[Maxima-bugs] [ maxima-Bugs-3515955 ] is (equal (...)) with realpart

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Bugs item #3515955, was opened at 2012-04-08 15:08
Message generated for change (Comment added) made by willisbl
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Ted Woollett (woollett)
Assigned to: Nobody/Anonymous (nobody)
Summary: is (equal (...)) with realpart

Initial Comment:
with 5.26.0 gcl (windows)

(%i1) display2d:false$

(%i2) bex : 1/sqrt(sin(x));
(%o2) 1/sqrt(sin(x))

(%i3) realpart(bex);
(%o3) cos(atan2(0,sin(x))/2)/sqrt(abs(sin(x)))

(%i4) imagpart(bex);
(%o4) -sin(atan2(0,sin(x))/2)/sqrt(abs(sin(x)))

(%i5) is (equal (bex, realpart(bex)));
(%o5) true            <==  wrong!

(%i6) is (equal (bex, imagpart(bex)));
(%o6) false          <== correct

Here we also show that if a calling program (test) 
gets the wrong "true" answer from is(equal(...)), 
and then calls a subprogram (test1), an incorrect
evaluation of realpart(expr) is found in test1.

This occurs in both 5.26.0gcl and 5.25.1gcl.

program:

test1(bex) :=
block([bexr],
   print (" test1 "),   
   print(" bex = ",bex),
   bexr : realpart(bex),   
   print(" bexr = ",bexr),
   bexr)$
   
   
   
test(aex) :=
 block([aexr,ans1,isr],
     print("  test  "),
     print(" aex = ",aex),
     
     aexr : realpart(aex),
     print(" aexr = ",aexr),     
     
     isr : is(equal(aex,realpart(aex))),
     print(" isr = ",isr),

     ans1 : test1(aex),          
     ans1)$
     
 display2d:false$

demonstration of problem :

(%i1) load(test);
(%o1) "c:/work2/test.mac"

(%i2) test(1/sqrt(sin(x)));

  test   
 aex =  1/sqrt(sin(x)) 
 aexr =  cos(atan2(0,sin(x))/2)/sqrt(abs(sin(x))) 
 isr =  t 
 
 test1  
 bex =  1/sqrt(sin(x)) 
 bexr =  1/sqrt(sin(x)) 
(%o2) 1/sqrt(sin(x))

(%i3) realpart(1/sqrt(sin(x)));
(%o3) cos(atan2(0,sin(x))/2)/sqrt(abs(sin(x)))

(%i4) is(equal(1/sqrt(sin(x)), realpart(1/sqrt(sin(x)))));
(%o4) true

(%i5) build_info();
Maxima version: 5.26.0
Maxima build date: 22:48 1/15/2012
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8



----------------------------------------------------------------------

>Comment By: Barton Willis (willisbl)
Date: 2012-06-11 06:12

Message:
Possible fix:  in meqp-by-csign  insert (clearsign)  just before the first
call to $csign.
That doesn't fix the bug in sign mentioned in the first posting.

----------------------------------------------------------------------

Comment By: Barton Willis (willisbl)
Date: 2012-06-11 03:21

Message:
This is due to a bug in sign:

(%i24)
sign((sqrt(abs(sin(x)))-cos(atan2(0,sin(x))/2)*sqrt(sin(x)))/(sqrt(sin(x))*sqrt(abs(sin(x)))));
(%o24) zero

But (for example)

(%i25)
subst(x=4,(sqrt(abs(sin(x)))-cos(atan2(0,sin(x))/2)*sqrt(sin(x)))/(sqrt(sin(x))*sqrt(abs(sin(x)))));
(%o25) 1/sqrt(sin(4))


----------------------------------------------------------------------

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