Clearly Robert has found a bug in maxima. Here's a little test further to
my earlier "puzzle":
If I write in sage as follows:
#$is
(equal(-(_SAGE_VAR_r13^2*_SAGE_VAR_r23-_SAGE_VAR_r23^3)/((-_SAGE_VAR_r23^4)+2*_SAGE_VAR_r13^2*_SAGE_VAR_r23^2-_SAGE_VAR_r13^4+_SAGE_VAR_r12^4),0))$
var('r12 r13 r23',domain='complex')
assume(r12>0, r13>0, r23>0)
#trace( "bool(-(r13^2*r23-r23^3)/((-r23^4)+2*r13^2*r23^2-r13^4+r12^4) ==
0)" )
bool(-(r13^2*r23-r23^3)/((-r23^4)+2*r13^2*r23^2-r13^4+r12^4) == 0)
then sage finishes without error! Instead, it returns "False".
Dropping into pydb, I recover the identical *statement* being shipped off
to Maxima!
>
/home/rllozes/sage-8.0/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py(452)_eval_line()
450 line = line[ind_semi+1:]
451 if statement:
5-> 452 result = ((result + '\n') if result else '') +
max_to_string(maxima_eval("#$%s$"%statement))
453 else:
454 statement = line[:ind_dollar]
ipdb> p statement
'is
(equal(-(_SAGE_VAR_r13^2*_SAGE_VAR_r23-_SAGE_VAR_r23^3)/((-_SAGE_VAR_r23^4)+2*_SAGE_VAR_r13^2*_SAGE_VAR_r23^2-_SAGE_VAR_r13^4+_SAGE_VAR_r12^4),0))'
This behavior is independent of whether the variables are declared 'real'
or 'complex'.
Conclusion: something else is going on in manifolds and/or in maxima.
Robert, what version of maxima did you test?
- Richard
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