Hi all,
I am wondering how to make some computations with rather specific
field
extensions. I cannot figure out how to solve the following on SAGE.
Mathematically, I have the following field:
Q(x,y,z,t,a)
Where x,y,z,t are indeterminates and "a" is an algebraic number over
the
rationals (lets s
On 20 mar, 14:07, Mike Hansen wrote:
> The best way to work with this object is to do like you did:
>
> sage: K.=NumberField(x^4+x+1)
> sage: R.=K['x,y,z,t']
>
> Then, we can construct some elements of this field:
>
> sage: f = (a^2*x + y)*(z+a*t); f
> (a^2)*x*z + y*z + (a^3)*x*t + (a)*y*t
> sa
On 17 dic, 11:48, "ma...@mendelu.cz" wrote:
> And another observation:
>
> maxima returns answer immediatelly (with a lag necessary to start
> maxima)
> m is the original matrix from x.py
>
> sage: m._maxima_().determinant().expand().sage()
> x0^2*x2^2*x3^2*x7^2 - 2*x0*x1*x2*x3*x4*x5*x6*x7 + x1^
I think you have more chances if you work in QQ['a']['t1,t2']. In any case,
it seems that it is better to convert to your ring using
P(f.polynomial(QQ)) than performing substitutions.
sage: K=QQ['a']['t1,t2']
sage: K1=SR['t1,t2']
sage: f=SR(K.random_elemen
The thing is with the sage windows appliance as has been said. In order to
keep the ova file to the minimum most programs has been erased, including
gedit. I think that in your case your best bet would be to download a
virtualbox image of a linux distibution that is supported by sage (fedora
or
>
>
> Nevermind, I found it.
>
> Call K2.structure() for the maps.
>
> Thank you!
>
>
Moreover, you can register these isomorphisms as coercions. I do
not recommend the following for noninteractive scripts. But I find it very
convenient:
sage: K=QQ[sqrt(2),sqrt(3)]
sage: s2,s3=K.gens()
sage:
On Monday, February 17, 2014 6:39:38 PM UTC+1, sahi...@gmail.com wrote:
>
> OK, I tried the following:
>
> S. = PolynomialRing(QQ,order='lex')
> I = ideal(i^2+1,(1+i)*x+y,x+(1-i)*y-(1-i))
> G = I.groebner_basis()
> G
>
> would give me
>
> [i - x - 1, x^2 + 2*x + 2, y - 2]
>
> which are the result
On Wednesday, March 26, 2014 10:34:35 AM UTC+1, John Cremona wrote:
>
> Looking at the code used, it uses the resultant formula which in turn
> evaluates a determinant. I agree with you that for small degrees it
> would be better (almost certainly in a lot of cases) be better to
> substitute in
On 1 mar, 20:46, Pierre wrote:
> oooh wait wait wait. I've said something totally confusing.
>
> My previous two posts apply to rational fractions... for which indeed,
> the numerator method gives the 'correct' answer ! The issue I raised
> in my original post is the 'funny' behaviour when you a
> -For the denominator: if there is a denominator function for the
> coefficients and these denominators have a lcm function, then return
> the lcm of the coefficients. This is an element of K, not K[x1,...,xn]
ooops
This sould read an element of wherever the denominator of elements in
K live.
--
.3.3/devel/sage-luisfe/sage/libs/ntl/ntl_ZZ.pxd":4
* include "decl.pxi"
*
* cdef class ntl_ZZ: # <<<<<<<<<<<<<<
* cdef ZZ_c x
* cdef public int get_as_int(ntl_ZZ self)
*/
str
On 24 mar, 06:13, Barukh Ziv wrote:
> Dear all,
>
> I would like to ask you about a problem I am encountering while using
> NTL library for p-adic numbers manipulation. Sometimes, I get the
> following internal error from NTL function:
>
> "can't grow this _ntl_gbigint"
Are you using ntl_ZZ_p o
On 24 mar, 12:53, Barukh Ziv wrote:
> Guys,
>
> Thank you for the quick reply. I will answer to both questions:
>
> > Are you using ntl_ZZ_p or ntl_ZZ_pE? I have experienced the same type
> > of errors with the latter (due to bad manipulations of
> > ntl_ZZ_pEContext by myself.
>
> Yes, I experi
On 19 abr, 12:07, "samuele.anni" wrote:
> Hello,
> I'm trying to implement an algorithm for complete my thesis work about
> congruence between modular forms and Galois representation.
> A step of the algorithm I am working on consists in replacing a
> generator of the number field with a fixed v
I found the following:
{{{
sage: N. = NumberField([x^2-2, x^2-3, x^2-5],'s2,s3,s5')
sage: M = N.absolute_field('gamma')
sage: N_to_M = M.structure()[1]
sage: phi = N.hom([N_to_M(s2)])
sage: phi(s2) == N_to_M(s2)
True
sage: phi(s3) == N_to_M(s3)
True
sage: phi(s5) == N_to_M(s5)
False
sage: phi(s5)
On Jul 7, 2:21 am, dmharvey wrote:
> sage: R. = PolynomialRing(Integers(16219299585*2^16612 - 1))
>
> Maybe not literally forever, but I got sick of waiting. Should be
> instantaneous.
>
> david
When constructing a polynomial ring over Z/nZ sage distingishes
between prime modulus or not. Moreov
On Sep 4, 5:54 am, Cary Cherng wrote:
> I have a rational function P(x)/Q(x) with numerators and denominators
> of very large degree. From the context I know that a certain
> polynomial p(x) should divide the denominator. If I multiply the
> numerator by p(x) giving p(x)*P(x)/Q(x) how do I get
On Sep 8, 2:49 am, Cary Cherng wrote:
> This works but is too slow for more complicated examples. Is there a
> way to speed up "x in I" for much bigger examples? Or does this
> already use the fastest algorithm based on groebner basis or something
> else.
Blind checking if a polynomial is in an
On Sep 27, 3:34 pm, Johannes wrote:
> Hi list,
> is there a way to get a sum of fraction to a common devisor? or even
> better into a product of a fraction like \frac{1}{something here} and a
> sum of integers?
> and my next step would be this, i dont have a single value, which i want
> to get as
On Oct 16, 1:59 pm, Thierry Dumont wrote:
> Hello,
>
> On our Sage server, we have a lot a students doing simple computer algebra.
> Our version of Sage is 4.5.3 on Debian Lenny.
>
> We have a lot of segfaults in maxima:
Could you post more information of the problem?
Did you install sage from
On 2 nov, 17:00, "Rob H." wrote:
> Hi,
>
> so here is some sample code:
>
> var('chi,k')
> R.=SR[]
> I=R.ideal(x^2)
> Rbar.=R.quotient_ring(I)
> expr=Rbar(epsilon-(chi^(k-1))^5+chi^(2*k-2)*(chi^(k-1))^3)
> view(expr)
> print (expr)
For the kind of operations you are doing, you should work in QQ[]
Suppose that I define a set of equalities and inequalities
{{{
sage: var('x,y,z,t')
(x, y, z, t)
sage: L = [x==y+z, x>=t-z, x+3*y<=0]
}}}
Is there an easy way to construct the Polhyedron of the solutions of
this system? The constructor of Polyhedron does not seem very user-
friendly for Hrepresen
On 28 oct, 18:05, VictorMiller wrote:
> Using sagenb.org:
>
> sage: G = SymmetricGroup(5)
> sage GA = G.algebra(QQ)
> sage: GA.gens()
>
> Traceback (click to the left of this block for traceback)
> ...
> RuntimeError: Free module generated by SymmetricGroup(5) over Rational
This is a known issue
On 14 oct, 22:07, "D. Monarres" wrote:
> Hello all,
>
> Just wondering if I am doing everything correctly or if I have
> stumbled onto a bug (or something that needs to be implemented)
>
> I am writing a tutorial for students using Sage in an introductory
> abstract algebra course and the follow
On 5 nov, 21:45, andrew ewart wrote:
> i want to write a polynomial p of variables x and y such that
> p(x,y)=0
>
> i also have that x and y can be expressed in terms of a variable u
> such that
> 2x=2u^2+2u-1 and
> -y^2=u^4+2u^3-2u-1
>
> how to write code to eliminate u, hence finding p
You cou
On 8 nov, 19:34, andrew ewart wrote:
> I want to write code that does the following
> Given ideals I,J in CC[x1,...,xn]
> check if Radical(I+J)=Radical(I)+Radical(J)
> also maybe throw in an example of yes and no just to see it working
>
> Radical(I)={f:there is an m such that f^m is in I} (f i
On Nov 21, 6:22 am, VictorMiller wrote:
> sage: T. = QQ[]
> sage: TJ = Ideal([t1^2 + u1^2 - 1,t2^2 + u2^2 - 1, (t1-t2)^2 + (u1-
> u2)^2 -1])
> sage: TJ.genus()
> 4294967295
> sage: TJ.dimension()
> 1
Yes, there is a bug in the code. If I try Sage 32 bits, the answer to
TJ.genus() is -1. Is I us
In this case, I tend to agree with Palmieri.
On Dec 4, 10:27 pm, William Stein wrote:
> I very strongly disagree. What's wrong with making a polynomial ring
> with two distinct variables whose *print* names you happen to set to
> be the same?The variables are different. It's just that they
On Dec 5, 1:58 pm, eggartmumie wrote:
> Hi,
> I am a newbie working in polynomial quotient rings:
> I want to implement the Patterson algorithm to decode Goppa Codes.
> Therefore, I need to split a polynomial p in a quotient ring in its
> even part p0 and its odd part p1
> such that p(z) = p0^2(z)
On Dec 7, 5:03 pm, andrew ewart wrote:
> I have the following code
>
> P. = PolynomialRing(QQ,order='degrevlex')
> I = Ideal(x0^4-y0,x0^3*x1-y1,x0*x1^3-y2,x1^4-y3)
> print I
> R. = PolynomialRing(QQ,order='degrevlex')
> I1=Ideal(1)
> J=I.intersection(I1)
> print J
> but gives error
> File "/usr/lo
On Dec 28, 5:27 pm, Santanu Sarkar
wrote:
> Is there any faster method to compute Hermite Normal Form
> of a matrix A and corresponding transformation matrix? I use
> A.hermite_form(transformation=true). However it is very slow.
>
> Also is there any transformation matrix corresponding to the L
On Dec 28, 6:23 pm, Santanu Sarkar
wrote:
> Size of my matrix is (90, 36) with entries are around 2^1000. What is the
> fastest
> method to compute Hermite Normal Form?
In that case, the fastest may be the default one you are already
using. Note that computing the Hermite form is fast, the hard
On Jan 26, 8:42 am, Loïc wrote:
> Hello list,
>
> Version: sage 4.6.1
> I'm quite a newbie with Sage but I'm really impressed this powerful
> software.
> Since an hour, I'm on a stupid problem:
>
> sage: sqrt(2)*sqrt(3)
> sqrt(2)*sqrt(3)
> sage: sqrt(2)*sqrt(3)-sqrt(6)
> sqrt(2)*sqrt(3)-sqrt(6)
>
I thought I have already asked this. But I do not see it on the
history of the group. Apologize for multiple posting.
Is there an equivalent in Sage to ParallelMap in mathematica?
I am looking a method that applies a given function to a list of
objects for a small presentation of Sage I am prepa
The first method creates the ring AND add the variables so that they
are available to the user by tipping their name. for instance:
sage: R.=QQ[]
sage: x
x
sage: type(x)
Note that this is not python, but a sage-specific shortcut.
However, the second creation of R only creates a polynomial ring
Just for the record. The problem seems to be related to RIF. For the
inexact ring RR, it works:
len(e.roots(ring=RR))
13
len(e.real_roots())
13
numeric approximations of the two missing roots are:
0.953956769342757, 0.957223630414975
This pair of roots is exactly the pair of most close roots am
Robert,
You have been answered how to solve the problem. But I would like to
remark Volker's advice.
Do not use ideals over CC. CC is an inexact ring, so most operations
will fail. Work instead over the rationals.
R. = PolynomialRing(QQ,2)
or if you need complex numbers, you may try with a numb
No, it is not an exact computation over the complex, they are gauss
rationals a+b*I where a and b are rationals. As far as I know there is
no exact complex field implementation that is good for working with
ideals.
What kind of generators of ideals are you dealing with?
Note that even if the inpu
On Mar 1, 12:59 pm, Robert Goss wrote:
> > What kind of generators of ideals are you dealing with?
>
> For reference all the input generators are in QQ.
>
> Robert
Then, definitely you should work in PolynomialRing(QQ,2)
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To post to this group, send email to sage-support@googlegroups.com
To u
hi Jose Luis,
By the error do you mean a NameError? There are no such global
functions defined in Sage.
I would rather use simplify_full and simplify_trig because there would
be easier to discover by a user writing simpl and pressing tab.
On the one hand it is true that for newcomers simplify_fu
On Apr 5, 2:10 pm, "Johan S. R. Nielsen" wrote:
> Oops, continuing:
>
> more precisely, we wish to find a q in Q[Y1, Y2] such that q(f1, f2) =
> g. In this case, we have
> q(Y1, Y2) = Y1^2 + Y1*Y2 - Y2
> as a solution, as
> f1^2 + f1*f2 - f2 = g
This is an elimination problem. Note that it is n
On Jul 14, 3:23 am, Mel wrote:
> Hi,
>
> I've been having an issue with a program I've written in sage. I need
> to calculate a polynomial mod 7. When I do this using the command
> line, I don't have any trouble. Example:
>
> sage: x = var('x')
> sage: y = var('y')
> sage: IntegerPolyRing. = ZZ
On Jul 16, 1:33 am, Johannes wrote:
> a very easy example would be this:
>
> sage: p1 = vector([-3,1,1])
> sage: p2 = vector([1,-3,1])
> sage: p = vector([0,-2,1])
>
> #now i'm looking for some x,y such that
> #x * p1 + y * p1 == p
>
> x,y = var('x,y')
> sage: assume(x > 0)
> sage: assume(y > 0)
>
On Jul 18, 3:48 pm, Johhannes wrote:
> thnx.
>
> I see that the problem can be also formulated as marix problem. but
> the way i did it is in this case the more natural one for me.
> is there any reason why it only works this way and solve does not lead
> to any result?
For me it looks like:
On Sep 13, 9:11 am, vasu wrote:
> Hi all
> I am trying to run a particular piece of code and it gives an error
> saying there is a bug in Pari/gp. It turns out that the bug is not
> present in previous versions of Pari like 2.3.4 (on Windows at least).
> And if I understand correctly that Sage shi
On Sep 15, 12:43 pm, Amir wrote:
> Hi
>
> I have the same problem. I am using sage 4.6 installed on windows
> vista. This is part of code I have written in sage. Is there anyway I
> can catch this error and make an exception?
>
> Thanks
An exception is not the way to dela with this error. We n
Hi list,
I have downloaded the virtualbox sage image to run under windows to
make a presentation of the capabilities of Sage. I wanted to try in
windows and an old machine to try to force things. So I took my five-
years good old laptop.
The problem is that sage in virtualbox does not run. Sage c
On Sep 23, 7:06 pm, Volker Braun wrote:
> I'll look into lowering the processor requirements. Though SSE3 has been out
> for a looong time...
>
> You can rebuild Sage inside the virtual machine. Just interrupt the notebook
> server (Ctrl-C), go to the Sage directory, run "make distclean" and the
> On Oct 17, 2:51 pm, Eric wrote:
> Does anyone know how to enlarge the memory limits set by sage?
>
> I get the following message when running a certain computation that
> involves computing large determinants.
>
> Memory limit reached. Please jump to an outer pointer, quit program
> and enlarge
> sage:
> F.=GF(2^8,name='x',modulus=z^8+z^4+z^3+z^2+1,check_irreducible=False)
> sage: F
> Finite Field in x of size 2^8
> sage: F.polynomial()
> x^8 + x^4 + x^3 + x^2 + 1
>
> Andrzej Chrzeszczyk
In this case sage does not complaint, but check_irreducible is not
intended for this use, but to avoi
On Jan 16, 5:53 pm, Ed Scheinerman
wrote:
> I'm confused by the fact that variables defined inside functions can
> "leak out" and become global variables. Here's what I've noticed.
The problem is twith the function var. According to its documentation:
(var?)
"The new variable is both returned
I have a problem to set an animation. I have the following:
sage: L1 =
sphere((0,0,0),5)
sage: L2 = L1.rotateZ(pi/3)
sage: L1.save('one.png',aspect_ratio=[1,1,1],frame=False)
sage: L2.s
On Thursday, September 13, 2012 9:46:38 AM UTC+2, moritz wrote:
>
> Note: The first time I tried to post this it didn't show on the google
> groups UI, so I try again..
> ---
>
> Let's consider a system of linear equations with integer coefficients:
>
> What is the best way to find an inte
On Wednesday, September 19, 2012 6:34:52 AM UTC+2, Georgi Guninski wrote:
>
> Hi,
>
> I may be missing something, but the resultant = 1 confuses me.
> According to wikipedia [1]
> the multivariate resultant or Macaulay's resultant of n homogeneous
> polynomials in n variables is a polynomial
On Thursday, September 20, 2012 1:05:56 PM UTC+2, Georgi Guninski wrote:
>
> pari disagrees with sage and maxima agrees with it.
>
> which way is it?
>
> maxima session:
> (%i12) p1:(x2)*(x3-x4);p2:x2*(x3-2*x4);
> (%i14) resultant(p1,p2,x1);
> (%o14) 1
>
In
Maple agrees with magma here and says that the genus is one. Moreover, it
computes a parametrization of the curve
sage: P=(((v + 2)*x^10 + (v - 2))/x^5, ((1/2*v - 3/2))/x^3)
sage: p(x=P[0],y=P[1])
0
The problem seems to be in singular.
sage: I = Ideal(p)
sage: I.genus()
10
If one looks at th
I can confirm the problem with sage 5.4, I cannot reproduce it with sage 5.3
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On Wednesday, November 28, 2012 9:27:58 PM UTC+1, Simon King wrote:
>
> Hi Georgi,
>
> On 2012-11-28, Georgi Guninski >
> wrote:
> > Probably the problem is in Singular.
>
> Probably not. If I am not mistaken, Singular is involved in polynomial
> factorisation over *finite* fields.
>
I agree
Sage interprets that matrices M acts on row vectors v on the left, v*M so
in fact the method image corresponds to row_space
>From the help of image:
Return the image of the homomorphism on *rows* defined by this matrix.
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On Wednesday, February 27, 2019 at 2:52:36 PM UTC+1, Daniel Krenn wrote:
> > I suppose in non-full-dimensional case you still can use
> > P.inequalities() as above,
> > projecting them on the affine hull of P.
>
> Yes, this is the interesting case. The problem then is going back from
> the p
On Monday, June 17, 2019 at 2:12:58 PM UTC+2, Peter Luschny wrote:
As I see it the problem is that the sum runs over (0..n-1).
> Thus for n = 0 it returns by convention the integer 0 for the
> empty sum (is this correct?) which of course has no list.
>
> But shouldn't it return the null polynomia
On Monday, June 17, 2019 at 2:12:58 PM UTC+2, Peter Luschny wrote:
As I see it the problem is that the sum runs over (0..n-1).
> Thus for n = 0 it returns by convention the integer 0 for the
> empty sum (is this correct?) which of course has no list.
>
> But shouldn't it return the null polynomi
On Tuesday, June 25, 2019 at 10:03:03 AM UTC+2, Peter Luschny wrote:
>
> How that? Look at the output above. Sage *knows* that the terms of the sum
> are polynomials. So it should return the zero of that ring, which is the
> null polynomial.
>
>
Not in the first case, look at what are you passi
Within a specific interactive session, you could do the following, when
creating the rings:
sage: R = PowerSeriesRing(GF(2),'t')
sage: F = R.residue_field()
sage: phi = R.hom([0], F)
sage: F.register_coercion(phi)
This way, you are indicating that the morphism phi should be considered a
coercio
Have you tried using elimination ideals?
K=QQ['s,t,a0,a1,a2']
K.inject_variables()
I = Ideal( a0-s^2, a1-t^2, a2 - (s^2+t^2))
I.elimination_ideal([s,t])
Ideal (a0 + a1 - a2) of Multivariate Polynomial Ring in s, t, a0, a1, a2
over Rational Field
So a2 = a0 + a1
The elimination ideal tells you wh
On Tuesday, June 9, 2015 at 5:36:01 PM UTC+2, black...@gmx.de wrote:
>
> Thank you,
>
> and i already tried this. In this case it obiously does work but in case i
> have denominators, can u explain me how to solve it?
> for example: K(s/(s+t),s^2*t^2) then i have to calculate the elimination
>
On Thursday, June 11, 2015 at 5:26:28 PM UTC+2, Phoenix wrote:
> I have two polynomials $p(x)$ and $q(x)$ and I want to know if there are
> roots of the equation $\frac{p'}{p} = \frac{q'}{q}$ in the domain
> $(a,\infinity)$ - where $a = max \{ roots(p),roots(q) \}$
>
> This is the same as asking
On Friday, June 12, 2015 at 11:17:37 AM UTC+2, Néstor wrote:
> Hello,
>
> I've got a rational expression in sage and I would like to convert it to a
> polynomial with coefficients in some fraction field.
>
> More precisely, I've got something like this:
>
> a , x = var( 'a , x' ) ;
> P = x/a ;
>
In general, I prefer to put the parameters a_i as variables and then
interpret the results.
Another approach you may try is to work in the field:
GF(2^d)['a_1,a_2,a_3'].fraction_field()['x_1,x_2,x_3']
but then you may encounter specialiation problems with denominators,
another problem is that
It looks right to me.
I am not a native English speaker so I could be (very) wrong, but I
understand that the comparison x<2 is evaluated, which is completely true,
independently if the condition is evaluated as True or False. In fact, next
lines tell why x<2 is evaluated False and that h(x) re
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