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Apr 8, 2013, 12:53:52 AM4/8/13

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Hi,

This is related to trac ticket http://trac.sagemath.org/sage_trac/ticket/14366 . That ticket is about ideals of number fields, but it made me look into the more general ideal code. I came across this:

sage: R.<x> = PolynomialRing(ZZ)

sage: I = R.ideal(2, x)

sage: 0 in I

NotImplementedError

This is because Ideal_generic's _contains_ is not implemented (understandable). A few thoughts come to mind. First off, is there a reason not to have __contains__ begin by checking if the input is the zero element of the ring (or coerces to such), and if so return True? Secondly, see this:

sage: S.<x,y> = PolynomialRing(ZZ)

sage: J = S.ideal(x,y)

sage: 0 in J

True

sage: M = S.ideal(2,x)

sage: 0 in M

True

This makes me think we should be able to deal with the univariate example above (I know next to nothing about Gröbner bases...).

Best,

Rob

This is related to trac ticket http://trac.sagemath.org/sage_trac/ticket/14366 . That ticket is about ideals of number fields, but it made me look into the more general ideal code. I came across this:

sage: R.<x> = PolynomialRing(ZZ)

sage: I = R.ideal(2, x)

sage: 0 in I

NotImplementedError

This is because Ideal_generic's _contains_ is not implemented (understandable). A few thoughts come to mind. First off, is there a reason not to have __contains__ begin by checking if the input is the zero element of the ring (or coerces to such), and if so return True? Secondly, see this:

sage: S.<x,y> = PolynomialRing(ZZ)

sage: J = S.ideal(x,y)

sage: 0 in J

True

sage: M = S.ideal(2,x)

sage: 0 in M

True

This makes me think we should be able to deal with the univariate example above (I know next to nothing about Gröbner bases...).

Best,

Rob

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