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Results tagged with differential-algebra
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user 18060
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algebraic extensions of (differential) function fields
The questions you are asking are actually different. To see this, consider $t=\sqrt{x}$. The derivative of $t$ is obviously $1/(2\sqrt{x})$ and so does not live in $\mathbb C(x)$, but its minimal poly …
- 149k
4
votes
"Canonical" form for gauge equivalence classes of matrices in $\mathfrak{gl}_n(x)$
For your second question, you may want to look at "Jordan decomposition for a class of singular differential operators" by A. H. M. Levelt, https://projecteuclid.org/download/pdf_1/euclid.afm/14858964 …
- 149k
79
votes
Why is differential Galois theory not widely used?
The theory of differential Galois theory is used, but in algebraic, not differential geometry, under the name of D-modules. A D-module is an object that is somewhat more complicated than a representat …
- 149k