[sage-support] Re: Computational geometry in the plane: in Sage?
I need same packages that Ed asked for. Nowadays I do geometry coding myself basic functions in SAGE worksheets (to do intersection of lines etc). I do this using the Rational Trigonometry philosophy :-)..see njwilderger youtube videos and book. Previously I played a little with Tex tools (pst-tricks and pst-eucl)..check about pstricks too...at that time and until now, I was interested with tilings. In SAGE we have the basics tools (vectors,matplotlib...) but I feel there are not the intermediate tools : convex hull, rules and compass constructions, origami tools and so on. I can code some (for example, convex hull: I know an algorithm paquet cadeau ...but everytime I feel to reinvent wheel. What is not enough with Tex is that all is static : for example, you cannot have the generic solution of two lines AB and CD where A,B,C,D are 2D points with variables coordinates...because it is no more static geometry but symbolic computations (solving equations / inequations). -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Installing Python module in Sage (Ubuntu)
Hello! On Wed, 23 Apr 2014 15:40:10 -0700 William Stein wst...@gmail.com wrote: 0. Install the necessary devel libraries for Ubuntu: sudo apt-get install h5utils libhdf5-dev libhdf5-doc 1. Install PIP: sage -sh wget https://raw.github.com/pypa/pip/master/contrib/get-pip.py; python get-pip.py NOTE -- this step 1 is silly -- we should include pip with Sage; sorry we don't yet. 2. Install hdf5 module, and a few other things you likely want : sage # start up sage sage: os.environ['NETCDF4_DIR']='/usr/'; os.environ ['HDF5_DIR']='/usr/'; sage: [(s, os.system(pip install %s%s)) for s in 'pandas statsmodels h5py netcdf4'.split()] I usually install the additional python packages this way: 1. wget 'http://python_package.tar.gz' 2. tar xvf python_package.tar.gz 3. cd python_package 4. sage -python setup.py install Is this a correct method? Thanks! Vladimir - v...@ukr.net -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Extension of a field extension
Ok! Thank you! Do you have some idea about the first question? *I want to add to A1 the square root of theta^3+3*theta+5.* *The problem is that when I consider the following:* gamma2=theta^3+3*theta+5 AA1.xbar=PolynomialRing(A1) AA.gamma=A1.extension(xbar^2-gamma2) (xbar^2-gamma2).roots(AA,multiplicities=False) it gives me a NotImplementedError. Any idea? Thank you in advance. *Irene* On Monday, April 21, 2014 3:52:53 PM UTC+2, John Cremona wrote: On 21 April 2014 13:58, Irene irene@gmail.com javascript: wrote: I forgot to write what is repsq(): You could use the builtin function power_mod: sage: power_mod? Type: function String Form:function power_mod at 0x1f78668 File: /usr/local/sage/sage-6.1.1/local/lib/python2.7/site-packages/sage/rings/arith.py Definition: power_mod(a, n, m) Docstring: The n-th power of a modulo the integer m. #repsq(a,n) computes a^n def repsq(a,n): B = Integer(n).binary() C=list(B) k=len(B)-1 bk=a i=1 while i = k: if C[i]==1: bk=(bk^2)*a else: bk=bk^2 i=i+1 return bk On Monday, April 21, 2014 11:48:10 AM UTC+2, Irene wrote: Hello, I have the following defined: p=371 Fp=GF(p) E=EllipticCurve([Fp(3),Fp(5)]) j_inv=E.j_invariant() l=13#Atkin prime n=((l-1)/2).round() r=2# Phi_13 factorize in factors of degree 2 s=12#Psi_13 factorize in factors of degree 12 Fps=GF(repsq(p,s),'a') a=Fps.gen() Fpr=GF(repsq(p,r),'b') b=Fpr.gen() FFps.X=PolynomialRing(Fps) FFpr.x=PolynomialRing(Fpr) EP=x^6 + (973912*b + 2535329)*x^5 + (416282*b + 3608920)*x^4 + (686636*b + 908282)*x^3 + (2100014*b + 2063451)*x^2 + (2563113*b + 751714)*x + 2687623*b + 1658379 A1.theta=Fpr.extension(EP) and now I want to add to A1 the square root of theta^3+3*theta+5. The problem is that when I consider the following: gamma2=theta^3+3*theta+5 AA1.xbar=PolynomialRing(A1) AA.gamma=A1.extension(xbar^2-gamma2) (xbar^2-gamma2).roots(AA,multiplicities=False) it gives me a NotImplementedError. Any idea? Thank you in advance. Irene -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support...@googlegroups.com javascript:. To post to this group, send email to sage-s...@googlegroups.comjavascript:. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: Installing Python module in Sage (Ubuntu)
Hi! On 2014-04-24, v...@ukr.net v...@ukr.net wrote: I usually install the additional python packages this way: 1. wget 'http://python_package.tar.gz' 2. tar xvf python_package.tar.gz 3. cd python_package 4. sage -python setup.py install Is this a correct method? Should work too, AFAIK. Usually, I do the same in a Sage shell, i.e. sage -sh python setup.py install but what you do should be equivalent. Nonetheless, having a dedicated tool such as pip seems good to me. Best regards, Simon -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: Installing Python module in Sage (Ubuntu)
v...@ukr.net wrote:
I usually install the additional python packages this way:
1. wget 'http://python_package.tar.gz'
2. tar xvf python_package.tar.gz
3. cd python_package
4. sage -python setup.py install
Is this a correct method?
Steps 2 to 4 *used to be* equivalent to simply doing
$ sage -i /path/to/python_package.tar{,.gz,.bz2}
Don't know whether that still works. (And IIRC, the name of the tarball
had to match the top-level folder in it, but that's /usually/ the case.
If not, simply renaming the tarball should be sufficient.)
-leif
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[sage-support] Re: Computational geometry in the plane: in Sage?
We do have convex hull and lines. What would be lacking for your application are discs and their intersection with polyhedra. sage: line = Polyhedron(vertices=[(0,-1)], lines=[(1,1)]) sage: (triangle line).vertices() (A vertex at (8/5, 3/5), A vertex at (3/2, 1/2)) On Thursday, April 24, 2014 7:02:21 AM UTC+1, Dominique Laurain wrote: I need same packages that Ed asked for. Nowadays I do geometry coding myself basic functions in SAGE worksheets (to do intersection of lines etc). I do this using the Rational Trigonometry philosophy :-)..see njwilderger youtube videos and book. Previously I played a little with Tex tools (pst-tricks and pst-eucl)..check about pstricks too...at that time and until now, I was interested with tilings. In SAGE we have the basics tools (vectors,matplotlib...) but I feel there are not the intermediate tools : convex hull, rules and compass constructions, origami tools and so on. I can code some (for example, convex hull: I know an algorithm paquet cadeau ...but everytime I feel to reinvent wheel. What is not enough with Tex is that all is static : for example, you cannot have the generic solution of two lines AB and CD where A,B,C,D are 2D points with variables coordinates...because it is no more static geometry but symbolic computations (solving equations / inequations). -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: wrong or nonexistent results for various infinite sums
which, to me, is a very useful answer. But other sums are simply wrong.
k = var('k')
sum(x^(2*k)/factorial(2*k),k,0,oo)
I'm working with Maxima 5.33.0. I get
simplify_sum ('sum(x^(2*k)/factorial(2*k),k,0,inf));
= sqrt(%pi)*bessel_i(-1/2,x)*sqrt(x)/sqrt(2)
which seems to be cosh(x).
sum(x^(3*k)/factorial(2*k),k,0,oo)
I get
simplify_sum ('sum(x^(3*k)/factorial(2*k),k,0,inf));
= sqrt(%pi)*bessel_i(-1/2,x^(3/2))*x^(3/4)/sqrt(2)
Yes, at the ticket in question Nils was able to diagnose it as what I
suspected, an incorrect translation from Maxima to Sage. Thanks!
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[sage-support] How to define a homomorphism between two algebras
I have defined two extensions A1 and A2 over a finite field Fp2 with generator b, A1.theta=Fp2.extension(Ep) A2.z=Fp2.extension(Q) being Ep and Q polynomials. Now I want to define a homomorphism between those algebras. I have already computed alpha, that is the element in A2 where theta is mapped, but Sage doesn't allow me to define it as: A1.hom([alpha], A2) Do you know how to do it? Irene -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Computational geometry in the plane: in Sage?
Glad to see this has gained some traction. Here is an illustration of the immediate issue for which this would have been helpful. I wanted to produce an illustration explaining lines in the hyperbolic plane using the Poincare disk model. It's the arc of a circle whose end points are on a given circle and the arc meets the given circle at right angles. (That's a lot to say but a picture makes it so much easier.) It took me a long time and a good deal of coding in Sage to get this how I wanted. My gut tells me there's go to be a better way! On Thu, Apr 24, 2014 at 9:31 AM, Volker Braun vbraun.n...@gmail.com wrote: We do have convex hull and lines. What would be lacking for your application are discs and their intersection with polyhedra. sage: line = Polyhedron(vertices=[(0,-1)], lines=[(1,1)]) sage: (triangle line).vertices() (A vertex at (8/5, 3/5), A vertex at (3/2, 1/2)) On Thursday, April 24, 2014 7:02:21 AM UTC+1, Dominique Laurain wrote: I need same packages that Ed asked for. Nowadays I do geometry coding myself basic functions in SAGE worksheets (to do intersection of lines etc). I do this using the Rational Trigonometry philosophy :-)..see njwilderger youtube videos and book. Previously I played a little with Tex tools (pst-tricks and pst-eucl)..check about pstricks too...at that time and until now, I was interested with tilings. In SAGE we have the basics tools (vectors,matplotlib...) but I feel there are not the intermediate tools : convex hull, rules and compass constructions, origami tools and so on. I can code some (for example, convex hull: I know an algorithm paquet cadeau ...but everytime I feel to reinvent wheel. What is not enough with Tex is that all is static : for example, you cannot have the generic solution of two lines AB and CD where A,B,C,D are 2D points with variables coordinates...because it is no more static geometry but symbolic computations (solving equations / inequations). -- You received this message because you are subscribed to a topic in the Google Groups sage-support group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/sage-support/Y0t4ShFLXJ4/unsubscribe. To unsubscribe from this group and all its topics, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout. -- Ed Scheinerman (e...@scheinerman.net) -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout. line-definition.pdf Description: Adobe PDF document
[sage-support] Re: How to define a homomorphism between two algebras
Can you post a complete example? The following (simple) example works for me (at least in 6.2.beta8): sage: F=GF(5).extension(2) sage: A1.y=F.extension(x^2+3) sage: A2.z=F.extension(x^2+3) sage: A1.hom([z],A2) Ring morphism: From: Univariate Quotient Polynomial Ring in y over Finite Field in a of size 5^2 with modulus y^2 + 3 To: Univariate Quotient Polynomial Ring in z over Finite Field in a of size 5^2 with modulus z^2 + 3 Defn: y |-- z Peter Op donderdag 24 april 2014 16:55:34 UTC+1 schreef Irene: I have defined two extensions A1 and A2 over a finite field Fp2 with generator b, A1.theta=Fp2.extension(Ep) A2.z=Fp2.extension(Q) being Ep and Q polynomials. Now I want to define a homomorphism between those algebras. I have already computed alpha, that is the element in A2 where theta is mapped, but Sage doesn't allow me to define it as: A1.hom([alpha], A2) Do you know how to do it? Irene -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Computational geometry in the plane: in Sage?
A certain amount of work on adding functionality for hyperbolic geometry to Sage has been done in recent years, see here: http://trac.sagemath.org/ticket/9439 There seem to be several different implementations by different authors; I am not sure about the status of all this work and how much of it is relevant to what you want to do. Peter Op donderdag 24 april 2014 18:54:32 UTC+1 schreef Ed Scheinerman: Glad to see this has gained some traction. Here is an illustration of the immediate issue for which this would have been helpful. I wanted to produce an illustration explaining lines in the hyperbolic plane using the Poincare disk model. It's the arc of a circle whose end points are on a given circle and the arc meets the given circle at right angles. (That's a lot to say but a picture makes it so much easier.) It took me a long time and a good deal of coding in Sage to get this how I wanted. My gut tells me there's go to be a better way! On Thu, Apr 24, 2014 at 9:31 AM, Volker Braun vbrau...@gmail.comjavascript: wrote: We do have convex hull and lines. What would be lacking for your application are discs and their intersection with polyhedra. sage: line = Polyhedron(vertices=[(0,-1)], lines=[(1,1)]) sage: (triangle line).vertices() (A vertex at (8/5, 3/5), A vertex at (3/2, 1/2)) On Thursday, April 24, 2014 7:02:21 AM UTC+1, Dominique Laurain wrote: I need same packages that Ed asked for. Nowadays I do geometry coding myself basic functions in SAGE worksheets (to do intersection of lines etc). I do this using the Rational Trigonometry philosophy :-)..see njwilderger youtube videos and book. Previously I played a little with Tex tools (pst-tricks and pst-eucl)..check about pstricks too...at that time and until now, I was interested with tilings. In SAGE we have the basics tools (vectors,matplotlib...) but I feel there are not the intermediate tools : convex hull, rules and compass constructions, origami tools and so on. I can code some (for example, convex hull: I know an algorithm paquet cadeau ...but everytime I feel to reinvent wheel. What is not enough with Tex is that all is static : for example, you cannot have the generic solution of two lines AB and CD where A,B,C,D are 2D points with variables coordinates...because it is no more static geometry but symbolic computations (solving equations / inequations). -- You received this message because you are subscribed to a topic in the Google Groups sage-support group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/sage-support/Y0t4ShFLXJ4/unsubscribe. To unsubscribe from this group and all its topics, send an email to sage-support...@googlegroups.com javascript:. To post to this group, send email to sage-s...@googlegroups.comjavascript: . Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout. -- Ed Scheinerman (e...@scheinerman.net javascript:) -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
