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25
votes
1answer
8k 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 ...
8
votes
0answers
220 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 ...
7
votes
0answers
173 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 ...
6
votes
2answers
247 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 ...
5
votes
4answers
582 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 ...
5
votes
2answers
237 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 ...
5
votes
1answer
170 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 ...
5
votes
1answer
228 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 ...
4
votes
0answers
73 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 ...
3
votes
1answer
215 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
votes
2answers
158 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 ...
3
votes
1answer
9k 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 ...
3
votes
1answer
854 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 ...
3
votes
1answer
101 views

On Hilbert Class Polynomial

Is there any open source software which computes Hilbert Class polynomial of an imaginary quadratic fields? Thank you in advance
3
votes
1answer
286 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
votes
0answers
88 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" ...
2
votes
1answer
142 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 ...
2
votes
3answers
576 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 ...
2
votes
1answer
248 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 ...
2
votes
1answer
340 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 ...
2
votes
2answers
65 views

Row echelon form of (augmented) matrix. Is there something wrong with Sage's implementation?

I am trying to solve the exercise RREF.C10 from the A first course in Linear Algebra free book. The exercise aims at finding the reduced row echelon form of the following linear system: ...
2
votes
1answer
148 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 ...
2
votes
2answers
442 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 ...
2
votes
1answer
237 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 ...
2
votes
1answer
34 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?
2
votes
0answers
46 views

Finding newforms with Sage

I am new to Sage and modular forms. I have some conceptual questions. When I write sage: S = CuspForms(Gamma0(55),2,prec=14) sage: S.new_subspace().basis() ...
2
votes
0answers
75 views

Modular forms on $\Gamma_0(N)$ with character in Sage

I'm trying to work with modular forms on $\Gamma_0(N)$ with character in Sage. In particular, I've been using the following: ...
1
vote
2answers
64 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 ...
1
vote
2answers
206 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 ...
1
vote
1answer
56 views

Implicit plot3d in Sage Math

I am currently trying out using the math software Sage. I am currently in a Calculus III class at my university so I was hoping to be able to leverage its 3D graphing capabilities. In one particular ...
1
vote
2answers
57 views

Sage usage to calculate a cardinality

I would like to compute the cardinality of an elliptic curve group over the finite field $\mathbb{F}_{991}$. I'm trying to use sage but I still have an error in the syntax (I never used it before and ...
1
vote
1answer
73 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 ...
1
vote
1answer
79 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 ...
1
vote
1answer
146 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: ...
1
vote
1answer
64 views

Why doesn't SAGE understand reduced expressions mod p in a finite field extension?

Suppose I have a finite field $\mathbb{F}_{13}$ and I would like to adjoin an element, $\zeta$, with order $3$, since $\mathbb{F}_{13}$ does not contain one. So consider $\mathbb{F}_{13}(\zeta)$. Then ...
1
vote
1answer
42 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 ...
1
vote
1answer
64 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 ...
1
vote
1answer
63 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 ...
1
vote
1answer
36 views

Convolving two functions doesn't work as expected in sage

I'm trying to convolve two functions as follows: ...
1
vote
2answers
328 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 ...
1
vote
1answer
693 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 ...
1
vote
1answer
78 views

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) ...
1
vote
1answer
113 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 ...
1
vote
0answers
33 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 ...
1
vote
1answer
90 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: ...
1
vote
0answers
38 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
1
vote
0answers
143 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 ...
1
vote
0answers
32 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 ...
1
vote
0answers
89 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.
0
votes
2answers
17 views

Non integral exponent for taylor expansion using sage

This is my function var('h,r') f=r^2*arccos((r-h)/r)-(r-h)*sqrt(2*r*h-h^2) taylor(f,h,0,3) Result: ...