[sage-support] Question About Primitive Element
Phi(z) since by in your example the reduction of z will be primitive by definition. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Minimal set of Generators(basis) for an ideal/module
I am working in a multi-variable polynomial ring over a field (e.g. QQ or CC). How do I get the minimal set of generators for an ideal I (or module M)? I am here referring to something I can do in Singular with the command minbase. (http://www.singular.uni-kl.de/Manual/latest/sing_266.htm) Thanks in advance -- VInay -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Minimal set of Generators(basis) for an ideal/module
I don't know if this particular function is wrapped in Sage. But this Singular function requires the ideal to be homogeneous or the ring to be local. You don't mention this in your email, so I just wanted to point it out. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Minimal set of Generators(basis) for an ideal/module
On 29 September 2011 09:44, Volker Braun vbraun.n...@gmail.com wrote:
I don't know if this particular function is wrapped in Sage.
Yes it is, as almost any function in Singular, thanks to the Singular function
interface :)
Using the example from
http://www.singular.uni-kl.de/Manual/latest/sing_266.htm
sage: P.x,y,z = PolynomialRing(GF(181),order='neglex')
sage: I = Ideal(x^2+x*y*z,y^2-z^3*y,z^3+y^5*x*z)
sage: from sage.libs.singular.function_factory import singular_function
sage: maxideal = singular_function('maxideal')
sage: J = maxideal(3,ring=P)+I
sage: minbase = singular_function('minbase')
sage: minbase(J)
[x^2, x*y*z, x*z^2, y^2, y*z^2, z^3]
Cheers,
Martin
--
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[sage-support] Question about congruence
How do a(x) congruence b(x)R(x) mod (g(x)) in sage? thanks by your answers -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Question about congruence
g(x) is prime polynomial On 29 sep, 07:28, juaninf juan...@gmail.com wrote: How do a(x) congruence b(x)R(x) mod (g(x)) in sage? thanks by your answers -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Using sagenb
Hi all, I'm teaching a new cohort of students this year and was hoping to give them a quick SAGE tutorial. Our IT guys have not been able to setup a SAGE server in time so I was wondering how stable sagenb is. Is it realistic to run a 90 minute lab session (tops) with about 40 odd students each logged in to sagenb? Thanks, Vince -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Question about congruence
in the paper that I reading say use Euclides Algorithm, but I dont know how On 29 sep, 07:29, juaninf juan...@gmail.com wrote: g(x) is prime polynomial On 29 sep, 07:28, juaninf juan...@gmail.com wrote: How do a(x) congruence b(x)R(x) mod (g(x)) in sage? thanks by your answers -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Bug in Graph.is_chordal
Hello Jan ! I am trying to write the patch corresponding to your modifications, but the file has changed much since and I have some trouble dealing with your diff file... Could you copy/paste the totality of the code ? :-) Thaanks ! Nathann -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Minimal set of Generators(basis) for an ideal/module
@Volker Thanks for pointing that out... I had forgotten to mention
that in my post. BY the way any idea, why such a restriction? Can we
get away with that in sage (of course for that now we cant use
Martin's code...)
@Martin Thanks for the code.
Actually I wanted to do this without going back and forth Singular.
(i.e. defining the object as Singular objects.) This is one more
trick I have learnt today wherein I can avoid going to Singular and
do almost everything I could have done there :-)
Thanks once again...
-- VInay
On 29 September 2011 14:53, Martin Albrecht
martinralbre...@googlemail.com wrote:
On 29 September 2011 09:44, Volker Braun vbraun.n...@gmail.com wrote:
I don't know if this particular function is wrapped in Sage.
Yes it is, as almost any function in Singular, thanks to the Singular function
interface :)
Using the example from
http://www.singular.uni-kl.de/Manual/latest/sing_266.htm
sage: P.x,y,z = PolynomialRing(GF(181),order='neglex')
sage: I = Ideal(x^2+x*y*z,y^2-z^3*y,z^3+y^5*x*z)
sage: from sage.libs.singular.function_factory import singular_function
sage: maxideal = singular_function('maxideal')
sage: J = maxideal(3,ring=P)+I
sage: minbase = singular_function('minbase')
sage: minbase(J)
[x^2, x*y*z, x*z^2, y^2, y*z^2, z^3]
Cheers,
Martin
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=getsearch=0x8EF0DC99
_otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF
_www: http://www.informatik.uni-bremen.de/~malb
_jab: martinralbre...@jabber.ccc.de
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Re: [sage-support] Using sagenb
I'm teaching a new cohort of students this year and was hoping to give them a quick SAGE tutorial. Our IT guys have not been able to setup a SAGE server in time so I was wondering how stable sagenb is. Is it realistic to run a 90 minute lab session (tops) with about 40 odd students each logged in to sagenb? AFAIK, sagenb would most probably (if not certainly) not support that many people -administrators of sagenb would of course be more knowledgeable. Actually, your situation is a recurring issue on this list and people are always advised to set up their own server. You can do a quick search in the archives for various tips. I personally had set up a server following these instructions within an hour: http://wiki.sagemath.org/SageServer Another approach: http://wiki.sagemath.org/DanDrake/JustEnoughSageServer Most important hardware concern is about RAM: A single instance of Sage worksheet seems to occupy ~90MB (version 4.7.1); so, assuming that each student work on his/her own worksheet, you would need about 5GB of RAM for 40 people. Also security may be another important concern, as you would likely want the server to be reachable. See also: http://www.sagemath.org/doc/reference/sagenb/notebook/notebook_object.html Regards, Berkin -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Using sagenb
On 9/29/11 8:00 AM, Berkin Malkoc wrote: AFAIK, sagenb would most probably (if not certainly) not support that many people -administrators of sagenb would of course be more knowledgeable. Actually, your situation is a recurring issue on this list and people are always advised to set up their own server. You can do a quick search in the archives for various tips. That used to be the case, but I think since the major upgrade in July, sagenb.org can probably handle this (no guarantees, of course). I don't know of a way to check this, though---I don't know if there is a log of simultaneous users of just sagenb.org. Here is a graph of simultaneous users of all of the *.sagenb.org servers, though: http://www.sagenb.org/home/pub/3257/ Thanks, Jason -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Using sagenb
That used to be the case, but I think since the major upgrade in July, sagenb.org can probably handle this (no guarantees, of course). But one could use all the various sub-nbs like demo, demo1, alpha, etc.? -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Strange behaviour in a simple function
Hi I have written very simple function, which code I paste below. The thing is that it produces completely unexpected results. I paste them below. Please let me know if this is a bug or I just do something completely wrong. I change in tests only the modulus M. def MLCG_S(B,M,N,x0): x = x0 L = [] for i in range(1,N): x = Mod(B*x, M) #MLCG(B,M,x) print x==B print (B-M) print (x-M) print M-B print M-x return L; 2^31-1 Invocation: LCG_16807 = MLCG_S(16807,2^31-1,2,1); Result: True -2147466840 16807 2147466840 2147466840 ___2^20-1 Invocation:LCG_16807 = MLCG_S(16807,2^20-1,2,1); Result: True -1031768 16807 1031768 1031768 ___2^10-1 Invocation:LCG_16807 = MLCG_S(16807,2^10-1,2,1); Result: True 15784 439 -15784 584 Above, not only the first two differences are different, but also the last two differences are different! Cheers -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Strange behaviour in a simple function
Mod(B*x, M) doesn't return an integer but an element of Integers(M) = the ring of integers modulo M. So the differences you see are because B is a normal integer so the subtractions involving B and M are just integer subtractions, but the substractions involing x and M are substractions in Integers(M) -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Strange behaviour in a simple function
Note that 439+584 = 1023 = 2^10-1, so -439 and 584 are congruent mod M=2^10-1. (While B, M, and N are integers, x is element of Z/MZ, so comparisons like x==B are done mod M. Any printing of numbers involving x are done mod M.) -- John -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Question about xgcd method
Hi everybody,
I want implement a modified extend Euclidean Algorithm, (egcd
function), but this give wrong results, below my egcd, please help me
to fix ...
def egcd(p1,p2):
if p2 == PR(0):
return (p1,1,0)
else:
(q1, r1) = (p1).quo_rem(p2)
(d,s1,t1) = egcd(p2, r1)
return (d,t1,(s1 - q1 * t1))
m = 4
F.x = GF(2)
Phi.x = GF(2^m);
PR = PolynomialRing(Phi,'z');
N = 2^m - 1;
X = PolynomialRing(Phi,repr('z')).gen();
g = X^4+X^3+X^2+1+x^2; # goppa polynomial
R = (x^3 + x^2 + 1)*X^3 + (x^3 + x^2 + x)*X^2 + (x^2 + 1)*X + x^3 + x
(a11,b11,c11) = egcd(g,R)
print 'testing',((c11.mod(g)*(R))).mod(g)
(a11,b11,c11) = xgcd(g,R)
print 'testing',((c11.mod(g)*(R))).mod(g)
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