I thought the below 2 versions would be the same but version 2 using
PolynomialRing(QQ,vars) seems to have problem as listed below. Am I missing
something ?
Version 1:
----------------------------------------------------------------------
| Sage Version 4.6.1, Release Date: 2011-01-11 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: R.<x,y,z,A,B,k,i,j,m>=QQ[]
sage: R
Multivariate Polynomial Ring in x, y, z, A, B, k, i, j, m over Rational
Field
sage: invs = [i*A+j*B-x,k*A+m*B-y,(i-k)*A+(j-m)*B-z]
sage: I = R*invs
sage: I
Ideal (A*i + B*j - x, A*k + B*m - y, -A*k + A*i + B*j - B*m - z) of
Multivariate Polynomial Ring in x, y, z, A, B, k, i, j, m over Rational
Field
sage: J=I.elimination_ideal([k,i,j,m,A,B])
sage:
Version 2:
$ sage
----------------------------------------------------------------------
| Sage Version 4.6.1, Release Date: 2011-01-11 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: vs = var('x,y,z,A,B,k,i,j,m')
sage: R = PolynomialRing(QQ,vs)
sage: R
Multivariate Polynomial Ring in x, y, z, A, B, k, i, j, m over Rational
Field
sage: invs = [i*A+j*B-x,k*A+m*B-y,(i-k)*A+(j-m)*B-z]
sage: I = R*invs
sage: I
Ideal (A*i + B*j - x, A*k + B*m - y, -A*k + A*i + B*j - B*m - z) of
Multivariate Polynomial Ring in x, y, z, A, B, k, i, j, m over Rational
Field
sage: J=I.elimination_ideal([k,i,j,m,A,B])
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/tnguyen/USB/SVN/DCBA/code/<ipython console> in <module>()
/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 elimination_ideal(self, variables)
1822 R = self.ring()
1823 Is = MPolynomialIdeal(R,self.groebner_basis())
-> 1824 return MPolynomialIdeal(R, eliminate(Is, prod(variables)) )
1825
1826 @redSB
/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)()
/home/tnguyen/Src/Devel/sage/local/lib/python2.6/site-packages/sage/libs/singular/function.so
in sage.libs.singular.function.call_function
(sage/libs/singular/function.cpp:10594)()
/home/tnguyen/Src/Devel/sage/local/lib/python2.6/site-packages/sage/libs/singular/function.so
in sage.libs.singular.function.Converter.__init__
(sage/libs/singular/function.cpp:5060)()
TypeError: unknown argument type '<type
'sage.symbolic.expression.Expression'>'
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