Editing List of undecidable problems (section)

==Problems in analysis==
* For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see [[Richardson's theorem]]);<ref>Keith O. Geddes, Stephen R. Czapor, George Labahn, ''Algorithms for Computer Algebra'', {{isbn|0585332479}}, 2007, p. 81ff</ref> the zeroes of a function; whether the indefinite integral of a function is also in the class.<ref name="stall"/> Of course, some subclasses of these problems are decidable. For example, there is an effective decision procedure for the elementary integration of any function which belongs to a field of transcendental elementary functions, the [[Risch algorithm]].
* "The problem of deciding whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic", a consequence of the [[Matiyasevich's theorem|MRDP theorem]] resolving [[Hilbert's tenth problem]].<ref name="stall">{{cite journal
| last1=Stallworth | first1=Daniel T.
| last2=Roush | first2=Fred W.
| title=An Undecidable Property of Definite Integrals
| journal=[[Proceedings of the American Mathematical Society]]
| volume=125
| issue=7
| date=July 1997
| pages=2147–2148
| doi=10.1090/S0002-9939-97-03822-7 | doi-access=free}}</ref>
* Determining the domain of a solution to an [[ordinary differential equation]] of the form
::<math>\frac{dx}{dt} = p(t, x),~x(t_0)=x_0,</math>
:where ''x'' is a [[vector (mathematics and physics)|vector]] in '''R'''<sup>n</sup>, ''p''(''t'', ''x'') is a vector of [[polynomial]]s in ''t'' and ''x'', and ''(t<sub>0</sub>, x<sub>0</sub>)'' belongs to '''R'''<sup>n+1</sup>.<ref>{{cite journal|last1=Graça|first1=Daniel S.|last2=Buescu|first2=Jorge|last3=Campagnolo|first3=Manuel L.|date=21 March 2008|title=Boundedness of the Domain of Definition is Undecidable for Polynomial ODEs|journal=Electronic Notes in Theoretical Computer Science|volume=202|pages=49–57|doi=10.1016/j.entcs.2008.03.007|doi-access=free|hdl=10400.1/1016|hdl-access=free}}</ref>