I get a strange error when i try to evaluate a polynomial in QQbar:
sage: R.<x,y>=QQbar[]
sage: f=x^2+x^3-y^2+y^4*x^4
sage: RX=PolynomialRing(QQbar,'x')
sage: RY=PolynomialRing(QQbar,'y')
sage: x0=3+2^-8
sage: y0=RY(f((x0,y))).roots(multiplicities=False)[0]
sage: f(x+x0,y0)
---------------------------------------------------------------------------
PariError Traceback (most recent call
last)
/home/mmarco/<ipython console> in <module>()
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/
polynomial/multi_polynomial_element.pyc in __call__(self, *x,
**kwds)
154 y =
K(0)
155 for (m,c) in
self.element().dict().iteritems():
--> 156 y += c*misc.mul([ x[i]**m[i] for i in range(n) if
m[i] != 0])
157 return
y
158
/usr/local/sage/local/lib/python2.6/site-packages/sage/structure/
element.so in sage.structure.element.ModuleElement.__iadd__ (sage/
structure/element.c:8264)
()
/usr/local/sage/local/lib/python2.6/site-packages/sage/structure/
element.so in sage.structure.element.ModuleElement._add_ (sage/
structure/element.c:8117)
()
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/
polynomial/multi_polynomial_element.pyc in _add_(self,
right)
212 def _add_(self,
right):
213 #return self.parent()(self.__element +
right.__element)
--> 214 return self.__class__(self.parent(),self.__element +
right.__element)
215
216 def _sub_(self,
right):
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/
polynomial/polydict.so in
sage.rings.polynomial.polydict.PolyDict.__add__ (sage/rings/polynomial/
polydict.c:7503)()
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/
polynomial/polydict.so in
sage.rings.polynomial.polydict.PolyDict.__init__ (sage/rings/
polynomial/polydict.c:1781)()
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in __eq__(self, other)
3049 if self is other: return
True
3050 if other._descr.is_rational() and
other._descr.rational_value() == 0:
-> 3051 return not
self.__nonzero__()
3052 if self._descr.is_rational() and
self._descr.rational_value() == 0:
3053 return not
other.__nonzero__()
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in __nonzero__(self)
3081 if self._value.prec() <
128:
3082
self._more_precision()
-> 3083 return
self.__nonzero__()
3084
3085 #
Sigh...
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in __nonzero__(self)
3084
3085 #
Sigh...
-> 3086
self.exactify()
3087 return
self.__nonzero__()
3088
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
2739 od =
self._descr
2740 if od.is_exact():
return
-> 2741
self._set_descr(self._descr.exactify())
2742
2743 def _set_descr(self,
new_descr):
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
5891 left =
self._left
5892 right =
self._right
-> 5893
left.exactify()
5894
right.exactify()
5895 gen =
left._exact_field().union(right._exact_field())
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
2739 od =
self._descr
2740 if od.is_exact():
return
-> 2741
self._set_descr(self._descr.exactify())
2742
2743 def _set_descr(self,
new_descr):
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
5891 left =
self._left
5892 right =
self._right
-> 5893
left.exactify()
5894
right.exactify()
5895 gen =
left._exact_field().union(right._exact_field())
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
2739 od =
self._descr
2740 if od.is_exact():
return
-> 2741
self._set_descr(self._descr.exactify())
2742
2743 def _set_descr(self,
new_descr):
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
5891 left =
self._left
5892 right =
self._right
-> 5893
left.exactify()
5894
right.exactify()
5895 gen =
left._exact_field().union(right._exact_field())
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
2739 od =
self._descr
2740 if od.is_exact():
return
-> 2741
self._set_descr(self._descr.exactify())
2742
2743 def _set_descr(self,
new_descr):
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
5892 right =
self._right
5893
left.exactify()
-> 5894
right.exactify()
5895 gen =
left._exact_field().union(right._exact_field())
5896 left_value =
gen(left._exact_value())
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
2739 od =
self._descr
2740 if od.is_exact():
return
-> 2741
self._set_descr(self._descr.exactify())
2742
2743 def _set_descr(self,
new_descr):
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
5891 left =
self._left
5892 right =
self._right
-> 5893
left.exactify()
5894
right.exactify()
5895 gen =
left._exact_field().union(right._exact_field())
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
2739 od = self._descr
2740 if od.is_exact(): return
-> 2741 self._set_descr(self._descr.exactify())
2742
2743 def _set_descr(self, new_descr):
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in exactify(self)
5109 den, my_factor = clear_denominators(my_factor)
5110
-> 5111 red_elt, red_back, red_pol = do_polred(my_factor)
5112
5113 field = NumberField(red_pol, 'a', check=False)
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/qqbar.pyc
in do_polred(poly)
1206 assert(best is not None)
1207 parent = poly.parent()
-> 1208 rev = parent(best_elt.Mod(pari_poly).modreverse().lift())
1209 return parent(best_elt), rev, parent(best)
1210
/usr/local/sage/local/lib/python2.6/site-packages/sage/libs/pari/
gen.so in sage.libs.pari.gen._pari_trap (sage/libs/pari/gen.c:49380)()
PariError: (5)
Strange thing is that if i do only one of the two substitutions, it
works fine.
sage: f(x,y0)
(-0.4436467746868897? + 0.00818072177704596?*I)*x^4 + x^3 + x^2 -
0.006140793684108297? - 0.666096452500658?*I
sage: f(x+x0,y)
x^4*y^4 + 769/64*x^3*y^4 + 1774083/32768*x^2*y^4 +
454756609/4194304*x*y^4 + 349707832321/4294967296*y^4 + x^3 +
2563/256*x^2 - y^2 + 2167811/65536*x + 606145025/16777216
Someone has a clue about what the problem migh be?
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