MLainz's profile - activity

I am trying to compute the rational parametrization of a plane curve. According to sage is irreducible and has genus 0, hence it should be possible.

B.<u,v> = AffineSpace(QQ,2)
p=Curve([2*u^2 + 2*u*v + 2*v^2 - 1],B)
p.rational_parameterization()

However, i get the following error

Singular crashed -- automatically restarting.

---------------------------------------------------------------------------
SingularError                             Traceback (most recent call last)
<ipython-input-10-db30bbca0c11> in <module>()
      1 B = AffineSpace(QQ,Integer(2), names=('u', 'v',)); (u, v,) = B.    _first_ngens(2)
      2 p=Curve([Integer(2)*u**Integer(2) + Integer(2)*u*v + Integer(2)    *v**Integer(2) - Integer(1)],B)
----> 3 p.rational_parameterization()

/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/schemes/    curves/affine_curve.py in rational_parameterization(self)
   1451                     ((-7*t^2 + 7)/((-a)*t^2 + (-a)), 14*t/((-a)*t^2 +     (-a)))
   1452         """
-> 1453         para = self.projective_closure(i=0).rational_parameterization().    defining_polynomials()
   1454         # these polynomials are homogeneous in two indeterminants, so     dehomogenize wrt one of the variables
   1455         R = para[0].parent()

/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/schemes/    curves/projective_curve.py in rational_parameterization(self)
   1569         singular.lib("paraplanecurves.lib")
   1570         R = singular.paraPlaneCurve(self.defining_polynomial())
-> 1571         singular.setring(R)
   1572         param = singular('PARA').sage().gens()
   1573         R = R.sage()

/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/interfaces/    singular.py in set_ring(self, R)
   1097         if not isinstance(R, SingularElement):
   1098             raise TypeError("R must be a singular ring")
-> 1099         self.eval("setring %s; short=0"%R.name(), allow_semicolon=True)
   1100 
   1101     setring = set_ring

/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/interfaces/    singular.py in eval(self, x, allow_semicolon, strip, **kwds)
    657         # Singular actually does use that string
    658         if s.find("error occurred") != -1 or s.find("Segment fault") !=     -1:
--> 659             raise SingularError('Singular error:\n%s'%s)
    660 
    661         if get_verbose() > 0:

SingularError: Singular error:
   ? sage19 is no name of a ring/qring
   ? error occurred in or before STDIN line 11: `setring sage19; short=0;`

Is this a SAGE or a Singular bug or am I missing something?

Suppose you have a curve gamma on a riemannian manifold (M,g). Can you check if gamma is a geodesic?

I tried

nabla =g.connection()
nabla(gamma.nabla.tangent_vector_fields())

But it seems to be impossible to compute covariant derivatives of vectors field along curves. Is there any way to do this?

For the record, one would have to write omega_inv = M.tensor_field(2, 0, om.inverse())

omega is not a form, but a general 2-tensor. Apart from that, the idea works (at least when we only have one chart).

I have a nondegenerate (0,2)-tensor omega on a manifold which is not a metric and I would like to compute its 'inverse', which is a (2,0)-tensor.

I tried omega[:].inverse() but I get the following error 'ChartFunctionRing_with_category' object has no attribute 'fraction_field'. This worked for me in older versions of Sagemath (I think it was 7.4).

I have created a list of variables, myvars

I'd like to create a function of those variables, but

myvars = var('x y z')
 f = function('f')(myvars)

doesn't work.

Of course in my actual code I'm creating myvars programatically, so doing

 f = unction('f')(myvars[0], myvars[1], myvars[2])

is not convenient

Thank you. Now I use the Jupyter notebook. It's much easier noticing that mistakes with syntax colouring.

I am trying to calculate all the perfect matchings of a graph G (i. e., the subgraphs of G such that every two points are connected)

def matchings(G):
    """Returns a list of the perfect matchings of G.
    It uses a recursive algorithm. Get a vertex x in G.
    Since all the perfect matchings contain exactly one edge for every vertex,
    we have that matchings(G) = {<x,y> U matchings(G\{x,y}) for y adjacent to x}.
    """
    Ms=[]   #List of mathchings
    x = G.random_vertex()
    for e in G.edges_incident(x):
        H=G.copy()
        H.delete_vertices([e[0],e[1]]
        for M in matchings(H):
            Ms.append(M.add_edge(e))
    return Ms

But this gives me

line 14 for M in matchings(H):
SyntaxError: invalid syntax

I don't understand the error (the loop seems fine to me). What's wrong?

I want to represent the Cayley graph of an abelian group (let's say $A=Z_5^2$) is a way that the element $g=a^i b^j$ is in the position $[i,j]$. I need a method .pos()such that:

A= groups.presentation.FGAbelian([n,n]);
g=A[2]

 ---> g = a*b*a^-1

g.pos()

 ---> [0,1]

How could I do that?

I have the abelian group (let's say, $Z_5^2$). I want to represent its Cayley graph as a grid, in which the element $a^i b^j$ occupies the $[i,j]$ position in the plane. For that, I need would need a method .pos(). which did the following.

A = groups.presentation.FGAbelian([n,n]);
e=A[2]

-->e=aba^-1

e.pos()

--> [0,1]

How can I create something like that?

As eric_g recommended in this post http://ask.sagemath.org/question/2959..., I tried SageManifolds (I had to give up index notation, since the current implementation is still very basic).

I tried to derive the formulas for Grad, Div and Curl in spherical coordinates. However, it only worked for Curl. This is my notebook: https://cloud.sagemath.com/projects/4...

I don't know what am I doing wrong. Also, I cannot simplify simple expressions such as the one for the divergence.

I am taking a course in general relativity, and I was planing to use sage for doing calculations.

I have

from sage.tensor.modules.tensor_with_indices import TensorWithIndices
M = FiniteRankFreeModule(QQ, 4, name='M')
e = M.basis('e')
a = M.tensor((2,0), name='a')
a[:] = [[2,0,1,-1], [1,0,3,2], [-1,1,0,0], [-2,1,1,-2]]
g = M.tensor((0,2), name='g')
g[:] = [[1,0,0,0], [0,1,0,0], [0,0,1,0],[0,0,0,1]]
v=M.tensor((1,0), name='v')
v[:]=[-1,2,0,-2]

I wanted to calculate $a^{^i,^j}$ Is there some way to tell Sage what is the metric, and do the index lowering automatically? I did it manually, but it's cumbersome for more complicated calculations.

 A=a['^ik']*g['_jk'];A[:]

Also, I don't know how to compute $vî v_i$, since

v['^i']*g['_ij']*v['i']

does not work.

Apart from that, I would like to know if there is a way to do this kind of computations with tensor fields and index notation, including derivatives, etc.

I want to visualize these functions in the complex plane:

$$f_n(z)=\exp(z) - \sum_{k=0}^{n} \frac{z^k}{k!}$$

I tried this code, but it gives me an error.

z,k = var('z,k')
@interact
    def _(n=(1..8)):
    complex_plot(exp(z)- sum(z^k/factorial(k), k, 0, n), (-5, 5), (-5, 5))

I am new to Sage (I previously used Mathematica). I wrote the code based on this example: http://wiki.sagemath.org/interact/ . How can I fix that?

EDIT: I would also like to know why doesn't this work either

def myPlot(n):
   complex_plot(exp(z)- sum(z^k/factorial(k), k, 0, n), (-5, 5), (-5, 5))

Then I type myPlot(2) in the notebook, but I get nothing. However, if I type:

complex_plot(exp(z)- sum(z^k/factorial(k), k, 0, 2), (-5, 5), (-5, 5))

I get the correct plot.

EDIT 2:

I tried

myPlot = lambda n: complex_plot(exp(z)- sum(z^k/factorial(k), k, 0, n), (-5, 5), (-5, 5))

And now I can evaluate it. However, I still can't use @Interact.

This doesn't make sense to me.