#2420: [with patch, needs work] Extending the gap interface to uni- and
multivariate polynomial rings over number fields
----------------------------------------------------------------------+-----
Reporter: SimonKing |
Owner: SimonKing
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-4.5
Component: interfaces |
Keywords: gap interface, polynomial rings, number fields, editor_mhansen
Author: Simon King |
Upstream: N/A
Reviewer: |
Merged:
Work_issues: Consider stacks of polynomial rings over number fields |
----------------------------------------------------------------------+-----
Changes (by SimonKing):
* work_issues: Side effect of GAP on Pari => Consider stacks of
polynomial rings over number fields
Comment:
OK, problem solved!
It is a bug in {{IntegerMod_int.log()}}}, which had a side effect in PARI
and is fixed at #9438. Apply
{{{trac_2420_GAP_interface_polynomials.patch}}} after applying the patches
from #8909, #9423 and #9438, and {{{sage -testall}}} passes!
Here is a summary of the features:
Univariate
{{{
sage: F.<zeta> = CyclotomicField(8)
sage: R.<x> = F[]
sage: gap(R)
PolynomialRing( CF(8), ["x"] )
sage: p = zeta^2*x+2*zeta
sage: gap(p)^3
(-E(4))*x^3+(-6*E(8))*x^2-12*x+8*E(8)^3
sage: p^3
-zeta^2*x^3 - 6*zeta*x^2 - 12*x + 8*zeta^3
}}}
Multivariate
{{{
sage: R.<x,y> = F[]
sage: p = zeta*x+zeta^2*y
sage: gap(p)^2
E(4)*x^2+2*E(8)^3*x*y-y^2
sage: p^2
(zeta^2)*x^2 + (2*zeta^3)*x*y - y^2
}}}
O dear! A stack of polynomial rings does not work as it should:
{{{
sage: P.<y> = QQ[]
sage: K.<tau> = NumberField(y^2+y+1)
sage: R.<x,y> = K[]
sage: S.<z> = R[]
sage: p = tau*x+tau^2*z+3*tau^3*x*y*z
sage: p
(3*x*y + (-tau - 1))*z + (tau)*x
sage: gap(p)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/king/SAGE/work/Tickets/9438/<ipython console> in <module>()
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/expect.pyc in __call__(self, x, name)
1032 return cls(self, x, name=name)
1033 try:
-> 1034 return self._coerce_from_special_method(x)
1035 except TypeError:
1036 raise
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/expect.pyc in _coerce_from_special_method(self,
x)
1056 s = '_gp_'
1057 try:
-> 1058 return (x.__getattribute__(s))(self)
1059 except AttributeError:
1060 return self(x._interface_init_())
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial._gap_
(sage/rings/polynomial/polynomial_element.c:27411)()
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/expect.pyc in __call__(self, x, name)
1030
1031 if isinstance(x, basestring):
-> 1032 return cls(self, x, name=name)
1033 try:
1034 return self._coerce_from_special_method(x)
/home/king/SAGE/sage-4.4.2/local/lib/python2.6/site-
packages/sage/interfaces/expect.pyc in __init__(self, parent, value,
is_name, name)
1449 except (TypeError, KeyboardInterrupt, RuntimeError,
ValueError), x:
1450 self._session_number = -1
-> 1451 raise TypeError, x
1452 self._session_number = parent._session_number
1453
TypeError: Gap produced error output
Error, no 1st choice method found for `PROD' on 2 arguments
executing
Read("/home/king/.sage//temp/gauss/30709//interface//tmp30709");
}}}
The string that was supposed to be executed is
{{{
sage: p._gap_init_()
'CallFuncList(function() local z; z:=Indeterminate($sage12,"z"); return
(CallFuncList(function() local x,y; x:=Indeterminate($sage5,"x");
y:=Indeterminate($sage5,"y"); return (GeneratorsOfField($sage5)[1])*x;
end,[]))*1+(CallFuncList(function() local x,y;
x:=Indeterminate($sage5,"x"); y:=Indeterminate($sage5,"y"); return
(3)*x*y+(-GeneratorsOfField($sage5)[1] - 1)*1; end,[]))*z; end,[])'
}}}
So, it is almost done, but I'd like to fix the last problem too.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2420#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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