Richard Fateman <fateman@cs.berkeley.edu> writes:
> Look at this: expand ( (abs(x)-x)*(abs(x)+x));
> more zero divisors, but these are not algebraic!
Interesting example! These are not zero-divisors for the rational
functions module itself (so they represent no danger for the gcd
functions):
(C1) algebraic:true;
(D1) TRUE
(C2) e:rat(x-abs(x));
(D2)/R/ - ABS(x) + x
(C3) f:rat(x+abs(x));
(D3)/R/ ABS(x) + x
(C4) e*f;
2 2
(D4)/R/ - ABS(x) + x
I'd think that anything in Maxima that simplifies this to rat(0)
(assuming that x is a real number) actually disreps it somewhere.
I realize that in my previous posting I obscured the point I wanted to
make by using is(... = 0), which in fact calls RATDISREP if necessary.
Nevertheless, my example is still valid:
(C1) algebraic:true;
(D1) TRUE
(C2) tellrat(u^2=t-1,v^2=t+1);
2 2
(D2) [v - t - 1, u - t + 1]
(C3) x:rat(sqrt(2)*sqrt(u*v+t));
(D3)/R/ SQRT(2) SQRT(u v + t)
(C4) e:rat(x-u-v);
(D4)/R/ SQRT(2) SQRT(u v + t) - v - u
(C5) f:rat(x+u+v);
(D5)/R/ SQRT(2) SQRT(u v + t) + v + u
(C6) e*f;
(D6)/R/ 0
I should also add that I don't want to imply that this is a bug. The
point is just that such CRE zero-divisors may occur in quite ordinary
circumstances.
Wolfgang