Opened 4 years ago

Last modified 3 years 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: | Emmanuel Charpentier | Owned by: | |
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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:2 Changed 3 years ago by

Milestone: | sage-8.8 |
---|

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).

**Note:**See TracTickets for help on using tickets.

This is still true in 8.8.beta7, which has maxima 5.42.2...