integrate (and defint) give the wrong Cauchy
principal value result for a non-convergent
integral:
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Maxima 5.28.0-2 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
(%i1) integrate(1/(x-1),x,0,2);
Principal Value
(%o1) %i*%pi
(%i2) assume(eps > 0, eps < 1);
(%o2) [eps > 0,eps < 1]
/* the limit of i1 plus i2 as eps --> 0 is zero */
(%i3) i1 : integrate(1/(x-1),x,0,1-eps);
(%o3) log(eps)
(%i4) i2 : integrate(1/(x-1),x,1+eps,2);
(%o4) -log(eps)
(%i5) lognegint:true;
(%o5) true
(%i6) log(-1);
(%o6) %i*%pi
(%i7) defint(1/(x-1),x,0,2);
Principal Value
(%o7) %i*%pi
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The correct Cauchy principal value is 0.
Ted Woollett