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7
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0answers
160 views

Prerequisites for Differential Galois theory

I would like to know the prerequisites for Differential Galois theory. I have taken Rings, Fields, Groups, Galois theory, and Algebraic Geometry + Commutative Algebra. Looking at the wikipedia page, ...
4
votes
0answers
38 views

If $D:A\to A$ is a derivation, what can be said about the range of $D$?

What can be said about the relation between the domain and range of a derivation as a function? If $A$ is the domain, any space of functions, what does $D(A)$ look like, where $D$ is a derivation? ...
3
votes
0answers
22 views

The spectral transfinite open spaces with quintic characteristics of second kind

Context: Beginning with the formal definition of transfinite spaces together with the Picker-Hansel theorem, we obviously get a relation $$ \bigcap\xi_{|\sigma|\mapsto \theta^*} \oplus_\psi ...
1
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0answers
76 views

May the integral $\int\root 3 \of{\cos(x)^2}\,dx$ be expressible by elementary functions?

I would like to decide by methods of differential algebra whether the integral $\int\root 3 \of{\cos(x)^2}\,dx$ might be contrary to the output of CAS Mathematica Online Integrator expressible by ...
1
vote
0answers
71 views

Algebras vs. rings in algebraic differential calculus

Vector fields (and differential operators of higher order) on a real manifold are often defined in terms of $\mathbb{R}$-algebra $C^\infty(M)$. However, it is not clear to me why is the ...
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0answers
13 views

Do these “algebraically well behaved” Function Spaces, exist?

Do there exist any Sets of Functions which are some combination of: Algebraically Closed: In the sense of Algebraic Functions. Differentially Closed: In the sense of Differentially Closed Fields. ...
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0answers
22 views

Existence of Differentially closed Field.

Is there any example of a differentially closed field? And in general is there any existence theorem for diff. closed fields over arbitrary diff. fields?
0
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0answers
37 views

The Risch algorithm

I tried to understand the Risch Algorithm and I was able to follow the cases for exponential and logarithmic extensions. However, I could not understand what problem arises in algebraic extension. I ...
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0answers
47 views

How we transform our differential algebraic equations (DAEs) to ordinary differential equations (ODEs)?

Higher index DAEs are difficult, we need to transform it to ODEs to make it easier to solve. My question is how do we transform DAEs to ODEs? I hope somebody can help me, thanks in advance and have a ...