Cas Functions On The Cmds Menu - HP 40gs User Manual

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CAS Functions on the CMDS menu

ABCUV
CHINREM
14-62
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
previous section for other CAS commands.)
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:
2
ABCUV(X
+ 2 · X + 1, X
gives:
-- - AND 1
1
-- -
2
2
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).
in the Equation Writer. (See the
2
– 1, X + 1)
Computer Algebra System (CAS)

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