#5618: Cyclotomic field elements are not converted to Gap correctly
-----------------------+----------------------------------------------------
Reporter: saliola | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-4.5
Component: algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-----------------------+----------------------------------------------------
Changes (by SimonKing):
* upstream: => N/A
Comment:
Here is some problem analysis:
{{{
sage: K = CyclotomicField(3)
sage: z = K.an_element(); z
zeta3
sage: gap(z)
zeta3
sage: K(gap(z))
zeta3
sage: gap.E(3)
E(3)
sage: gap.E(3) == gap(z)
False
sage: K(gap.E(3)) == K(gap(z)) == z
True
}}}
So, apparently GAP treats "the same" elements of a cyclotomic field
differently if they have different names. But this isn't particularly
surprising, since the two cyclotomic fields seem to have a totaly
different representation in GAP:
{{{
sage: ZFgap = gap('CyclotomicField(3)')
sage: Kgap = gap(K)
sage: Kgap
<algebraic extension over the Rationals of degree 2>
sage: ZFgap
CF(3)
sage: ZFgap.GeneratorsOfField()
[ E(3) ]
sage: Kgap.GeneratorsOfField()
[ zeta3 ]
}}}
Note that comparison of the two field in the GAP interface results in an
error:
{{{
sage: Kgap == ZFgap
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (47, 0))
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call
last)
/home/king/<ipython console> in <module>()
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/structure/element.so in
sage.structure.element.Element.__richcmp__
(sage/structure/element.c:7061)()
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/structure/element.so in
sage.structure.element.Element._richcmp (sage/structure/element.c:6943)()
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/expect.pyc in __cmp__(self, other)
1527 other.name())) ==
P._true_symbol():
1528 return 0
-> 1529 elif P.eval("%s %s %s"%(self.name(), P._lessthan_symbol(),
other.name())) == P._true_symbol():
1530 return -1
1531 elif P.eval("%s %s %s"%(self.name(),
P._greaterthan_symbol(), other.name())) == P._true_symbol():
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/gap.pyc in eval(self, x, newlines, strip, **kwds)
478 input_line += ';'
479
--> 480 result = Expect.eval(self, input_line, **kwds)
481
482 if not newlines:
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/expect.pyc in eval(self, code, strip,
synchronize, locals, **kwds)
981 try:
982 with gc_disabled():
--> 983 return '\n'.join([self._eval_line(L, **kwds) for L
in code.split('\n') if L != ''])
984 except KeyboardInterrupt:
985 # DO NOT CATCH KeyboardInterrupt, as it is being
caught
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/gap.pyc in _eval_line(self, line, allow_use_file,
wait_for_prompt)
720 return ''
721 else:
--> 722 raise RuntimeError, message
723
724 except KeyboardInterrupt:
RuntimeError: Gap produced error output
Error, no 1st choice method found for `LT' on 2 arguments
executing $sage2 < $sage8;
}}}
But GAP indeed considers the two fields to be different:
{{{
sage: gap.eval(Kgap.name() + ' = ' + ZFgap.name())
'false'
}}}
So, what does all this mean?
1. The {{{__cmp__}}} method of the GAP interface has a bug. An error
raised by GAP when attempting "<" or ">" should be caught and then "="
should be tried.
2. A GAP cyclotomic field is different from the GAP version of a Sage
cyclotomic field. This is since the GAP version of a Sage cyclotomic field
is a number field. It could be solved by providing a genuine
{{{_gap_init_}}} method for Sage cyclotomic fields (currently, it is
inherited from number fields).
It seems likely to me that after implementing 2., things will already
work. But 1. should be fixed as well.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5618#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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