AndroidDebugKey Keystore was tampered with, or password was incorrect
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image of polynomial map is not an algebraic set I am doing an exercise about algebraic geometry, where the exercise  tell us to provide example of the image of polynomial map $f:\mathbb{C}^{m}\rightarrow \mathbb{C}^{n}$ that is not an algebraic set. But I am thinking that the image of every polynomial is $\mathbb{C}$ thus every polynomial map is surjective. What have I misunderstand? Let $R=\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1 \rangle}$. Prove that (1) $R$ is an integral domain. (2) Any nonzero prime ideal of $R$ is maximal.  My idea: (1) The first part is easy. Since $x^2-y^2-1\in \mathbb{C}[y][x]$ is Eisenstein with respect to the prime $y+i$, it is irreducible. Hence the ideal generated by it is a prime ideal. (2) I am struggling with this part. I have one approach (not sure if correct). Approach : Let $I=\langle x^2-y^2-1 \rangle$. Then $R=\mathbb{C}[x,y]/I$.  Any ideal of $R$ is of the form $J/I$ where $J\subseteq \mathbb{C}[x,y]$ is an ideal containing $I$. If we can show that any prime ideal $J$ containing $I$ is maximal, then we are done. How to prove this? Is there any other way to prove the second part? Edit: I am trying to avoid Hilbert Nullstellensatz and the notion of dimension of a ring, as these concepts are not there in the syllabus of the exam from which I found this question. Is there a way to monitor an SSD state and predict its failure in case of active read-write usage? As far as I know, the only con against switching to an SSD except its price is the tendency to fail soon (relatively to conventional HDDs) in case used in active read-write operation. Is there an efficient way to predict the failure? What is the closed form of $\int e^{x^2} \, dx$? How can I do a closed form expansion of $\int e^{x^2} \, dx$? Please be specific as to which method I must use. RegEx match open tags except XHTML self-contained tags How can I prove that the set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?  Edit:  This answer came to mind.  Is it correct?  This answer just came to mind.  By contradiction suppose the set is $\{f_n\}_{n \in \mathbb{N}}$.  Define the function $f: \mathbb{N} \to \{0,1\}$ by $f(n) \ne f_n(n)$.  Then $f \notin\{f_n\}_{n \in \mathbb{N}}$. I remember my English teacher saying that there are only two valid ways to make a one-word sentence:   A question:      Why? Where?  A command:     Go! Stop!    Is this correct? Here is a question from my number theory class.  Prove  $$(p-k)!(k-1)!\equiv (-1)^k \text{ mod p} $$ Help please! Getting a System.Type from type's partial name I want to get a System.Type given only the type name in a string.  For instance, if I have an object:  MyClass abc = new MyClass();   I can then say:  System.Type type = abc.GetType();   But what if all I have is:  string className = "MyClass"; I'm hoping someone could check my work. I'm trying to simplify the equation for $x$. $$(\frac{x}{a})^{3.2} + (\frac{y}{b})^{3.2} = 1$$ $$\frac{a}{b} = \frac{174.1}{86}$$ Thus I began by substituting $a$ with: $$a = \frac{174.1}{86}b$$ $$((\frac{86}{174.1})(\frac{x}{b}))^{3.2} + (\frac{y}{b})^{3.2} = 1$$ $$((\frac{86}{174.1})(\frac{x}{b}))^{3.2} = 1 - (\frac{y}{b})^{3.2}$$ $$(\frac{x}{b})^{3.2} = \frac{(1 - (\frac{y}{b})^{3.2})(174.1)^{3.2}}{(86)^{3.2}}$$ $$x^{3.2} = \frac{(1 - (\frac{y}{b})^{3.2})(174.1)^{3.2}(b)^{3.2}}{(86)^{3.2}}$$ $$x^{3.2} = \frac{(1 - (\frac{y}{b})^{3.2})((174.1)(b))^{3.2}}{(86)^{3.2}}$$ $$x^{\frac{16}{5}} = \frac{(1 - (\frac{y}{b})^{3.2})((174.1)(b))^{3.2}}{(86)^{3.2}}$$ $$x = [\frac{(1 - (\frac{y}{b})^{3.2})((174.1)(b))^{3.2}}{(86)^{3.2}}]^{\frac{5}{16}}$$ Is my work correct, or am I completely off the board? We need to prove that $$\dfrac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$$  I have tried and it gets confusing. Why do the Localization of a Ring This question may be a bit vague, but neverthless, i would like to see an answer. Wikipedia tells me that:   In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring.   It is clear that for integral domains, we have the Field of Fractions, and we work on it. It's obvious that a Field has multiplicative inverses. Now if we consider any arbitrary ring $R$, by the definition of localization, it means that we are adding multiplicative inverses to $R$ thereby wanting $R$ to be a division ring or a field. My question, why is it so important to look at this concept of Localization. Or how would the theory look like if we never had the concept of Localization. I've used "//" and "\" to create this "W", and have made them into outlines, as I'm trying to give the different layers a colour, as well as having a white space where the lines touch and I would like to remove the top of the second "\".   I'm struggling with the white space at the moment and now I've added a stroke, the fill has decreased. Is there another way I could do this?   I've also tried to use my pen tool to remove the top of the "\" but when using "Path Finder" I cannot find an option to "Minus Forward". I'm a newbie so any advice would be lovely :) Cannot sort on numeric field with SOQL in Custom Metadata Cannot sort on a soql-request in a custom meta data type. When i perform SELECT .. FROM x__mdt WHERE ... ORDER BY x. Then field x cannot be numeric to get a correct order. Change it to a string-field ordering works ok. Playing with ASC/DESC makes no difference! Possible Duplicate:          If I am using the word model in the context of financial models and the UK, then which of these words should I use? Also, are there any key difference in the meanings of the two? uint color;  bool parsedhex = uint.TryParse(TextBox1.Text, out color);  //where Text is of the form 0xFF0000 if(parsedhex)    //...   doesn't work. What am i doing wrong? When you boot from live CD, or doing the first boot after installing Ubuntu, splash screen looks awesome. But as soon as you enable nvidia-current driver, installed with apt-get, splash screen goes all crazy.  With crazy I mean that resolution is very low, font(I assume) is very weird and it all looks like it's been broken.  This happened with 10.04 and now again with 10.10.  How do I fix splash screen after enabling nvidia drivers? I want to executed command from file (which is script) in current shell in terminal.  Example: I have file ch_dir contains following:  #!/bin/bash cd /usr   Now if I execute file usually as following then it executes commands in different shell:  pandya@pandya-desktop:~$ ./ch_dir pandya@pandya-desktop:~$   Here cd /user is executed in different shell.  But I want to execute in Current shell. How do I do that?  Note: Here cd is only used to explain. Question's aim is to execute any command in current shell Looking for title & author - short story - possibly called "Arms Race" - about rediscovery of manual arithmetic short story - possibly called "Arms Race" - about rediscovery of manual arithmetic.   The hero rediscovers manual calculation - e.g., how to do long division with pencil and paper - in a world where everyone has ben using calculators for aeons. Brought before the president to demonstrate this, the great line in the story is the president, after using his calculator to check the hero's answer, says, "My God -- he's right." A great national project to exploit this advance over the enemy is obviously necessary... In a letter-class document that had no previous errors I am suddenly getting the error message:  "There's no line here to end" \opening{text}   I've used this file many times and today it starts giving this error. How do I troubleshoot this?