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Convert from algebra of differential forms

asked 2018-02-28 23:14:15 +0200

victoriamiran gravatar image

I have differential forms of that look like x^2*y or y^3, so, just 0 forms. The parent ring is the algebra of differential forms in the variables x,y, but I was wondering if there was a way to convert the forms to live in a polynomial ring instead. Thanks.

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answered 2018-03-01 12:40:15 +0200

tmonteil gravatar image

updated 2018-03-01 23:31:30 +0200

Let me first try to reproduce your situation (you should provide some code so that we do not have to guess):

sage: x, y = var('x, y')
sage: U = CoordinatePatch((x, y))
sage: F = DifferentialForms(U)
sage: form1 = DifferentialForm(F, 0, x^2*y); form1
sage: form1.parent()
Algebra of differential forms in the variables x, y

If you want to turn this form into a polynomial over the rationals (say), you can do the following convertion:

sage: R.<x,y> = PolynomialRing(QQ)
sage: R(form1)
sage: R(form1).parent()
Multivariate Polynomial Ring in x, y over Rational Field
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Asked: 2018-02-28 23:14:15 +0200

Seen: 203 times

Last updated: Mar 01 '18