Timeline for Randomly fixing elements and transcendence degree
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| S Aug 31 at 19:06 | history | bounty ended | CommunityBot | ||
| S Aug 31 at 19:06 | history | notice removed | CommunityBot | ||
| S Aug 23 at 17:49 | history | bounty started | Rishabh Kothary | ||
| S Aug 23 at 17:49 | history | notice added | Rishabh Kothary | Draw attention | |
| Aug 23 at 17:48 | history | edited | Rishabh Kothary | CC BY-SA 4.0 |
Mentioned the progress and added the case I am interested in.
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| Aug 20 at 11:14 | answer | added | Will Sawin | timeline score: 4 | |
| Aug 20 at 6:29 | history | edited | Rishabh Kothary | CC BY-SA 4.0 |
Added context
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| Aug 20 at 1:40 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 80 characters in body
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| Aug 19 at 20:23 | comment | added | Rishabh Kothary | @AlexeiEntin that is a good example. I am interested in the case where the field extension is much larger than degree such that Schwartz-Zippel Lemma plays a role. I have added the condition that $deg(f_i) \leq d< q$ | |
| Aug 19 at 20:21 | history | edited | Rishabh Kothary | CC BY-SA 4.0 |
Added a crucial condition
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| Aug 19 at 17:13 | comment | added | Alexei Entin | You need at least some conditions on $f_1,\ldots,f_n$ to not get probability 0. E.g. consider $f_i=(x_1^q-x_1)x_i$. | |
| Aug 19 at 17:00 | comment | added | Rishabh Kothary | @AlexeiEntin Yes transcendence degree is the maximal number of algebraically independent polynomials from the given set. I am interested in both regimes | |
| Aug 19 at 15:17 | comment | added | Alexei Entin | By the transcendence degree do you mean the maximal number of algebraically independent polynomials from the given set? Also, are you interested in a fixed $q$ regime, or is the case of large $q$ (compared to $n.m$) also interesting? | |
| Aug 19 at 12:45 | history | edited | Rishabh Kothary | CC BY-SA 4.0 |
Corrected the problem
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| Aug 19 at 12:39 | history | asked | Rishabh Kothary | CC BY-SA 4.0 |