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4
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2answers
129 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 ...
0
votes
0answers
30 views

Requesting programming implementations for $\mathbb{F}_{p^n}$ and $SL_2(\mathbb{F}_{p^n})$.

I would like a programming language capable of doing computations over finite fields and matrix groups over those finites fields. I do not want to have to construct bases and what not on my own. What ...
2
votes
0answers
25 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
votes
1answer
30 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
28 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 ...
1
vote
0answers
36 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 : ...
-1
votes
1answer
53 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 ...
4
votes
0answers
82 views

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

This is more a question about the weird behavior of SAGE: ...
3
votes
2answers
93 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
89 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
votes
0answers
30 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 ...
4
votes
1answer
51 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 ...
1
vote
1answer
31 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. ...
2
votes
1answer
38 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 ...
4
votes
4answers
171 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 ...
0
votes
2answers
31 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 ...
1
vote
1answer
86 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
votes
1answer
100 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: ...
1
vote
1answer
93 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 : ...
2
votes
3answers
76 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
56 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
votes
1answer
98 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
votes
1answer
67 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
votes
1answer
65 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
57 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() ...
0
votes
2answers
44 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: ...
1
vote
1answer
163 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
votes
1answer
78 views

SAGE: Is it possible to extract the irreducible factor of a polynomial for the purpose of constructing a Number Field?

I'm in the middle of making a program that tests a certain fact for many number fields. At this current step I get say a hundred polynomials, which are reducible. I want to factor them (over Q), take ...
2
votes
0answers
96 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
0answers
195 views

SAGE vs. Mathematica for Lie algebras / groups?

What math software is better for working with Lie algebras and Lie groups, SAGE or Mathematica?
2
votes
2answers
151 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: ...
0
votes
1answer
35 views

Multivariate Polynomials Sage

Sorry if I'm in the wrong Stackexchange (but sage is a math program...) I'm computing something on multivariate polynomials: I have a primary variable $x$ and several other variables $a, b, c, ...
1
vote
2answers
79 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 ...
4
votes
1answer
202 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
1
vote
1answer
72 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
181 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
54 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
161 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
42 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 ...
0
votes
1answer
89 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 ...
-1
votes
1answer
289 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 ...
7
votes
0answers
192 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 ...
1
vote
1answer
121 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
1answer
114 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 ...
3
votes
2answers
214 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 ...
0
votes
1answer
326 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: ...
0
votes
1answer
89 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 ...
1
vote
1answer
65 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 ...
10
votes
2answers
377 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 ...
2
votes
1answer
166 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 ...