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Results tagged with differential-algebra
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user 25510
1
vote
Is there a bound on the number of connected components of a zero set of an integrable function?
In your example, you can eliminate $\alpha$ by one more differentiation, and obtain that $f=\cos\alpha x$ satisfies
$$f'''f-f''f'=0,$$
so the number of components of the zero set cannot be estimated i …
- 91.8k
1
vote
Books/Lecture notes which contrast Risch algorithm with basic standard procedure of finding ...
J. H. Davenport, On the integration of algebraic functions. Lecture Notes in Computer Science, 102. Springer-Verlag, Berlin-New York, 1981.
J. H. Davenport, Integration in closed form. Computers in ma …
- 91.8k
33
votes
Is it always possible to calculate the limit of an elementary function?
EDITED. I use the definition of "elementary function" of Liouville and Ritt (also repeated in Wikipedia). See Ritt's papers in TAMS 25 (1923) 211-222, and
TAMS 27 (1925) 68-90. This definition include …
- 91.8k
30
votes
When can an invertible function be inverted in closed form?
I recommend the following paper:
MR1501299
Ritt, J. F.
Elementary functions and their inverses.
Trans. Amer. Math. Soc. 27 (1925), no. 1, 68–90.
(freely available on the web). It indeed gives a short …
- 91.8k
6
votes
Decidability of differential equations
If $f$ is a polynomial, then $C^1$ solution is the same as analytic solution.
For analytic solutions, very similar questions are considered in the paper
MR1011182
Denef, J., Lipshitz, L.
Decision pro …
- 91.8k