HI Jason, I tried what you posted and get some errors , I am using
the latest Sage version 4.5.2
----------------------------------------------------------------------
| Sage Version 4.5.2, Release Date: 2010-08-05 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: R.<x,y>=CC['x','y']
sage: f = x-y
sage: g = x^2 -y^2
sage: I = R.ide
R.ideal R.ideal_monoid
sage: I = R.ideal([f]).radical()
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/tnguyen/Desktop/DK/<ipython console> in <module>()
/home/tnguyen/Src/Devel/sage/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.pyc in __call__(self, *args,
**kwds)
405 if not R.base_ring().is_field():
406 raise ValueError("Coefficient ring must be a field
for function '%s'."%(self.f.__name__))
--> 407 return self.f(self._instance, *args, **kwds)
408
409 require_field = RequireField
/home/tnguyen/Src/Devel/sage/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.pyc in wrapper(*args, **kwds)
367 """
368 with RedSBContext():
--> 369 return func(*args, **kwds)
370
371 from sage.misc.sageinspect import sage_getsource
/home/tnguyen/Src/Devel/sage/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.pyc in radical(self)
1404 import sage.libs.singular
1405 radical = sage.libs.singular.ff.primdec__lib.radical
-> 1406 r = radical(self)
1407
1408 S = self.ring()
/home/tnguyen/Src/Devel/sage/local/lib/python2.6/site-packages/sage/
libs/singular/function.so in
sage.libs.singular.function.SingularFunction.__call__ (sage/libs/
singular/function.cpp:9634)()
TypeError: Cannot call Singular function 'radical' with ring parameter
of type '<class
'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain'>'
On Sep 3, 11:56 am, Jason Bandlow <jband...@gmail.com> wrote:
> Hello,
>
> For polynomial equations, the following should work in general.
>
> sage: R.<x,y> = CC['x','y']
> sage: f = x-y
> sage: g = x^2 - y^2
> sage: I = R.ideal([f]).radical()
> sage: g in I
> True
>
> In general, to see if the equation g == 0 is implied by the equations
> f1==0, f2==0, ..., fn==0 you can do
>
> I = R.ideal([f1, f2, ..., fn]).radical()
> g in I
>
> and sage should appropriately return True or False. I should mention
> that I don't actually use this very much, so there may be some caveats
> that I'm not aware of.
>
> -Jason
>
> On 09/03/2010 12:30 PM, tvn wrote:
>
>
>
> > Hi, I wonder if there's any 'imply' kind of function in Sage ? For
> > example
>
> > eq1 = x -y == 0
> > eq2 = x^2 - y^2 == 0
>
> > eq1 implies eq2 (but not the other way around).
>
> > If no then is there any efficient way to do it ? one way I can
> > think of (that might not work) is get the factor_list of eq1 and
> > eq2 , if eq2 has a factor that is the same as eq1 then eq1 implies
> > eq2 -- something like that.
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