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In SAGE, what function factors a polynomial whose coefficients are parameters?

In SAGE the function "factor" will factorize elementary polynomials with coefficients in $\Bbb Q$. For example: x,y = var('x,y') poly = x^3-y^2*x factor(poly) SAGE: x*(x-y)*(x+y) ...
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1answer
32 views

Checking if a polynomial expression is constant in SAGE

I have a huge fractional-polynomial expression in SAGE that I have good reasons to believe is the constant function. Is there a command in SAGE like "== constant function" that I could use to check ...
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1answer
55 views

Good software package to help Maths learning

I'm a mature student enrolling at a Maths degree course soon at the university. I'd like to be able to use some software package to help me visualize equations, graphs, play around with variables with ...
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0answers
24 views

In Sage, how to look at orbits of conjugation in GL(2,q). Actually, their image in PGL(2,q)?

I have a matrix $A$ in $\text{GL}(2,q)$ or order $m$. The cyclic group of order $m$ acts upon $\text{GL}(2,q)$ by conjugation powers of $A$ (choose a generator of the cyclic group to act by ...
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1answer
36 views

Solving an equation in charcateristic 2 in sage OR finding 3-torsion points of an elliptic curve over field with char 2

Problem: show that an elliptic curve over a field of char 2 has nontrivial 3-torsion points Method: I used SAGE to unwind the duplication formula for an elliptic curve given in short Weierstrass form ...
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45 views

In Sage Math, how do you implement a symbolic product? specifically I want the qPochhammer

Note : on math.stackexchange I searched for the following keyword combinations: sage math prod sage math prod product and found nothing so I think this is a new question. I want to implement a ...
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152 views

Genus of the graph $K_{4,2,2,2}$.

What is the genus of the complete $4-$partite graph $K_{4,2,2,2}$? What i know: Since $K_{4,4,2}$ is a subgraph of $K_{4,2,2,2}$, and genus of $K_{4,4,2}$ is 2, $K_{4,2,2,2}$ has genus greater than ...
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1answer
50 views

How can I increase the resolution of a 3d plot in Sage to see all the details of the noodle? [closed]

I want to plot my noodle with a high resolution to see all the details. How can I achieve this with Sage? Here is my parametric, piecewise function: ...
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1answer
36 views

labels used in SAGE for automorphisms of graphs

When I create a graph in SAGE and then look at its automorphism group, the permutation group obtained acts on points $1,\ldots, n$ (where $n$ is the number of vertices of the graph), but it is not ...
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2answers
99 views

Calling GAP's StructureDescription from SAGE

Given a sage group object $G$, I want to obtain its structure description using GAP, as follows: sage: gap.StructureDescription(G) The command works fine in ...
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1answer
78 views

SageMath: Embed all roots of a polynomial

I have a polynomial, and I would like to make a number field in Sage that would contain all roots of this polynomial. I have tried the following code but it throws an error: ...
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1answer
59 views

Numerical integration problem

How can I solve integral equations of the form $$\int_{-3}^x e^{e^t}dt=3?$$ Is there for example Sage code for that kind of equations? Is there better method that evaluating numerically ...
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1answer
59 views

Common Primes…

In SageMath, the software, I was trying to create a visualization of how common it is for a number to be prime. Can anyone help me with the code? I am a super beginner and lost. I was going to post ...
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141 views

Math-related open source software to contribute to

I'm interested in finding a math-related open source project that I can contribute to. I've studied maths and stats at undergraduate level, but I'm a professional software developer and I'll have some ...
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1answer
113 views

Is there a computer programm or CAS (maybe GAP?) that can calculate with projective (indecomposable) A-modules (A is a finite dimensional k-algebra)?

I have the following question(s): I have an "Algebra-With-One" $R$ as a subalgebra of a full matrix algebra in GAP. Furthermore, I have 5 primitive orthogonal idempotents $e_1,...,e_5$, which sum up ...
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1answer
44 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
278 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
167 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
64 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
159 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 ...
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2answers
263 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
178 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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40 views

Reducing a System of Polynomial Equations to a Minimal Number of Variables and Equations

If I have a set of polynomial equations $\{f_{1} =0 ,\ldots,f_{k} =0\}$ each of which are a function of $n^2$ variables, that is, $f_{i}(x_{11},x_{12},\ldots,x_{1n},x_{21},\ldots,x_{nn})$, what is an ...
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189 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 ...
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1answer
123 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
22 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
30 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
42 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 ...
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1answer
143 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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130 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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79 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
56 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
30 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
247 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 ...
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1answer
195 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 ...
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1answer
198 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
419 views

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

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
116 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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72 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
294 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
127 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
410 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
106 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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80 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.
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1answer
166 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 ...
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1answer
6k 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
384 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 ...
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1answer
6k 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
195 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 ...