Opened 19 months ago
Last modified 18 months ago
#27816 new defect
sqrt(-r_0^2 + r_1^2 + 2*r_0*x - x^2): Maxima gives an antiderivative but *crashes* on definite integral
Reported by: | charpent | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | |
Component: | symbolics | Keywords: | definite integral |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | Not yet reported upstream; Will do shortly. | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Inspired by this ask.sagemath.org question:
var("x, y, t, r_0, r_1, X", domain="real") rr=var("rr") assume(r_0>0,X<r_0,r_1>0,r_1<2*r_0,rr>0) with assuming(y>0): foo=solve(x^2 + y^2 == r_0^2, y)[0].rhs() Y_0(x)=foo with assuming(y>0): foo=solve((r_0-x)^2 + y^2 == r_1^2, y)[0].rhs() Y_1(x)=foo X=solve(Y_1(x)^2==Y_0(x)^2,x)[0].rhs() g(x)=integrate(Y_1(x),x).expand()
So far, so good :
sage: (g(X)-g(r_0-r_1)).expand() 1/4*pi*r_1^2 - 1/2*r_1^2*arcsin(1/2*r_1/r_0) - 1/8*sqrt(4*r_1^2 - r_1^4/r_0^2)*r_1^2/r_0
But integrate(Y_1(x),x,r_0-r_1,X).expand()
crashes Maxima (and Sage) :
sage: integrate(Y_1(x),x,r_0-r_1,X) ;;; ;;; Detected access to protected memory, also kwown as 'bus or segmentation fault'. ;;; Jumping to the outermost toplevel prompt ;;;
repeated /ad nauseam/...
This can be reproduced in Maxima. This works as expected:
assume(r_0>0,X<r_0,r_1>0,r_1<2*r_0,rr>0); assume(y>0); define(Y_0(x),rhs(solve(x^2+y^2=r_0^2,y)[2])); define(Y_1(x),rhs(solve((r_0-x)^2+y^2=r_1^2,y)[2])); X:rhs(solve(Y_0(x)^2=Y_1(x)^2,x)[1]); Y:Y_0(X); define(g(x),expand(integrate(Y_1(x),x))); g(X)-g(r_0-r_1);
But asking for integrate(Y_1(x),x,r_0-r_1,X);
crashes Maxima with the same error messages...
This seems different from bugs already reported on definite integration.
FWIW, both giac
and fricas
give acceptable answers (different in their integration process : one uses arcsin
, the other arctan
, with similar geometric interpretation...).
Change History (2)
comment:1 Changed 18 months ago by
comment:2 Changed 18 months ago by
- Milestone sage-8.8 deleted
As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).
This is strill true in 8.8.beta7, which has maxima 5.42.2...