Let $Y \subset \mathbb{A}^3$ be the set $Y=\{(t,t^2,t^3) \}$.  Show that dim $Y =1$.  To do so, I have to reveal what is the closed set of $Y$.  Please give me a hint.  This differs the , in which the ideal are discussed. However I want to consider the dimension. To do so, I need the sequence of irreducible distinct closed subset $Z_1 \subset Z_2 \subset ...$
The following exercise comes from Fulton's Algebraic Curves:     Let $k$ be an infinite field and $V = \{(t,t^2,t^3) \, ; \, t \in k \} \subset \mathbb{A}^3(k)$. Show that $V$ is algebraic and compute $I(V)$ by giving a finite set of generators.   Now, showing $V$ is algebraic is easy by noting that $V = V(X^2-Y, X^3-Z)$, but I can't find a way to describe $I(V)$ explicitly. Obviously $(X^2-Y)(X^3-Z) \in V$, but how can I find the actual generators of this ideal?
How do I select text nodes with jQuery? I would like to get all descendant text nodes of an element, as a jQuery collection. What is the best way to do that? Bold italic vectors I am trying to display vectors as bold and italic. The command \mathbf sets the letters non-italic. I also googled a bit and stumbled upon \mathbf{\em y} or \mathbfit{y}, which all didn't work.  I hope someone can help me on this. In the Unity3D game engine, a common code sequence for getting remote data is this:  WWW www = new WWW("http://remote.com/data/location/with/texture.png"); yield return www;   What is the underlying mechanism here?  I know we use the yield mechanism in order to allow the next frame to be processed, while the download is being completed. But what is going on under the hood when we do the yield return www ?   What method is being called (if any, on the WWW class)? Is Unity using threads? Is the "upper" Unity layer getting hold of www instance and doing something?  EDIT:   This question is specifically about Unity3D internals. I'm not interested in explanations of how yield statement works in C#. Instead, I'm looking for an inside view of how Unity deals with these constructions, to allow, for example, to WWW to download a piece of data in a distributed manner across several frames. What's /System/Volumes/Data? New mac user here (Linux background). I'm running macOS Catalina (Beta5). I've noticed there are 5 volumes in my main disk container. One is mounted at /, that I understand, it's the system, another is /System/Volumes/Data, which I tough it would be the Linux /home, but it's not, so what it it?  Also what are the other two unmounted volumes? One might be the recovery one, but the other? Thanks! I have purchased a rather large bag of long-grain white rice (25 lbs.) and need to know the best way for storing it long-term. This rice will be used as both a food-storage food source and as my everyday source of rice for cooking, so the storage solution should (hopefully) be resealable, rather than once-it's-open-it's-open. I eat rice maybe three times a month, so it isn't really "everyday" but it will be my go-to when I have it. Can different gauge wiring be used in the same circuit? Sum of digits of repunits is that function must be constant under the following conditions I'm talking about complex function   $f$ is analytic function on a region $D$ that include the point $z=0$. for every $n\in N$ such $\frac{1}{n}$ is in $D$ , the function follows this condition $|f(\frac{1}{n})| \leq \dfrac{1}{2^n}$   is that function must be constant ? Should I round my uncertainty to nearest hundred? I was doing some exercises on error propagation when I came across this problem:  $4\pi^2/(0,034 \pm 0,004 \space s^2/cm)$  I calculated my uncertainty to be $\Delta$ = 136 $cm/s^2$  And so the hole thing gives me: $(1200 \pm 136) \space cm/s^2$.  Now going into my question I rounded $4\pi^2/0,034 = 1161.12993$ to $1200$ which makes sense since my uncertainty is 136 but in the solution to this problem $136$ is rounded to $100$ and that's not making much sense to me.  So should I always round my uncertainty to the nearest hundred (assuming my uncertainty has 3 digits)? Probability Math Question...? Bag A contains 3 white and 2 red balls. Bag B contains 6 white and 3 red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will the be the same color? Express your answer as a common fraction. Where can I find a reference to the format of the comment field (field 5) of the /etc/passwd file? In the /etc/passwd file on my system, the "comment" field, field 5, is inconsistent in its contents.  I thought that I could extract it to get the full name of the user.  fullname=`awk -F: '$1 == name {print $5}' name=$LOGNAME /etc/passwd`   However this returns with $fullname containing a name with 0, 3, or 4 commas following.  Exploring the man page (man 5 passwd) provides no details of this field other than describing it as "user name or comment field."  Perhaps there is additional information that is stored along with the user name? Do you use degrees or radians for trig functions? I was just wondering if you use degrees or radians in trig functions. For example if I have a degree of 0.5 would I do: Sin(0.5) or would I have to convert that to radians?  Or does it not matter either way? A known identity of binomial coefficients is that $$ \sum_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}. $$ Is there a combinatorial proof/explanation of why it holds? Thanks. $6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$ Variable with colon dash ${VAR:-} Link2SD not working completely My Link2SD doesn't seem to be fully working. I noticed this when updating the Facebook application. Google Play prompted me of insufficient storage. I first uninstalled some apps but I got curious so I checked Link2SD's storage info, I got this:   (Click image to enlarge)  As you can see, the internal storage only has mere 70mb left. What's peculiar is, these are the only apps I have NOT linked:   (Click image to enlarge)  I tried moving one linked app (Amazing Alex) to the sd card (normal Android way) and sure enough, the free space on my internal storage got bigger by about an additional 20mb-ish.  Why is this happening? Why isn't Link2SD moving the data to my sdext2? How do I solve it? Dynamic Object Intellisense How to keep font preferences in TexWorks 4 The default font is too small on my screen at the resolution I have it, so I like to reset the font to size 12, but it appears I have to do this everytime I launch the program.  How do I make it remember my preferences? I'm having some trouble understanding cosets.  If I understand it correctly, cosets form a partition. So, if I have $|G:H| = 2$, then $G = H \cup xH$. Right?  In an exercise, I'm asked the following:  "For $G$ group and $H \le G$ such that $|G:H| = 2$, prove that $x^2 \in H$ for any $x \in G$"  If $x \in H$, then $x^2 \in H$ because $H$ is a group. But, if $x \notin H$, then $x \in gH$ for any $g \in G$, right? Then $x^2$ = $(gh)^2$ but I can't see why this is in $H$.  Can you give me some hint? Thanks for stopping by. Reading the target of a .lnk file in Python? I'm trying to read the target file/directory of a shortcut (.lnk) file from Python. Is there a headache-free way to do it? The  is way over my head. I don't mind using Windows-only APIs.  My ultimate goal is to find the "(My) Videos" folder on Windows XP and Vista. On XP, by default, it's at %HOMEPATH%\My Documents\My Videos, and on Vista it's %HOMEPATH%\Videos. However, the user can relocate this folder. In the case, the %HOMEPATH%\Videos folder ceases to exists and is replaced by %HOMEPATH%\Videos.lnk which points to the new "My Videos" folder. And I want its absolute location.