Timeline for Differential ideal membership problem
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| May 20, 2011 at 17:17 | comment | added | Michael Bächtold | @Mark: Ok thanks. Maybe it is obvious but I don't see how this last statement is a consequence of your original answer. I'd be grateful if you could add some remarks. | |
| May 20, 2011 at 16:59 | comment | added | user6976 | @Michael: Yes it is correct. | |
| May 20, 2011 at 16:28 | comment | added | Michael Bächtold | @Mark: I interpret your second to last sentence as saying: given any element $D'\in W_n$ decide if there are $C_i\in W_n$ such that $D'=\sum C_i\circ D_i$ where the $D_i$ are the components of $D$. Is that right? | |
| May 20, 2011 at 14:43 | comment | added | user6976 | @Michael: As I understood it (and it was long ago, so I may have forgotten), you can do the following. Consider the Weyl algebra and its action of the ring of polynomials: $d_x\cdot p=\partial p/\partial_x$, $x\cdot p=xp$. Then a differential equation with polynomial coefficients can have the form $D\cdot \vec u=\vec 0$ with $D$ from $W_n$ (a diff. operator). Of course $\vec u$ is a vector of polynomials. Now with every such equation, you associate a left ideal in $W_n$, and I interpreted the question as the membership in that left ideal. I suspected (still do) that it is not decidable. | |
| May 20, 2011 at 14:23 | comment | added | Michael Bächtold | Dear Mark: sorry if I'm being dense, but could you explain how this is related to the undecidability of the differential ideal membership? How I interpret Ougaos question it ask: given a system of polynomial differential equations, how to decide if another differential equation $F=0$ is a differential consequence of the system. | |
| Nov 30, 2010 at 4:00 | comment | added | Jiang | @Sapir:we work in the ordinary differential ring k{y},so $y$ is the indeterminate,$y_i$ is its i-th derivative. | |
| Nov 29, 2010 at 18:54 | comment | added | user6976 | What is $y$ ($y_i$)? I do not have Ritt's book here, and I do not have time to read it. It would be better if you update your question, making it more concrete. You are not seem to be interested in the general membership problem for differential ideals. | |
| Nov 29, 2010 at 15:49 | comment | added | Jiang | @Sapir: I was motivated by Ritt's one problem.In his classical book on differential algebra(page 177), Ritt asked the following question: For p,i>0,what is the least q such that (y_i)^q mod 0 ([y^p])? | |
| Nov 29, 2010 at 12:03 | history | answered | user6976 | CC BY-SA 2.5 |