#1047 another example of assume + asksign failure

open
nobody
5
2012-11-18
2006-12-26
No

For many expressions FOO, Maxima does not know sign(FOO) even after assume. Here is another example.

(%i2) prederror : false;
(%o2) false

(%i3) declare (a, real);
(%o3) done

(%i4) assume (sqrt (-2 * sqrt (a^2 + 1) + a^2 + 2) - a < 0);
(%o4) [a-sqrt(-2*sqrt(a^2+1)+a^2+2) > 0]

(%i5) is (sqrt (-2 * sqrt (a^2 + 1) + a^2 + 2) - a < 0);
(%o5) true

(%i6) is (sqrt (-2 * sqrt (a^2 + 1) + a^2 + 2) - a > 0);
(%o6) unknown

(%i7) is (equal (sqrt (-2 * sqrt (a^2 + 1) + a^2 + 2) - a, 0));
(%o7) unknown

(%i8) sign (sqrt (-2 * sqrt (a^2 + 1) + a^2 + 2) - a);
(%o8) pnz

(%i9) asksign (sqrt (-2 * sqrt (a^2 + 1) + a^2 + 2) - a);
Is sqrt(-2*sqrt(a^2+1)+a^2+2)-a positive, negative, or zero?

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