Hi all:
Do any of you know what is going wrong with the variety() command in
the example below? Sometimes it works, and sometimes it doesn't. The
problem seems to be variety()'s call to triangular_decomposition().
Alex
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| Sage Version 3.2, Release Date: 2008-11-20 |
| Type notebook() for the GUI, and license() for information. |
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sage: R.<w,z>= PolynomialRing(QQ,2,order='lex')
sage: F= 19 -20*z -20*w +5*z^2 +14*z*w +5*w^2 -2*z^2*w -2*z*w^2
+z^2*w^2
sage: G= (w*z-1)*F
sage: for f in [F,G]:
....: I= ideal([f] +f.gradient())
....: I= ideal(I.groebner_basis())
....: print I
....: I.vector_space_dimension()
....: I.variety()
....:
Ideal (w - 1, z - 1) of Multivariate Polynomial Ring in w, z over
Rational Field
1
[{z: 1, w: 1}]
Ideal (w^2 - 2*w - 17/5*z^4 + 434/25*z^3 - 817/25*z^2 + 672/25*z -
179/25, w*z - w + 33/28*z^4 - 433/70*z^3 + 869/70*z^2 - 839/70*z +
641/140, z^5 - 27/5*z^4 + 56/5*z^3 - 56/5*z^2 + 27/5*z - 1) of
Multivariate Polynomial Ring in w, z over Rational Field
6
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/arai021/<ipython console> in <module>()
/Applications/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/multi_polynomial_ideal.pyc in variety(self, ring)
1528 P = self.ring()
1529 if ring is not None: P = P.change_ring(ring)
-> 1530 T = self.triangular_decomposition
('singular:triangLfak')
1531
1532 V = []
/Applications/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/multi_polynomial_ideal.pyc in triangular_decomposition
(self, algorithm, singular)
777 Tbar = Ibar.triangL()
778 elif algorithm == "singular:triangLfak":
--> 779 Tbar = Ibar.triangLfak()
780 elif algorithm == "singular:triangM":
781 Tbar = Ibar.triangM()
/Applications/sage/local/lib/python2.5/site-packages/sage/interfaces/
expect.pyc in __call__(self, *args, **kwds)
1248
1249 def __call__(self, *args, **kwds):
-> 1250 return self._obj.parent().function_call(self._name,
[self._obj] + list(args), kwds)
1251
1252 def help(self):
/Applications/sage/local/lib/python2.5/site-packages/sage/interfaces/
expect.pyc in function_call(self, function, args, kwds)
1168
1169 return self.new("%s(%s)"%(function, ",".join([s.name()
for s in args]+
-> 1170 ['%s=%s'%
(key,value.name()) for key, value in kwds.items()])))
1171
1172 def call(self, function_name, *args, **kwds):
/Applications/sage/local/lib/python2.5/site-packages/sage/interfaces/
expect.pyc in new(self, code)
1028
1029 def new(self, code):
-> 1030 return self(code)
1031
1032
###################################################################
/Applications/sage/local/lib/python2.5/site-packages/sage/interfaces/
singular.pyc in __call__(self, x, type)
591 x = str(x)[1:-1]
592
--> 593 return SingularElement(self, type, x, False)
594
595
/Applications/sage/local/lib/python2.5/site-packages/sage/interfaces/
singular.pyc in __init__(self, parent, type, value, is_name)
1007 except (RuntimeError, TypeError,
KeyboardInterrupt), x:
1008 self._session_number = -1
-> 1009 raise TypeError, x
1010 else:
1011 self._name = value
TypeError: Singular error:
? wrong range[2] in ideal/module(1)
? error occurred in triang.lib::Erw_ggt_oT line 509: `parameter
poly f; parameter poly g; parameter int v; parameter ideal T; `
? wrong type declaration. type 'help poly;'
? leaving triang.lib::Erw_ggt_oT
? `f` is undefined
? error occurred in triang.lib::Erw_ggt_oT line 511: ` poly p1 =
f;`
? expected poly-expression. type 'help poly;'
? leaving triang.lib::Erw_ggt_oT
skipping text from `;` error at token `)`
? leaving triang.lib::invertieren_oT
? leaving triang.lib::normieren_oT
? leaving triang.lib::Erw_ggt_oT
? leaving triang.lib::invertieren_oT
? leaving triang.lib::invertieren
? leaving triang.lib::triangLbas
? leaving triang.lib::triangLfak
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