[Maxima] mydefint1

[Edwin Woollett]

On Mar. 15, Stavros Macrakis wrote
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>I was wondering why you assume both not equal (x,a) and x>a, since the
>second implies the first?  Have you found problematic cases?  If so, those
>should be reported as bugs.
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You are correct that I found cases where I needed to insert both
assumptions to avoid integrate questions.

One case I can find quickly is (using 5.26.0gcl):
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(%i1) display2d:false$

(%i2) facts();
(%o2) []

(%i3) assume ( x  >=  0, x  <=  1 )$

(%i4) integrate (integrate (log (x+y), y, 0, 1), x, 0, 1);

Is  x - 1.0  negative or zero?

n;

(%o4) (4*log(2)-3)/2

(%i5) forget( x  >=  0, x  <=  1)$

(%i6) assume( x  >=  0, x  <  1, not equal (x, 1));

(%o6) [x  >=  0, x  <  1,  redundant]

(%i7) facts();

(%o7) [ x  >=  0, 1  >  x]

(%i8) integrate (integrate (log (x+y), y, 0, 1), x, 0, 1);
(%o8) (4*log(2)-3)/2

(%i9) forget( x  >=  0, x  <  1, not equal (x,1));

(%o9) [ x  >=  0, x  <  1, notequal (x, 1)]

(%i10) facts();
(%o10) []

(%i11) assume (not equal (x,0), x  >  0, x  <  1, not equal (x, 1));

(%o11) [notequal (x, 0), x  >  0, x  <  1, redundant]

(%i12) facts();

(%o12) [notequal (x, 0), x  >  0, 1  >  x]

(%i13) integrate (integrate (log (x+y), y, 0, 1), x, 0, 1);
(%o13) (4*log(2)-3)/2
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Although the code considered not equal(x,1) to be "redundant",
and it was not included in the list of facts(), the method
avoided the question from integrate.

Ted