exercise in commutative algebra
Comaximal ideals in a commutative ring
Accessing a property of derived class from the base class in C# In C#, what is the best way to access a property of the derived class when the generic list contains just the base class.  public class ClassA : BaseClass {    public object PropertyA { get; set; } }  public class ClassB: BaseClass {     public object PropertyB { get; set; } }  public class BaseClass { }  public void Main {     List&lt;BaseClass&gt; MyList = new List&lt;BaseClass&gt;();     ClassA a = new ClassA();     ClassB b = new ClassB();      MyList.Add(a);     MyList.Add(b);      for(int i = 0; i &lt; MyList.Count; i++)     {         //I would like to access PropertyA abd PropertyB from the derived classes             } } Macroscopic quantum phenomena and tunneling About integer factorization How do I save terminal output to a file? How do I save the output of a command to a file?  Is there a way without using any software? I would like to know how. I have a loop going, but there is the possibility for exceptions to be raised inside the loop. This of course would stop my program all together. To prevent that I catch the exceptions and handle them. But then the rest of the iteration runs even though an exception occurred. Is there a keyword to use in my except: clause to just skip the rest of the current iteration? What, exactly, is transferred along supply lines? sliding a tangent line along a curve I am relatively new to game development, and am working on a simple 2D platformer. I have created a tilemap and painted some tiles for the character to walk on.. but he is getting stuck. Yes, I know this is a common question and I did find some answers (including this one: ), but none seem relevant for me. The thing is my tiles are not flat.. they have pointy edges due to grass.. see the image below:  As you can see, the edge is not flat. I have overcome the problem of getting stuck by changing the &quot;Edge Radius&quot; to what you see in the above screenshot and that works, but the character now looks like he is floating slightly above the ground. Is there any way I can just tell Unity to ignore the jagged grass and make the collider flat and move the edge of it down a bit? That way it would fix the issue and also have the added bonus of looking like some of the grass is behind him and some in front.. help me to find a volume of the ring shaped solid A cylindrical drill with radius 5 is used to bore a hole through the center of a sphere of radius 8. Find the volume of the ring shaped solid that remains.  Alright, my thing is that i did not understand how to set the integral How long can cooked food be safely stored at room/warm temperature? When do "well" and "good" mean the same? How can I fix "unbalanced brackets" in my data tag? Often, when making a command block contraption, you need to set an entity's data tag. These tags can sometimes be very long, with many layers of nested curly and square brackets. For example, this is the command to summon a villager with a single custom trade:  /summon Villager ~ ~ ~ {Profession:3,Career:2,Offers:{Recipes:[{buy:{id:minecraft:diamond,Count:6b}},sell:{id:minecraft:diamond_hoe,tag:{ench:[{id:16s,lvl:10s}]}]}}   The single-line command block interface of Minecraft makes it incredibly difficult to find and fix errors, especially when it comes to mismatched brackets. In fact, for illustration purposes, I put an error in the above command.  What techniques can I use to find and fix unbalanced square or curly brackets when writing long and complicated data tags? Possible Duplicate:          Sounds like a silly question, but bear with me..  If you go into Peet's Coffee and access the wifi, you're taken to a web page that requires a 4-digit code you get with a purchase.   If you do the same at Starbucks you're taken to a page and asked to OK the terms of service.   I want to build something similar for a local independent coffee shop, something that requires the user to write a little about themselves before they can access the Internet.  I'm not sure which way to go -- looking for wifi routers that run an internal web server, or finding one that lets you direct users to an external website for authentication, somehow redirecting back to the access point once successful.   Has anyone done anything like this and can share their experience? Support showing image in original size in overlay about Linux's zip utility says this about the -u flag:     Replace (update) an existing entry in the zip archive only if it has been modified more recently than the version already in the zip archive. For example:          zip -u stuff *   will add any new files in the current directory, and update any files which        have been modified since the zip archive stuff.zip was last created/modified.   My question is, if a particular file has been removed since the last time it was zipped, whether -u will recognize that the file has been removed and thus remove it from the *.zip file?  Or, lacking timestamp information (since the file is now removed), it will leave the backed up file in *.zip, since there is no "newer" file? This question came up after reading , in which it is re-iterated (as it has been many times on this site), that investing in the stock market, especially an index fund that tracks the top 100 / 500 companies in a country, basically always has great returns in the long run.  So my question is: Why isn't everybody rich?  If it is so easy (basically invest as heavily as you can in your youth to be rich into middle age and older), why doesn't everyone do this? There would be no need for pensions or any other savings or financial security that way, why even bother investing in assets like property that you have to manage when you can just have an index fund work for you?  I'm guessing that something is being missed here. Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups In Microsoft Word, the following sentence is flagged.  It tells me to use "was" instead of "were"     There were half a dozen books strewn about the floor.   I would think that you would use "were" since it's a quantity more than one.  You wouldn't say, "There was twelve books strewn about the floor."  Does the use of the "half" modify it somehow? Splitting of primes in the compositum of fields If $L_i/K$ are Galois extensions of number fields, $i=1,\ldots,n$, and $L=L_1\cdots L_n$ is the compositum. Then it's true that a prime $\mathfrak{p}$ of $K$ splits in $L$ if and only if it splits in all of $L_i$. Does this also hold if the $L_i$ are not Galois extensions of $K$?  The proof that I know regarding the compositum uses the fact that the $L_i/K$ are Galois, so is this true in the more general setting and how would one prove it? Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$, but $\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}$ is not a compact set.   (Can we use definition of compact set for this problem? )