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20171204 03:08:48 0500  asked a question  How to visualise complex functions on a disk? Let $f$ be a function on the unit disk $\mathbb{D}$. I want to look at the images of $f(\mathbb{D})$? How to do this? How to see the contours of $f(z)$? How to see the argument (if possible)? 
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20161115 02:41:15 0500  asked a question  Trying to find prime factorization of ideals in number fields Let $L=\mathbb{Q}(\sqrt{5}, i)$ and $K=\mathbb{Q}(\sqrt{5})$. Let $O_K$ and $O_L$ be the rings of algebraic integers of $K$ and $L$. It can be checked that $$2O_K=\langle 2, \sqrt{5}+1\rangle^2 $$ I want to find the factorization of the ideal $\langle 2, \sqrt{5}+1\rangle O_L$ in $O_L$ ? The problem I am having is this. I don't know the syntax for the ideal generated by $\langle 2, \sqrt{5}+1\rangle O_L$. What to do ? 
20161107 09:50:42 0500  asked a question  Is there any way to find decomposition group and ramification groups Let $L/K$ be a Galois extension of number fields with Galois group $G$. Let $O_K$ and $O_L$ be the ring of algebraic integers of $K$ and $L$ respectively. Let $P\subseteq O_K$ be a prime. Let $Q\subseteq O_L$ be a prime lying over $P$. The decomposition group is defined as $$D(QP)=\lbrace \sigma\in G\text{ }\text{ }\sigma(Q)=Q\rbrace$$ The $n$th ramification group is defined as $$E_n(QP)=\lbrace \sigma\in G:\sigma(a)\equiv a\text{ mod } Q^{n+1}\text{ for all } a\in O_L\rbrace$$ I want to compute the decomposition group and ramification groups of the cyclotomic field $\mathbb{Q}(\zeta)$ over $\mathbb{Q}$ where $\zeta$ is a root of unity. How to do this ? Any idea ? 
20161031 01:51:08 0500  commented answer  Finding prime factorization of ideals in number rings The discriminant of $K=\mathbb{Q}(\sqrt{2}+i)$ is $256$. As $3\nmid 256$, the ideal $\langle 3\rangle$ should remain inert in $O_K$. So how come it splits in $O_K$ ? 
20161022 02:32:15 0500  commented answer  Finding prime factorization of ideals in number rings What is a ? 
20161021 08:28:30 0500  asked a question  Finding prime factorization of ideals in number rings Let $K$ be a number field and $O_K$ its ring of algebraic integers. Let $p\in\mathbb{Z}$ be a rational prime. I want to find the factorization of the ideal $pO_K$. What is the syntax for this ? For clarity, I request you to demonstrate with an example (say $K=\mathbb{Q}(\sqrt{2}+i)$ and $p=2$ and $p=3$). 
20161020 16:21:28 0500  commented question  irreducibility of a polynomial thanks @slelievre 
20161018 06:21:16 0500  marked best answer  if loop not working I have to use an if loop in my program. I am checking the irreducibility of a collection of polynomials. If f(x) is a reducible polynomial, then I want to find its factor. This is my code But I am getting a syntax error. Can someone help me ? 
20161014 09:08:47 0500  marked best answer  how to find minimal polynomial How to find the minimal polynomial of an element ? Let $\zeta_n$ be a primitive $n$th root of unity. I want to find the minimal polynomial of $\zeta_n$ over $\mathbb{Q}(\zeta_n+\zeta_{n}^{1})$. How do I do that ? 
20161008 14:54:40 0500  asked a question  How to find the discriminant of a number field ? I want to find the discriminant of the number field $\mathbb{Q}(\sqrt2)$ and the field $\mathbb{Q}(\sqrt2,i)$ and $\mathbb{Q}(\sqrt3+i)$ ? How to do this ? 
20161001 11:28:42 0500  asked a question  Listing elements of (Z/nZ)* I want to find all the elements of (Z/nZ)*. Is there a command for that ? For example if the user gives input 8, the the output will be {1,3,5,7}. 
20160923 10:41:06 0500  asked a question  Number of factors of a polynomial Given a polynomial f, the command The polynomial ring is assumed to be 
20160902 12:33:45 0500  asked a question  multivariate polynomial ring over complex numbers I want to factorize bivariate polynomials over C. For single variable case we do this as follow: How to do this for multivariate case ? 
20160902 02:10:29 0500  asked a question  finding the order of a matrix in GL(3,Z) I am working in GL(3,Z). I want to find all the elements with order less than or equal to 6. I have the follwoing questions

20160902 01:57:13 0500  edited question  Checking conjugacy of two matrices
