posible bug - clashing variable names in integrals

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
>
>Scotland,?with?registration?number?SC005336.
>
>
>
>
>
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