Hi all, This is a sequel of my former question:
http://groups.google.com/group/sage-support/browse_thread/thread/ed74c71c01cb9f26/63a88bb12708c275?lnk=gst&q=fractional+ideal#63a88bb12708c275 I use SAGE 4.4.alpha0 (with Virtual Machine) and the online SAGE. Note that the former contains PARI/GP 2.3.3 and the latter contains PARI/GP 2.3.5. I am now trying to decompose the fractional ideal (3) in the following number field: K.<a> = NumberField(x^6 + 9*x^5 - 8410*x^4 - 88580*x^3 + 18705368*x^2 + 99820416*x - 12230355456) In fact, what I exactly want to do is to find various residue fields of this number field at primes above 3. I also used proof.number_field(False) to avoid the Minkowski bound error. When I used K.primes_above(3), I got the following error message (in both SAGEs): *** Warning: precision too low for generators, not given. Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_28.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Sy5wcmltZXNfYWJvdmUoMyk="),globals()) +"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpgLCFVa/___code___.py", line 3, in <module> exec compile(u'K.primes_above(_sage_const_3 ) File "", line 1, in <module> File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/misc/ displayhook.py", line 174, in displayhook print_obj(sys.stdout, obj) File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/misc/ displayhook.py", line 142, in print_obj print >>out_stream, `obj` File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/rings/ number_field/number_field_ideal.py", line 1259, in __repr__ return "Fractional ideal %s"%self._repr_short() File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/rings/ number_field/number_field_ideal.py", line 377, in _repr_short return '(%s)'%(', '.join(map(str, self.gens_reduced()))) File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/rings/ number_field/number_field_ideal.py", line 630, in gens_reduced dummy = self.is_principal(proof) File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/rings/ number_field/number_field_ideal.py", line 839, in is_principal g = K(bnf.getattr('zk') * v[1]) File "element.pyx", line 1431, in sage.structure.element.RingElement.__mul__ (sage/structure/element.c: 11356) File "gen.pyx", line 9232, in sage.libs.pari.gen._pari_trap (sage/ libs/pari/gen.c:44342) sage.libs.pari.gen.PariError: impossible (44) Even I used pari commands in both SAGEs: K_nf = gp(K.pari_nf()) ; K_nf K_nf.idealprimedec(3) Then I still got the error. Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_31.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("S19uZi5pZGVhbHByaW1lZGVjKDMp"),globals()) +"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpBRkZps/___code___.py", line 3, in <module> exec compile(u'K_nf.idealprimedec(_sage_const_3 ) File "", line 1, in <module> File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/ interfaces/expect.py", line 1408, in __call__ return self._obj.parent().function_call(self._name, [self._obj] + list(args), kwds) File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/ interfaces/expect.py", line 1316, in function_call return self.new(s) File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/ interfaces/expect.py", line 1097, in new return self(code) File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/ interfaces/expect.py", line 1032, in __call__ return cls(self, x, name=name) File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/ interfaces/expect.py", line 1451, in __init__ raise TypeError, x TypeError: Error executing code in GP/PARI: CODE: sage[25]=idealprimedec(sage[21],sage[24]); GP/PARI ERROR: *** idealprimedec: precision too low in get_norm. However, when I just use PARI/GP (version 2.3.4), the decomposition works, even very fast. PARI gave me the following: [[3, [-2, 1, 1, 1, 1, -1]~, 1, 1, [2, 0, 0, 0, 2, 1]~], [3, [1, -1, -1, 0,-1, 0]~, 2, 1, [1, 1, 1, 1, 2, 1]~], [3, [1, 1, 0, -1, 1, -1]~, 1, 1, [1, 2, 1,0, 0, 0]~], [3, [2821, 14, -20, -2, 0, -4]~, 1, 2, [-1, -1, 1, 1, 0, -1]~]] I wonder what happens here and want to find another method to avoid this error.. Sincerely, Chan-Ho -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
