

+ 2 · X + 1, X

– 1, X + 1)

gives:

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).

AND

–

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