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1answer
82 views

Defining a function in Sage

How do I define the following function in Sage and compute some values? The function is $$P(n) = \sqrt{\frac{e^{-h}h^n}{n!}},$$ where $h$ is a real variable and $n$ is a nonnegative integer. I want ...
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4answers
875 views

Graphing Compex Functions 3D (x,y,i axes) Instead Of Color-Coded (SAGE).

Following this guide to Sage: and using Sage Online produced the following graphs: Graphing $\frac{1}{1-z}$ that way yeilds: Graphing $\frac{1}{1-z^2}$ that way yields: It would be nice to see ...
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1answer
340 views

verifying differential equation solution with sage

I solved the linear ODE system of equations: \begin{equation} x' = \begin{pmatrix}3&0&4\\0&2&0\\0&0&-3\end{pmatrix}x \end{equation} Skipping the details I got the following ...
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1answer
86 views

Check solutions of vector Differential Equations

I have solved the vector ODE: $x\prime = \begin{pmatrix}1& 1 \\ -1 &1 \end{pmatrix}x$ I found an eigenvalue $\lambda=1+i$ and deduced the corresponding eigenvector: \begin{align} (A-\lambda ...
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1answer
391 views

Programmatically solving a system of nonlinear equations over GF(2)

I have the following relatively large system of nonlinear equations over $GF(2)$: $ 0 = w7x7 + w7x5 + w7x4 + w7x0 + w6x6 + w6x5 + w6x1 + w5x7 + w5x6 + w5x2 + w4x7 + w4x3 + w3x4 + w2x5 + w1x6 + w0x7 ...
3
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2answers
599 views

Why is this curve nonsingular?

Let $C$ be the projective closure of $Z(f) \subset \mathbf{A}^2$ where $f$ is an irreducible polynomial of degree 4 in $x$ and degree 2 in $y$, so $C = Z(f^*) \subset \mathbf{P}^2$ where $f^*$ is the ...
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2answers
320 views

Definition of Modular Forms over finite Fields

I'm still severely lacking in background at the moment, but I'm interested in doing something with congruence properties of modular forms (relations between coefficients of the q-expansions that hold ...
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2answers
343 views

Find the rational points on $1 + 18 x + 81 x^2 + 44 x^3 = y^2$ with Sage

I'm trying to use Sage on-line,but I meet some trouble with the code of it. I want to find the rational points on an ellipse curve,such as $$1 + 18 x + 81 x^2 + 44 x^3 = y^2,\tag1$$ I know that ...
2
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1answer
170 views

Some questions about SAGE

I search a programmable calculator like PARI/GP. In the net, I came across SAGE. I have some questions about the download of SAGE Is it really absolutely free ? Is it faster than PARI/PG ? Has it ...
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1answer
46 views

Convolving two functions doesn't work as expected in sage

I'm trying to convolve two functions as follows: ...
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0answers
45 views

How to append integers in sage

Does anyone know how to append integers using sage or python? Example: v = 11; x = 45; After appending: 1145 Please help
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1answer
45 views

Number of four-term GPs consisting of positive integers under 100: how to write a program

Note: This is a past question from Brilliant.org I was recently thinking about how to write a program which fetches you the number of 4-term geometric progressions consisting of positive integers ...
5
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1answer
207 views

Finding irreducible representations of the following group using GAP

Given the following group of order 24, $$ G = \langle a,b \mid a^2=b^3=(abab^2)^2=1\rangle$$ how can one find (all) the irreducible representations using GAP? Since I have not installed GAP yet, I ...
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0answers
150 views

Necessary and sufficient conditions for Hensel lifting in the multidimensional case

in Multidimensional Hensel lifting, @Hurkyl gave a neat sufficient condition for the existence of $p$-adic liftings in the multidimensional case. I have finally gotten around (but please also see ...
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0answers
106 views

p-adic liftings on SAGE

I asked a question the other day: Multidimensional Hensel lifting which @Hurkyl kindly and very elegantly answered. A follow-on from this is that I have tried to implement exactly the "algorithm" ...
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2answers
71 views

What does the $[(0 : 3 : 1)]$ means in Sage.

I tried to solve the integer points of $y(y+2)=x^3+(x+3)(x+5)$ by using Sage's command E.integral_points(). Its output was $[(0 : 3 : 1)]$. I tried that ...
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0answers
36 views

Running gp in sage how do I access. e.g.. e.j

I am new to sage and I am trying to run the gp interface. In gp I can define an elliptic curve e and then access j by e.j ...
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2answers
388 views

Fitting normal distribution to the data

I have been given a set of data points. How can I find the best fit of the form $$\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-\mu)^2}{\sigma^2}}?$$ Even better if Sage can do it. And how can I approximate ...
5
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1answer
264 views

Create Graph In Sage

I want define new graph in sage. Let $V$ be vector space over finite field $GF(q)$. The graph's vertices are 1-dimensional subspace from $V$ and $n-1$ -dimensional subspace from $V$ and two vertices ...
3
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2answers
329 views

Converting GAP groups into SAGE permutation groups.

I have been working with SAGE online, and have made some programs to test some hypothesis about finite groups. However, the pre-defined "named" groups in SAGE are quite limited (basically, the ...
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1answer
1k views

In Sage, how to extract coefficient of a polynomial in a ring [closed]

For instance, $f=x^2y^2+1$ is an element of $\mathbb{C}[x,y]$, I want to extract the coefficient of $x^2$, which is $y^2$. However "f.coefficient(x,2)" only works for symbolic expressions, are there ...
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1answer
213 views

How to define a polynomial with abstract coefficients in Sage

Let $f=ax^2+b$ be a polynomial in $Q[x]$, how to define $f$ in sage?
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0answers
77 views

Using sage to test for squares in residue fields

Let $K$ be a number field, $x \in \mathcal{O}_K$, and $\mathfrak{p} $ a prime of $K$. I want to find out using sage whether or not the reduction of $x$ modulo $\mathfrak{p}$ is a square in the ...
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1answer
367 views

How to draw a Frenet Trihedron in Sage?

How would I draw this in sage? It's a Frenet Trihedron along a given curve: Tools other then Sage are welcome too. Im just interested in which equations I need to input, besides the curve to ...
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1answer
176 views

How to draw a cone in Sage?

Given a cone with equation z^2 = x^2 + y^2, how would I draw it in Sage? I tried turning it into a function and passing arguments but it didn't work out for me.
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1answer
1k views

Prove that curve lies on a cone?

I have a curve given by this equation: $$c(t) = (t\cos t,t \sin t,t)$$ I need to prove that this curve lies on a cone, and draw that cone and curve in Sage. I've read somewhere that I could prove it ...
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1answer
180 views

Sage returning 0 for curve arc length (integrals)

I'm using Sage to calculate a curve arc length. Basically, the curve is given by this equation: In sage, I'm calculating it's arc length by using this formula: ...
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0answers
94 views

How to calculate $L'(1,\chi)/L(1,\chi)$ in SAGE?

Question as in title, where $L(s,\chi)$ is the Dirichlet $L$-function associated with the nontrivial character modulo $3$. Please provide complete SAGE code. Thank you in advance.
3
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1answer
244 views

A question about modular forms in SAGE

I was trying to solve Exercise 1.4.5 in Alvaro Lozano-Robledo's book Elliptic Curves, Modular Forms and Their L-functions, which is about representations of integers as sums of 6 squares and its ...
3
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1answer
12k views

Is there a symbolic math package for octave?

I am using Octave (3.6) on Ubuntu 10.0.4 LTS. I want to do some research involving symbolic math. I was thinking of downloading sage (I just found about it today) - but thought I'd better ask in here ...
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3answers
729 views

How to load and use a PARI/GP script in Sage notebook?

I don't know whether this is the correct place to ask such a question, but I am dealing with this problem for a couple of days. Take for example the script ...
25
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1answer
10k views

Is Sage on the same level as Mathematica or Matlab for graph theory and graph visualization?

The context: I'm going to start working on a project that involves running predefined algorithms (and defining my own) for very big graphs (thousands of nodes). Visualization would also be welcome if ...
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2answers
211 views

Help need in Mathematica or Sage

I want to find the common positive solutions of two polynomials $f_{a,b}(x,y)$, $g_{a,b}(x,y)$ where $a,b$ runs from 0 to 1 with an interval 0.01. Let $(x_0,y_0)$ be a common positive solution. Then ...