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1answer
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kummer extension on SAGE

I want to calculate the relative discriminant of field extensions of this kind: $$\mathbb{Q}(\zeta_5)(\sqrt[5]{a})$$ Where $a \in \mathbb{Q}(\zeta_5)$. So I use SAGE and make this calculations: ...
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1answer
57 views

Questions that SAGE, MAGMA can answer?

I practice theoretical mathematics and I know (almost) nothing about SAGE, MAGMA. I would like to know (in general) what type of questions can I ask SAGE to do? For example, I know that given an ...
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2answers
156 views

Integer Partition Refinement in Sage

A partition of an integer $n$ is a non-decreasing list of positive integers summing to $n$. For example, $3$ can be partitioned as $1 + 1 + 1$, $1 + 2$ or just $3$, but $2 + 1$ is indistinct from $1 + ...
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0answers
11 views

Using Sage to calculate the size of fibers of a map between curves.

Is it possible to use Sage to calculate the size of the fibers of a map between curves (over a finite field)? I would be happy with the more simple example of finding the size of the fibers when ...
2
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1answer
46 views

Plot Cayley graphs for generic element groups

I'm a beginner in Abstract Algebra, currently trying to solve all exercises in "A Book of Abstract Algebra" by Pinter. I was wondering if there is a way to draw Cayley graphs for generic element ...
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0answers
28 views

Computing Galois groups of function fields in sage

I found documentation on how to compute galois groups for number fields in sage. Is it possible to do the same for function field extensions? I only need it in the simple case of $t - f(x)$ over $k(t)$...
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0answers
51 views

Software for computing generators of the invariant rings of the symmetric groups

(Please skip to the last paragraph if you are interested in just the question) I wish to compute the generators of the ring of invariants for a symmetric group acting on a polynomial ring using a ...
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0answers
15 views

How to change position of the axes values of a Sage plot.

I am plotting 2D functions on Sage, and I would like to move the values displayed along the $y$ axis (the ticks) from the left of the axis to the rigth, because they bother me there. I had a look and ...
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2answers
32 views

Set density of random matrix in Sage

I'm using Sage to calculate a bunch of matrix operations over GF(2), using the code below to randomly generate an invertible matrix: ...
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0answers
40 views

How to use CVXOPT to solve an semidefinite programming problem

I'm using Sage to solve a problem and would like to use cvxopt to solve a sdp problem. Specifically, I have a list of expressions of the form $$c + \sum_{i,j} a_{i,j} q_{i,j}$$ where each $c$ and all ...
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0answers
54 views

Finite field and its element with symbols [Sage / Python / …]

I have a finite field $T=GF(2^3)$, normal basis $(a, a^2, a^4)$ and polynomial $f$ from field $T$, which contains unknown variables / symbols. Is it possible to get vector with coordinates of f in ...
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0answers
54 views

Computing center of an algebra

Let us define an associative algebra over $\mathbb{C}$ with generators $x, y, z$ and the following relations: $x^2=x, y^2=y, z^2=z, 2yxy=y, 3zyz=z, xz=zx$. I am interested in finding center of this ...
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0answers
20 views

Computationally check for roots/positiveness of a big polynomial in a given interval

For a proof, I need to check that given a little interval $(0, 0.28)$ some concrete polynomials $\in \mathbb{Q}[w]$ (polynomials in one variable ranging over the real numbers, with degrees around 50) ...
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0answers
24 views

Finding equilibrium points of a system of nonlinear differential equations

I am currently working on a spatially explicit ODE model with dispersion to study the population dynamics of mosquitoes. I wish to compute the equilibrium values of the populations as functions of the ...
2
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1answer
88 views

Different number field discriminants in Sage and Magma

I have been working with towers of number fields. My problem is that when computing the absolute discriminant of such number fields, Sage and Magma give different values. You can see this by doing in ...
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0answers
31 views

Evaluating a sum on binomial coefficients

I'm reading Casella's and Berger's Statistical Inference. On page 239 they gives a claim that $$\sum_{x=0}^{330}\binom{300+x-1}x\left(\frac{1}{2}\right )^{300}\left (\frac{1}{2}\right )^x\approx 0....
2
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1answer
49 views

Books with SAGE portions

I recently finished working through Adventures in Group Theory and really appreciated the use of SageMath it employs. I considered myself moderately proficient with Sage, but I found working through ...
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1answer
33 views

Plotting piecewise constant function in Sage gives “no way to make fast_float from None” error

I need to plot following piecewise constant function is Sage: ...
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2answers
75 views

“unable to simplify to float approximation” error in Sage on calling a function

I have following python code in Sage: ...
2
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1answer
64 views

Looking Portable Mathematical Notation(s) [LaTeX, Mathematica, Maple, Macsyma] that are open

I'm looking for a portable Mathematical notation. What I mean by that is: I want to create a collection of (open-source) math problems that can be: Rendered for the Web or say in ePS format for ...
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2answers
88 views

(Soft Question) Is it bad to use Sage built in functions instead of creating my own?

I've been doing Project-Euler just as a way to increase my competency in computer science. I'm currently a Pure and Applied Math major who recently adopted computer science as a minor in order to ...
0
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1answer
65 views

SageMath non-GUI mode

I'm not sure where to post this, but is it possible to run Sage without a GUI/notebook interface? The idea is to be able to run Sage solely in the terminal so that I can detach from the Tmux session ...
2
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2answers
133 views

Solve multivariate equations in MATLAB/MAGMA/GP-PARI/SAGE

I want to solve equations of the form $$a_1 x_1 + a_2 x_2 + a_3 x_3 + \dots + a_n x_n + b_1 x_1 x_2 + b_2 x_1 x_3 + \dots + b_n x_{n-1} x_n$$ where all the coefficients are in $GF(p)$ and variables ...
0
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1answer
36 views

How do I force Sage to order my expressions a particular way, in LaTeX code? [closed]

I started learning Sage a couple of weeks ago and I'm working on getting output which I can copy/paste into LaTeX. I've got the general idea but I have to tweek things to get it how I really want it, ...
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1answer
36 views

hasse diagram of a subset of a poset in sage

E = {1,2,3} P = SetPartitions(E) This gives the set of all partitions of E,. I have a subset Q of P and I want to construct the directed graph whose vertex set is this set Q and we draw an arrow ...
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2answers
139 views

Compute Automorphism Group using Computer Software

Is there a computer software that can compute Automorphism Groups. For instance $Aut(\mathbb{Z}_4\times\mathbb{Z}_2)$. I tried Sage, but could not get it to work. Output: ...
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1answer
27 views

putting a sage program inside a loop with out modifying the indentation

I have written a simple program on sage, in which I will define a graph G at the beginning , and the program will return a matrix. now I want the program to return all such matrices corresponds to all ...
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2answers
326 views

Advantages to learning Sage?

I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search ...
2
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0answers
34 views

Can SAGE or othe software compute or guess growth rates of infinite discrete groups?

I am interested in the growth rate of some finitely generated (infinite, non-abelian) discrete groups. Knowing very little about geometric group theory, I am wondering if I can plug them into sage and ...
3
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1answer
65 views

Mapping boundaries in SAGE

I'm trying to find the fundamental domain of congruence subgroups in SAGE by mapping the boundaries of the fundamental domain of $\mathrm{SL}_2(\mathbb{Z})$ by certain matrices. How can I transform ...
1
vote
1answer
42 views

Reverse engineering a differential equation from singular points

I've been struggling to find a way to reverse engineer a differential equation based on knowing it's singular points. In this case, I'd like to create a flow on $[-1,1] \times [-1,1]$, which has ...
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0answers
83 views

Bezout Coefficient for polynomials in sage?

I want to find the bezout coefficient for those 2 polynomials : $f = 1+x-x^2-x^4+x^5$ and $g = -1+x^2+x^3-x^6$ when I use the gcd function in sage the output is : ...
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1answer
87 views

Fraction modulo integer in sage [closed]

I'm working on a sage script right now, I have some polynomials coefficients that are rational, and I want to apply a congruence on these coefficientss, for example: $p = 1 + (7/2)x$ the function ...
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0answers
92 views

$\mathbb{Q}$ isn't a number field for SAGE

This is more a question about the weird behavior of SAGE: ...
3
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2answers
179 views

Faster Sage Code for Diophantine Equation? [closed]

I'm having trouble with the computation time. Does anyone have any ideas for faster code? ...
2
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1answer
178 views

How to compute the pointwise stabilizer subgroup of a fixed-point subspace?

Definitions: Let $W$ be a representation of a group $G$, $K$ a subgroup of $G$, and $X$ a subspace of $W$. Let the fixed-point subspace $W^{K}:=\{w \in W \ \vert \ kw=w \ , \forall k \in K \}$. Let ...
3
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0answers
45 views

Squares of finite fields (mod p*q)

Lets say we have $\mathbb{Z}_p$, where p is prime. For each element(x) we have two squares(y) so that $y^2=x$ ie if $p=7$ for $x=4$ we have $y_1=2,y_2=7-2=5,y=\pm2 $ ok, lets have $\mathbb{Z}_{3*5},...
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1answer
61 views

Question about direuler command in Pari/GP

From the Pari/GP users guide: 3.4.16 direuler(p=a,b,expr,{c}). Computes the Dirichlet series associated to the Eulerproduct of expression expr as p ranges through the primes from a to b. expr must ...
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1answer
69 views

How to truncate decimal points especially .000000… on floats in an expression in Sage?

I have typed out the following block of code in LaTex/SageTex. ...
3
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1answer
109 views

$p$-adic numbers in SAGE

The standard output in SAGE for $p$-adic numbers is in the series representation: sage: x = Zp(7)(12495) sage: x 3*7^2 + 7^3 + 5*7^4 + O(7^22) Is there a way to ...
5
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4answers
316 views

Why can you not omit the '*' sign for multiplication in Sage, Matlab, and other mathematical software? [closed]

Question I have some experience with Sage and Matlab. Both mathematical software packages require you to have the '*' sign when multiplying symbolic variables with integers. For example, in Matlab ...
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2answers
33 views

Solutions to $1 - \frac{r'^2}{2c^2} + \frac{r r''}{c^2}=0$?

Sage says that$$\sqrt{2 \, c^{2} - e^{K_{1}} r\left(t\right)} e^{\left(-K_{1}\right)} = K_{2} + t$$$$-2\sqrt{2 \, c^{2} - e^{K_{1}} r\left(t\right)} e^{\left(-K_{1}\right)} = K_{2} + t$$are solutions ...
2
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1answer
544 views

Simplify-function of SAGE?

Entering simplify(x/(x^2 + x)) SAGE gives me x/(x^2 + x). What do I have to do to get ...
3
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1answer
182 views

How to implement a group action in Sage ( for educational purposes )?

Let S= {"A","B","C","D"} and S4= SymmetricGroup(4). I want to create a table of the action S4 x S -> S which standardly permutes the letters in the set. The table should look like: ...
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1answer
159 views

How to list all subgroup info of a (n abelian) group with Sage?

Using the Magma calculator at http://magma.maths.usyd.edu.au/calc/ I listed all subgroups of C3XC3 : ...
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3answers
85 views

How to do a group StructureDescription in Sage?

In Sage I executed the following commands: F.<x, y> = FreeGroup() G=F / [x^2*y^-1, x^3*y^2, x*y*x^-1*y^-1] Now G is isomorphic to C7. In GAP I could ...
3
votes
1answer
62 views

Computer program for factorization into irreducible polynomials over $\mathbb{Z}_{p^k}$

Hensel's Lemma allows us to factor a polynomial uniquely into basic irreducible factors over $\mathbb{Z}_{p^k}$. Is there a SAGE or Magma command that gives this factorization? Or can anyone help in ...
5
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2answers
137 views

Maps of primitive vectors and Conway's river, has anyone built this in SAGE?

I am attempting to teach number theory from John Stillwell's Elements of Number Theory in the upcoming semester. There are two sections (5.7 and 5.8) which describe the diagrammatic method for the ...
0
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1answer
76 views

How to solve $(t +1) ^2=5$ in Sage?

I want to execute solve($(t+1)^2==5, t$) in Sage and using the Ring $\mathbb {Z}[X]/(x^2-2)$ so that $(t+1)^2$ evaluates to $2t+3$ and the solution of the solve is [t == 1]. My question is how to ...
2
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1answer
148 views

Sage problem - numeric solving trigonometric equation

I am relatively new to Sage. Can someone please help me how to solve: $$ \tan (x) - x/10 = 0$$ numerically?