[Maxima] posible bug - clashing variable names in integrals

[Barton Willis]

is(equal(..,, ...)) knows something about dummy variables for lambda
forms and sums, but not integrals:

 (%i5) is(equal(integrate(f(x),x,a,b), integrate(f(y),y,a,b)));
 (%o5) unknown

 (%i6) is(equal(sum(f(x),x,0,n), sum(f(y),y,0,n)));
 (%o6) true

 (%i7) is(equal(lambda([x], f(x)), lambda([y], f(y))));
 (%o7) true

If integrate(f(x),x,a,b) is undefined, you could argue that (%o5) is
correct and (%o6) and (%o7) are spurious--after all,
is(equal(und,und)) --> false (and correctly so, I think). but I guess
that most users prefer (%o6) and (%o7) over (%o5).

Barton

-----maxima-bounces at math.utexas.edu wrote: -----

>To: Leo Butler <l.butler at ed.ac.uk>
>From: Nathaniel Virgo <nathanielvirgo at gmail.com>
>Sent by: maxima-bounces at math.utexas.edu
>Date: 10/03/2009 08:17AM
>cc: maxima <maxima at math.utexas.edu>
>Subject: Re: [Maxima] posible bug - clashing variable names in integrals
>
>Ok, sorry, yes, I think I understand this now.  So it's not a bug per se
>that 'is' returns 'false' in that situation.
>
>It is, however, still annoying that it doesn't treat integrate(f(x),x,a,b)
>in exactly the same way as integrate(f(y),y,a,b).  It should do because x
>and y are bound variables in those expressions, so their name should not
>make any difference in any situation.  This difference in the way it
>treats these two expressions is likely to be a problem for a lot of the
>things I wanted to use Maxima for.
>
>
>
>Nathaniel
>
>
>2009/10/3 Leo Butler <l.butler at ed.ac.uk>
>
>
>
>
>
>
>On Sat, 3 Oct 2009, Nathaniel Virgo wrote:
>
>
>
>< On a similar note, am I right to say the following should not return
>false?
>
><
>
>< (%i20) A: 'integrate(f(x),x,a,b);
>
>< (%o20) integrate(f(x),x,a,b)
>
>< (%i21) B: 'integrate(f(y),y,a,b);
>
>< (%o21) integrate(f(y),y,a,b)
>
>< (%i22) is(A=B);
>
>< (%o22) false
>
><
>
>< the two expressions are equivalent, the only difference being the name
>of a
>
>< bound variable.  So it should return "true" or "maybe" but not false. It
>
>< works with ordinary (non-integral) functions:
>
><
>
>< (%i24) f(x):=x^2;
>
>< (%o24) f(x):=x^2
>
>< (%i25) g(y):=y^2;
>
>< (%o25) g(y):=y^2
>
>< (%i26) is(f(z)=g(z));
>
>< (%o26) true
>
><
>
>< Nathaniel
>
><
>
><
>
>< 2009/10/3 Nathaniel Virgo <nathanielvirgo at gmail.com>
>
><
>
>< > Hi
>
>< >
>
>< > I just came across the following.  Should it be considered a bug?
>
>< >
>
>< >
>
>< > this works fine:
>
>< >
>
>< > (%i10) C:integrate(g(y),y,c,d);
>
>< > (%o10) integrate(g(y),y,c,d)
>
>< >
>
>< > (%i11) A: integrate(C*f(x),x,a,b);
>
>< > (%o11) integrate(f(x),x,a,b)*integrate(g(y),y,c,d)
>
>< >
>
>< > it has successfully taken the constant outside the integral
>
>< >
>
>< > (%i12) B: C*'integrate(f(x),x,a,b);
>
>< > (%o12) integrate(f(x),x,a,b)*integrate(g(y),y,c,d)
>
>< >
>
>< > so A and B are the same
>
>< >
>
>< > (%i13) is(A=B);
>
>< > (%o13) true
>
>< >
>
>< > however, if I do the following, which should be exactly equivalent, it
>
>< > fails:
>
>< >
>
>< > (%i14) C:integrate(g(x),x,c,d);
>
>< > (%o14) integrate(g(x),x,c,d)
>
>< >
>
>< > (%i15) A: integrate(C*f(x),x,a,b);
>
>< > (%o15) integrate(f(x)*integrate(g(x),x,c,d),x,a,b)
>
>< >
>
>< > it has failed to realise that the x in the subexpression is a
>different
>
>< > variable from the x in the outer integral, so it keeps the constant
>inside
>
>< > the integral
>
>< >
>
>< > (%i16) B: C*'integrate(f(x),x,a,b);
>
>< > (%o16) integrate(f(x),x,a,b)*integrate(g(x),x,c,d)
>
>< >
>
>< > (%i17) is(A=B);
>
>< > (%o17) false
>
>< >
>
>< > ...and it now thinks the two expressions A and B are provably not the
>same,
>
>< > even though they are in fact equivalent.  It would be ok (although a
>bit
>
>< > lame) if it answered "maybe" here, but it seems to me that "false" is
>just
>
>< > incorrect.
>
>< >
>
>< >
>
>< > Nathaniel
>
>< >
>
>< >
>
><
>
>
>
>Nathaniel,
>
>You slide between equal and equivalent and are not clearly
>
>distinguishing between the two. Maxima does. From
>
>
>
>? =
>
>
>
> `is(<a> = <b>)' evaluates `<a> = <b>' to `true' when <a> and <b>
>
>     are syntactically equal (that is, identical).  Expressions can be
>
>     equivalent and not syntactically equal.
>
>
>
>Try
>
>
>
>is(equal(A,B));
>
>
>
>
>
>Leo
>
>
>
>--
>
>The University of Edinburgh is a charitable body, registered in
>
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>
>
>
>
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