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25
votes
1answer
9k 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 ...
9
votes
1answer
293 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
183 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
288 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
763 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
296 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
193 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
83 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 ...
5
votes
1answer
246 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
4answers
132 views

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

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 ...
4
votes
1answer
134 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
4
votes
0answers
74 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
2answers
288 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 ...
3
votes
1answer
228 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
182 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
11k 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
34 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 ...
3
votes
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 ...
3
votes
1answer
342 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
2answers
66 views

Faster Sage Code for Diophantine Equation? [closed]

I'm having trouble with the computation time. Does anyone have any ideas for faster code? ...
3
votes
0answers
26 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 ...
3
votes
1answer
51 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 ...
3
votes
0answers
99 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
3answers
670 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
156 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
71 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 ...
2
votes
1answer
358 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
1answer
60 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: ...
2
votes
2answers
95 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
159 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
525 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
74 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 ...
2
votes
1answer
297 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
29 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 ...
2
votes
1answer
45 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
54 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
86 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
66 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
1answer
848 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
2answers
209 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
46 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 ...
1
vote
1answer
67 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 : ...
1
vote
1answer
104 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
69 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
70 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
96 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
84 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
173 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
21 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. ...
1
vote
1answer
48 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 ...