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broken link fixed, cf. https://math.meta.stackexchange.com/a/34713/228959
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Glorfindel
Glorfindel
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In "Some constructions in rings of differential polynomials" Gallo and Mishra show that for certain infinitely generated differential ideals the membership problem is undecidable.

Which does not exclude that membership is decidable for finitely generated ideals (the case mainly encountered in real life). According to thisthis article from 2006 that problem is still open.

But maybe this is useful: in 2009 Gao, Van der Hoeven, Yuan and Zhang showed that perfect ideal membership is decidable. (I think "perfect" means "radical" in differential algebra terminology)

In "Some constructions in rings of differential polynomials" Gallo and Mishra show that for certain infinitely generated differential ideals the membership problem is undecidable.

Which does not exclude that membership is decidable for finitely generated ideals (the case mainly encountered in real life). According to this article from 2006 that problem is still open.

But maybe this is useful: in 2009 Gao, Van der Hoeven, Yuan and Zhang showed that perfect ideal membership is decidable. (I think "perfect" means "radical" in differential algebra terminology)

In "Some constructions in rings of differential polynomials" Gallo and Mishra show that for certain infinitely generated differential ideals the membership problem is undecidable.

Which does not exclude that membership is decidable for finitely generated ideals (the case mainly encountered in real life). According to this article from 2006 that problem is still open.

But maybe this is useful: in 2009 Gao, Van der Hoeven, Yuan and Zhang showed that perfect ideal membership is decidable. (I think "perfect" means "radical" in differential algebra terminology)

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Michael Bächtold
Michael Bächtold
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In "Some constructions in rings of differential polynomials" Gallo and Mishra show that for certain infinitely generated differential ideals the membership problem is undecidable.

Which does not exclude that membership is decidable for finitely generated ideals (the case mainly encountered in real life). According to this article from 2006 that problem is still open.

But maybe this is useful: in 2009 Gao, Van der Hoeven, Yuan and Zhang showed that perfect ideal membership is decidable. (I think "perfect" means "radical" in differential algebra terminology)