Raymond Toy

1/(1-x^5) can be factored as -1/(x-1)/(x^4+x^3+x^2+x+1), and we can use quad_qawc to compute the integral like so: (%i29) quad_qawc(-1/(x^4+x^3+x^2+x+1),x,1,0,100); (%o29) [0.8648062684772098, 2.8888229703493868e-11, 385, 0] And for [100,inf]`: (%i30) quad_qagi(1/(1-x^5),x,100,inf); (%o30) [- 2.500000000111111e-9, 2.7250808692222103e-18, 225, 0] (%i31) %o29[1]+%o30[1]; (%o31) 0.8648062659772098 That's pretty close.

Maybe? At least in these cases, the expression is real everywhere for real x. Unlike sqrt(sin(x)-1) which is real only for appropriate multiples of pi. I don't know what the answer should be. I almost never use sign for anything myself, and if I do it's usually for a simple variable.

Sorry for the delay. You wrote: (kill(ff,x,dx,y,dy,t),assume(x<1),ff:xsqrt(1-y^2)+ysqrt(1-x^2),t1:diff(ff,x)dx+diff(ff,y)dy,t2:(sqrt((1-x^2)(1-y^2)) -xy)*(dx/sqrt(1-x^2)+dy/sqrt(1-y^2)),disp(["t1"=t1,"t2"=t2]),t:radcan(t1-t2),disp(["t"=t]) ); and that's just one giant line. I find that hard enough to read that I don't want to figure it out. But that's just me. I could run it, but, presumably, that would just reproduce what you said you got.

It could return complex since it is complex except on a set of measure zero. That's probably pretty difficult to define too in maxima. I don't even know how maxima figured out that it could be zero. Because sin(x) has a range of [-1,1] so the expression could be zero?

But it should return a result when the result is real somewhere. For example, sign(sqrt(sin(x)-1)) => zero (correct), even though it is only real and zero when x is a multiple of %pi. Is that really how sign is supposed to work? The docs kind of hint at that, but I was certainly surprised about that. I don't think anyone would expect zero as the answer either.

Merge branch 'rtoy-rename-preserve-direction'

Rename preserve-direction to *prserve-direction*

Just curious and irrelevant to the bug, but do you really type in huge long lines into maxima? I find them really hard to read and therefore hard to figure what what is the setup and what is the bug. Hence that discourages me from looking at the issue.