HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 244

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-- AND -1-- 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). 14-62 Computer Algebra System (CAS)