[sage-support] Re: Quotient ring over Finite Field 2^n
Hi Peter, Your solution can be used in some applications. However, I guess the call is more natural and understandable. It can be also used in the following: K = GF(2^8, 'a') P.x = PolynomialRing(K) Q.y = P.quotient_ring(x^256 - x) f = Q.random_element() f.subs(Q.random_element()) Albeit... K = GF(2^8, 'a') P.x = PolynomialRing(K) Q.y = P.quotient_ring(x^256 - x) f = Q.random_element() ev_a = Q.hom([Q.random_element()]) # homomorphism: Q - Q f = Q.random_element() b = ev_a(f) The code above works fine! Regards, Oleksandr On Tuesday, August 12, 2014 10:40:34 PM UTC+2, Peter Bruin wrote: Hello, It seems like quotient_ring doesn't have '__call__'. Does it a bug or a feature? sage: K = GF(2^8,'a') sage: P = PolynomialRing(K,'x') sage: Q = P.quotient_ring(P(x^256+x),'y') sage: f = Q.random_element() sage: f.subs(y=K.random_element()) # random (a^7 + a^6 + a^3 + a)*y^255 + (a^7 + a^4)*y^254 ... sage: Q Univariate Quotient Polynomial Ring in y over Finite Field in a of size 2 ^8 with modulus x^256 + x I expect that the output will be in K. It would in principle not be hard to implement the functionality you are asking for, but I would recommend a solution like the following: sage: K = GF(2^8, 'a') sage: P.x = PolynomialRing(K) sage: Q.y = P.quotient_ring(x^256 - x) sage: a = K.random_element() sage: ev_a = Q.hom([a]) # homomorphism evaluation in a: Q - K sage: f = Q.random_element() sage: b = ev_a(f) sage: b # random a^7 + a^5 + a^3 + a^2 + a + 1 sage: b.parent() is K True In this way, the fact that ev_a is well-defined is checked during its construction, so it doesn't have to be checked when doing the actual evaluation. Peter -- 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] Quotient ring over Finite Field 2^n
Hello everyone, It seems like quotient_ring doesn't have '__call__'. Does it a bug or a feature? sage: K = GF(2^8,'a') sage: P = PolynomialRing(K,'x') sage: Q = P.quotient_ring(P(x^256+x),'y') sage: f = Q.random_element() sage: f.subs(y=K.random_element()) # random (a^7 + a^6 + a^3 + a)*y^255 + (a^7 + a^4)*y^254 ... sage: Q Univariate Quotient Polynomial Ring in y over Finite Field in a of size 2^8 with modulus x^256 + x I expect that the output will be in K. Kind regards, Oleksandr -- 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: Overflow creating finite field element
Hi Samuel, I guess t_INT is the 64-bit sign integer in the pari library, which is written in C. It means the positive size is 63 bits. The number 2^63 corresponds to -1 and pari raises an error. The following code works fine. sage: p = previous_prime(2^64) sage: F.x = GF(p^2) sage: x * (2**63 - 1) Kind regards, Oleksandr On Saturday, July 26, 2014 5:39:42 AM UTC+2, Samuel Neves wrote: I seem to have run across a potential bug on Sage: p = previous_prime(2^64) F.x = GF(p^2) x * 2**63 throws a overflow in t_INT--long assignment exception creating the element x * 2**63. Reproduced here: https://sagecell.sagemath.org/?z=eJwrULBVKChKLcvMLy2OLyjKzE3VMIozM9Hk5XLTs6mwA8q6u2kUxBkBBSq0jLS0zIwBihANsg==lang=sage -- 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: Symmetric polynomials over a ring of polynomials
Hi Tom, Your code works perfectly in Sage 6.2 on Mac R.x1,x2,x3 = PolynomialRing(ZZ,3) C.c1,c2 = PolynomialRing(R,2) Sym = SymmetricFunctions(R) e = Sym.elementary() def ElemSym(p): # checks whether a polynomial is symmetric (coefficients in ZZ[l1,l2,l3]) f = Sym.from_polynomial(p) return e(f) p = ((x1^3 - 2*x1*x2 + x3)*c1^2 - (x1*x2 - x3)*c1 + x3)*c2^2 + x1^3 + c1^2*x3 - (x1*x2 - x3)*c1 - ((x1*x2 - x3)*c1^2 - (x1^3 - x1*x2 + x3)*c1 + x1*x2 - x3)*c2 - 2*x1*x2 + x3 ElemSym(p) == ElemSym(((x1^3 - 2*x1*x2 + x3)*c1^2 - (x1*x2 - x3)*c1 + x3)*c2^2 + x1^3 + c1^2*x3 - (x1*x2 - x3)*c1 - ((x1*x2 - x3)*c1^2 - (x1^3 - x1*x2 + x3)*c1 + x1*x2 - x3)*c2 - 2*x1*x2 + x3) True Best regards, Oleksandr On Saturday, May 24, 2014 4:29:38 PM UTC+2, Tom Harris wrote: Hi all, I am new to sage, so please forgive me if this is a trivial question. I am trying to express certain polynomials, which are symmetric in a subset of the variables, in terms of elementary symmetric polynomials on the symmetric subset (with coefficients that are polynomials in the other variables. Here is my setup: _ R.x1,x2,x3 = PolynomialRing(ZZ,3) C.c1,c2 = PolynomialRing(R,2) Sym = SymmetricFunctions(R) e = Sym.elementary() def ElemSym(p): # checks whether a polynomial is symmetric (coefficients in ZZ[l1,l2,l3]) f = Sym.from_polynomial(p) return e(f) _ If one enters some polynomials of the desired form by hand, e.g., g = (x1^2 - 2*x2^2)*c1 +c1*c2 + (x1^2 -2*x2^2)*c2 and calls ElemSym(g) then sage returns (x1^2-2*x2^2)*e[1] + e[2] as expected. Now I have some code to generate the polynomial which I am interested in, I store it as p: p = (output of some functions) ( p is ((x1^3 - 2*x1*x2 + x3)*c1^2 - (x1*x2 - x3)*c1 + x3)*c2^2 + x1^3 + c1^2*x3 - (x1*x2 - x3)*c1 - ((x1*x2 - x3)*c1^2 - (x1^3 - x1*x2 + x3)*c1 + x1*x2 - x3)*c2 - 2*x1*x2 + x3) Now the curious thing: p is (naively at least) symmetric in c1 and c2, but calling ElemSym(p) returns an error: ValueError: x0 + 2*x1 + x2 is not a symmetric polynomial but if I copy the polynomial itself and call ElemSym(((x1^3 - 2*x1*x2 + x3)*c1^2 - (x1*x2 - x3)*c1 + x3)*c2^2 + x1^3 + c1^2*x3 - (x1*x2 - x3)*c1 - ((x1*x2 - x3)*c1^2 - (x1^3 - x1*x2 + x3)*c1 + x1*x2 - x3)*c2 - 2*x1*x2 + x3)), then it works and I get (x1^3-2*x1*x2+x3)*e[] + (-x1*x2+x3)*e[1] + x3*e[1, 1] + (x1^3-x1*x2-x3)*e[2] + (-x1*x2+x3)*e[2, 1] + (x1^3-2*x1*x2+x3)*e[2, 2] + (3*x1*x2-3*x3)*e[3] + (-2*x1^3+4*x1*x2-2*x3)*e[3, 1] + (2*x1^3-4*x1*x2+2*x3)*e[4] as expected. Can somebody help me understand what is going on here? -- 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: Possible bug in algebraic_immunity( ) function in crypto toolbox
Yes, I agree with this statement. However, this is not useful. Suppose I
(as an user) want to find an annihilator of f (only f). I alway must
write a cycle to find degree and corresponding function.
I propose to add an option to annihilator which will allow return the
function with smallest degree. And one more option, which returns all
annihilators instead of one function.
On Wednesday, August 21, 2013 7:57:17 AM UTC+2, Yann wrote:
From the doc of .algebraic_immunity :
Returns the algebraic immunity of the Boolean function. This is the
smallest integer i such that there exists a non trivial annihilator
for self or ~self.
The annihilator you get is for ~f1 (or if you prefer 1+f1)
You can check that: (1+f1)*annihilator_f1 == 0
Best regards
Le mardi 20 août 2013 20:01:03 UTC+2, Martin Albrecht a écrit :
Hi Yann,
I believe you are the original author of this code?
Cheers,
Martin
-- Forwarded Message --
Subject: [sage-support] Re: Possible bug in algebraic_immunity( )
function in
crypto toolbox
Date: Tuesday 20 August 2013, 08:54:18
From: Oleksandr Kazymyrov vrona.ak...@gmail.com
To: sage-s...@googlegroups.com
I have the same problem.
My output (Mac OS 10.8.4 with sage 5.11) for
#!/usr/bin/env sage
from sage.crypto.boolean_function import BooleanFunction
P = BooleanPolynomialRing(4,'x')
P.inject_variables()
f = BooleanFunction(x0*x2 + x2*x3 + 1)
print f.algebraic_immunity() = {0}.format(f.algebraic_immunity())
print f.annihilator(f.algebraic_immunity()) =
{0}.format(f.annihilator(f.algebraic_immunity()))
print f.algebraic_immunity(annihilator=True) =
{0}.format(f.algebraic_immunity(annihilator=True))
g = BooleanFunction(f.algebraic_immunity(annihilator=True)[1])
print f = {0}.format(f.algebraic_normal_form())
print g = {0}.format(g.algebraic_normal_form())
print g*f =
{0}.format(g.algebraic_normal_form()*f.algebraic_normal_form())
is
Defining x0, x1, x2, x3
f.algebraic_immunity() = 1
f.annihilator(f.algebraic_immunity()) = None
f.algebraic_immunity(annihilator=True) = (1, x2 + 1)
f = x0*x2 + x2*x3 + 1
g = x2 + 1
g*f = x2 + 1
Therefore algebraic_immunity returns wrong degree. g*f = 0 for degree 2,
which is the correct answer.
On Tuesday, February 12, 2013 6:35:05 PM UTC+1, akhil wrote:
Hello,
SAGE returns an incorrect annihilator when
algebraic_immunity(annihilator
= True) is used in the following code:
from sage.crypto.boolean_function import BooleanFunction
R = BooleanPolynomialRing(4,'x')
f1 = R.gen(0)*R.gen(1)*R.gen(2) + R.gen(0)*R.gen(1)*R.gen(3) +
R.gen(0)*R.gen(2)*R.gen(3) + R.gen(1)*R.gen(2)*R.gen(3) + 1
annihilator_f1 = BooleanFunction(f1).algebraic_immunity(annihilator =
True)[1]
print (annihilator_f1 * f1)
annihilator_f1 is incorrect, because the response comes as:
x0 + x1 + x2 + x3 + 1
and not 0 as expected.
The annihilator( ) function however, returns the correct answer, as
checked with the following code:
for i in range(1,f1.total_degree() + 1):
if BooleanFunction(f1).annihilator(i) == None:
continue
else:
p = BooleanFunction(f1).annihilator(i)
print p
print (p*f1 == 0)
break
Output:
x0*x1*x2 + x1*x2*x3
True
The above code was written in online notebook version of SAGE.
Thanks,
AKHIL.
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-
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=getsearch=0x6532AFB4
_otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF
_www: http://martinralbrecht.wordpress.com/
_jab: martinr...@jabber.ccc.de
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[sage-support] Label of vertices
How can I get a graph with two vertices and one label? I want to create something like thishttp://upload.wikimedia.org/wikipedia/commons/9/91/BDD.png . -- 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/groups/opt_out.
[sage-support] Re: Possible bug in algebraic_immunity( ) function in crypto toolbox
I have the same problem.
My output (Mac OS 10.8.4 with sage 5.11) for
#!/usr/bin/env sage
from sage.crypto.boolean_function import BooleanFunction
P = BooleanPolynomialRing(4,'x')
P.inject_variables()
f = BooleanFunction(x0*x2 + x2*x3 + 1)
print f.algebraic_immunity() = {0}.format(f.algebraic_immunity())
print f.annihilator(f.algebraic_immunity()) =
{0}.format(f.annihilator(f.algebraic_immunity()))
print f.algebraic_immunity(annihilator=True) =
{0}.format(f.algebraic_immunity(annihilator=True))
g = BooleanFunction(f.algebraic_immunity(annihilator=True)[1])
print f = {0}.format(f.algebraic_normal_form())
print g = {0}.format(g.algebraic_normal_form())
print g*f =
{0}.format(g.algebraic_normal_form()*f.algebraic_normal_form())
is
Defining x0, x1, x2, x3
f.algebraic_immunity() = 1
f.annihilator(f.algebraic_immunity()) = None
f.algebraic_immunity(annihilator=True) = (1, x2 + 1)
f = x0*x2 + x2*x3 + 1
g = x2 + 1
g*f = x2 + 1
Therefore algebraic_immunity returns wrong degree. g*f = 0 for degree 2,
which is the correct answer.
On Tuesday, February 12, 2013 6:35:05 PM UTC+1, akhil wrote:
Hello,
SAGE returns an incorrect annihilator when algebraic_immunity(annihilator
= True) is used in the following code:
from sage.crypto.boolean_function import BooleanFunction
R = BooleanPolynomialRing(4,'x')
f1 = R.gen(0)*R.gen(1)*R.gen(2) + R.gen(0)*R.gen(1)*R.gen(3) +
R.gen(0)*R.gen(2)*R.gen(3) + R.gen(1)*R.gen(2)*R.gen(3) + 1
annihilator_f1 = BooleanFunction(f1).algebraic_immunity(annihilator =
True)[1]
print (annihilator_f1 * f1)
annihilator_f1 is incorrect, because the response comes as:
x0 + x1 + x2 + x3 + 1
and not 0 as expected.
The annihilator( ) function however, returns the correct answer, as
checked with the following code:
for i in range(1,f1.total_degree() + 1):
if BooleanFunction(f1).annihilator(i) == None:
continue
else:
p = BooleanFunction(f1).annihilator(i)
print p
print (p*f1 == 0)
break
Output:
x0*x1*x2 + x1*x2*x3
True
The above code was written in online notebook version of SAGE.
Thanks,
AKHIL.
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Main.sage
Description: Binary data
[sage-support] Binary decision diagrams
Hi all, Could I receive a binary decision diagrams for a boolean function? I saw some information here http://planet.sagemath.org/, but I'm not sure that she (they) do the same what I need. -- 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/groups/opt_out.
[sage-support] How to build documentation for separate files?
I have a class and want to generate html page with the description of functions (like thathttp://www.sagemath.org/doc/reference/cryptography/sage/crypto/mq/sbox.html)). How to do this? P.S. I know that examples inside the description (for separate files) can be tested by sage -t filename. Is it possible to produce the output in html or pdf in the same way? -- 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/groups/opt_out.
[sage-support] Re: How to build documentation for separate files?
Thanks, it should work. However, it would be great to add such functionality to sage. On Wednesday, August 14, 2013 5:31:28 PM UTC+2, Volker Braun wrote: Afaik there is no simple one-command solution. But its relatively easy to take the Sage docbuilder minus the parallelism stuff and just process your own rst. I did this here: https://github.com/sagemath/git-developer-guide On Wednesday, August 14, 2013 4:10:29 PM UTC+1, Oleksandr Kazymyrov wrote: I have a class and want to generate html page with the description of functions (like thathttp://www.sagemath.org/doc/reference/cryptography/sage/crypto/mq/sbox.html)). How to do this? P.S. I know that examples inside the description (for separate files) can be tested by sage -t filename. Is it possible to produce the output in html or pdf in the same way? -- 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/groups/opt_out.
[sage-support] Re: power representation of finite field elements
Today is easiest way and *secure* to use multiplicative_generator function:
sage: K=GF(2^4,'a')
sage: K
Finite Field in a of size 2^4
sage: b=K.random_element()
sage: b.log(K.multiplicative_generator())
14
sage: K.multiplib.log(K.multiplicative_generator())
K.multiplication_table K.multiplicative_generator
sage: K.multiplicative_generator()^b.log(K.multiplicative_generator()) == b
True
Because the function log_repr() works only in some special cases.
sage: K=GF(2^4,'a',modulus=ZZ['x']('x^4 + x^3 + x^2 + x + 1'));
sage: K.list()
[0, a + 1, a^2 + 1, a^3 + a^2 + a + 1, a^3 + a^2 + a, a^3 + a^2 + 1, a^3,
a^2 + a + 1, a^3 + 1, a^2, a^3 + a^2, a^3 + a + 1, a, a^2 + a, a^3 + a, 1]
sage: b=K.random_element()
sage: b
a^3 + a
sage: b.log_repr()
'14'
sage: b^ZZ(b.log_repr()) == b
False
sage: K.multiplicative_generator()
a^2 + a + 1
sage: K.multiplicative_generator()^ZZ(b.log(K.multiplicative_generator()))
== b
True
On Monday, September 17, 2012 11:07:58 PM UTC+2, Mike OS wrote:
HI
I was asking myself this question and couldn't find an answer in the
documentation, not
in past posts (which is how I found this email).
So I re-ask the question is there a way to have finite field elements
printed as powers of the primitive element?
Thanks
Mike
On Saturday, October 31, 2009 2:34:38 AM UTC-7, Kwankyu wrote:
Hi,
Is it possible to get elements of a finite field printed as powers of
a primitive element if the modulus is a primitive polynomial? That
will save a lot of screen space.
Kwankyu
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[sage-support] Re: Modulus operation in PolynomialRing with many variables
I have found the way how to fix it. If I use order 'deglex' P=PolynomialRing(GF(2^8,'a'),['x','c','b'],order='deglex') the result looks like correct sage: f.mod(x^2+1) (a^7 + a^6 + a^5 + 1)*x*c^3*b + (a^7 + a^4 + a^3 + a^2 + a + 1)*x*c*b^6 + (a ^7 + a^5 + a)*c^5*b + (a^7 + a^6 + a^5 + a^4 + a^3 + a^2 + 1)*c*b^2 + (a^6 +a ^4 + a + 1)*b But in general case I think that it is bug. On Wednesday, August 1, 2012 10:13:22 PM UTC+2, Oleksandr Kazymyrov wrote: How to get polynomial by modulus in PolynomialRing with many variables? sage: P=PolynomialRing(GF(2^8,'a'),['x','b','c']) sage: f=P.random_element(8) sage: f (a^7 + a^4 + a^3 + a^2 + a + 1)*x*b^6*c + (a^6 + a^4 + a + 1)*x^6*b + (a^7 + a^5 + a)*b*c^5 + (a^7 + a^6 + a^5 + a^4 + a^3 + a^2 + 1)*x^2*b^2*c + (a^7 + a^6 + a^5 + 1)*x*b*c^3 sage: f.mod(P(x^2+1)) (a^7 + a^4 + a^3 + a^2 + a + 1)*x*b^6*c + (a^6 + a^4 + a + 1)*x^6*b + (a^7 + a^5 + a)*b*c^5 + (a^7 + a^6 + a^5 + a^4 + a^3 + a^2 + 1)*x^2*b^2*c + (a^7 + a^6 + a^5 + 1)*x*b*c^3 I expect that all monomials have degree at most 1. -- -- 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] Modulus operation in PolynomialRing with many variables
How to get polynomial by modulus in PolynomialRing with many variables? sage: P=PolynomialRing(GF(2^8,'a'),['x','b','c']) sage: f=P.random_element(8) sage: f (a^7 + a^4 + a^3 + a^2 + a + 1)*x*b^6*c + (a^6 + a^4 + a + 1)*x^6*b + (a^7 + a^5 + a)*b*c^5 + (a^7 + a^6 + a^5 + a^4 + a^3 + a^2 + 1)*x^2*b^2*c + (a^7 + a^6 + a^5 + 1)*x*b*c^3 sage: f.mod(P(x^2+1)) (a^7 + a^4 + a^3 + a^2 + a + 1)*x*b^6*c + (a^6 + a^4 + a + 1)*x^6*b + (a^7 + a^5 + a)*b*c^5 + (a^7 + a^6 + a^5 + a^4 + a^3 + a^2 + 1)*x^2*b^2*c + (a^7 + a^6 + a^5 + 1)*x*b*c^3 I expect that all monomials have degree at most 1. -- -- 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: slow symbolic computation
Hi, I have the same problem: sage: time floor(log(4)/log(2)) 2 Time: CPU 7.04 s, Wall: 7.05 s But you can use n() before floor: sage: time floor(log(4).n()/log(2).n()) 2 Time: CPU 0.00 s, Wall: 0.00 s It should help you. Regards, Oleksandr On Friday, June 22, 2012 1:19:55 PM UTC+2, dmharvey wrote: -- | Sage Version 5.0, Release Date: 2012-05-14 | | Type notebook() for the GUI, and license() for information.| -- sage: time floor(log(4)/log(2)) 2 Time: CPU 1.07 s, Wall: 1.07 s sage: time floor(log(4)/log(2)) 2 Time: CPU 1.07 s, Wall: 1.07 s This seems very slow to me. Am I doing something wrong? david -- 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: Error message when use vectors in Sage 5 with Ubuntu 12.04...
Hi, I haven't the problem on Ubuntu 12.04: sage: vector( [-1,2] ) (-1, 2) sage: version() 'Sage Version 5.0, Release Date: 2012-05-14' sage: exit Exiting Sage (CPU time 0m1.48s, Wall time 0m18.12s). hamsin@hamsin:~$ uname -a Linux hamsin 3.2.0-25-generic #40-Ubuntu SMP Wed May 23 20:33:05 UTC 2012 i686 i686 i386 GNU/Linux and sage: vector( [-1,2] ) (-1, 2) sage: version() 'Sage Version 5.0.1, Release Date: 2012-06-10' hamsin@hamsin-PC:~$ uname -a Linux hamsin-PC 3.2.0-25-generic #40-Ubuntu SMP Wed May 23 20:30:51 UTC 2012 x86_64 x86_64 x86_64 GNU/Linux Regards, Oleksandr On Sunday, June 17, 2012 4:13:05 AM UTC+2, Chris Seberino wrote: I installed Ubuntu 12.04 about 2 weeks ago along with Sage 5. I just now tried using vectors for the first time and got this error... sage: vector( [-1,2] ) --- AttributeErrorTraceback (most recent call last) /home/cs/Ws/Lone_Star/1401/Exams/ipython console in module() /usr/local/sage-5.0-linux-32bit-ubuntu_12.04_lts-i686-Linux/local/lib/python2.7/site-packages/sage/modules/free_module_element.so in sage.modules.free_module_element.vector (sage/modules/free_module_element.c:3789)() /usr/local/sage-5.0-linux-32bit-ubuntu_12.04_lts-i686-Linux/local/lib/python2.7/site-packages/numpy/__init__.py in module() 134 return loader(*packages, **options) 135 -- 136 import add_newdocs 137 __all__ = ['add_newdocs'] 138 /usr/local/sage-5.0-linux-32bit-ubuntu_12.04_lts-i686-Linux/local/lib/python2.7/site-packages/numpy/add_newdocs.py in module() 7 # core/fromnumeric.py, core/defmatrix.py up-to-date. 8 9 from numpy.lib import add_newdoc 10 11 ### /usr/local/sage-5.0-linux-32bit-ubuntu_12.04_lts-i686-Linux/local/lib/python2.7/site-packages/numpy/lib/__init__.py in module() 11 12 import scimath as emath --- 13 from polynomial import * 14 #import convertcode 15 from utils import * /usr/local/sage-5.0-linux-32bit-ubuntu_12.04_lts-i686-Linux/local/lib/python2.7/site-packages/numpy/lib/polynomial.py in module() 9 import re 10 import warnings --- 11 import numpy.core.numeric as NX 12 13 from numpy.core import isscalar, abs, finfo, atleast_1d, hstack AttributeError: 'module' object has no attribute 'core' sage: -- 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] Polynomial representation over GF(2^n)
Hi all,
Continuing the
questionhttps://groups.google.com/forum/?fromgroups#!topic/sage-support/cvtz4Zh-WYQ
...
Input data:
sage: K=GF(2^8,'a',modulus=ZZ['x'](x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1))
sage: K.multiplicative_generator()
a^4 + a^3 + a
sage: P=PolynomialRing(K,'x')
sage: pol=P.random_element(5)
sage: pol
(a^7 + a^5 + a^3 + 1)*x^5 + (a^5 + a^4 + a^3 + a^2 + a + 1)*x^4 + (a^7 +
a^3 + a^2 + a)*x^3 + (a^5 + a^2)*x^2 + (a^6 + a^5 + a^4 + 1)*x + a^3
1. How to represent *pol *using multiplicative generator? The output must
be b^(i1)*x^5 + b^(i2)*x^4 + b^(i3)*x^3 + b^(i4)*x^2 + b^(i5)*x + a^3,
where b = K.multiplicative_generator(), i1-i5 logarithmic representation of
(a^7
+ a^5 + a^3 + 1), (a^5 + a^4 + a^3 + a^2 + a + 1)...
I have a correct function:
sage: b=K.multiplicative_generator()
sage: P([({0})^{1}.format(b,i.log(b)) for i in pol.coeffs()]) == pol
True
sage: [({0})^{1}.format(b,i.log(b)) for i in pol.coeffs()]
['(a^4 + a^3 + a)^27', '(a^4 + a^3 + a)^234', '(a^4 + a^3 + a)^195', '(a^4
+ a^3 + a)^134', '(a^4 + a^3 + a)^79', '(a^4 + a^3 + a)^101']
If I have one program then the above method suits me. But if two, i.e. one
program represents polynomial in the form b^(i1)*x^5 ... and returns b and
another program tries to restore it, then I worry about the phrase
The docs for multiplicative_generator() say: return a generator of
the multiplicative group, then add Warning: This generator might
change from one version of Sage to another.
2. So the question is how to uniquely reconstruct the original *pol*, if I
have *modulus*, *multiplicative generator *and* representation of pol as *
b^(i1)*x^5...?
Regards,
Oleksandr
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[sage-support] Re: Polynomial representation over GF(2^n)
And one more.
The following is quite strange:
sage: K=GF(2^8,'a',modulus=ZZ['x'](x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1))
sage: b=K.multiplicative_generator()
sage: c=K(0)
sage: c.log(b)
0
sage: c=K(1)
sage: c.log(b)
0
How to determine when c is 0 and when 1? Perhaps log should return
-1 for finite fields when c=0?
Kind regards,
Oleksandr
On Wednesday, June 13, 2012 3:02:46 PM UTC+2, Oleksandr Kazymyrov wrote:
Hi all,
Continuing the
questionhttps://groups.google.com/forum/?fromgroups#!topic/sage-support/cvtz4Zh-WYQ
...
Input data:
sage: K=GF(2^8,'a',modulus=ZZ['x'](x^8 + x^7 + x^6 + x^4 + x^3 + x^2 +
1))
sage: K.multiplicative_generator()
a^4 + a^3 + a
sage: P=PolynomialRing(K,'x')
sage: pol=P.random_element(5)
sage: pol
(a^7 + a^5 + a^3 + 1)*x^5 + (a^5 + a^4 + a^3 + a^2 + a + 1)*x^4 + (a^7 +
a^3 + a^2 + a)*x^3 + (a^5 + a^2)*x^2 + (a^6 + a^5 + a^4 + 1)*x + a^3
1. How to represent *pol *using multiplicative generator? The output must
be b^(i1)*x^5 + b^(i2)*x^4 + b^(i3)*x^3 + b^(i4)*x^2 + b^(i5)*x + a^3,
where b = K.multiplicative_generator(), i1-i5 logarithmic representation of
(a^7
+ a^5 + a^3 + 1), (a^5 + a^4 + a^3 + a^2 + a + 1)...
I have a correct function:
sage: b=K.multiplicative_generator()
sage: P([({0})^{1}.format(b,i.log(b)) for i in pol.coeffs()]) == pol
True
sage: [({0})^{1}.format(b,i.log(b)) for i in pol.coeffs()]
['(a^4 + a^3 + a)^27', '(a^4 + a^3 + a)^234', '(a^4 + a^3 + a)^195', '(a^4
+ a^3 + a)^134', '(a^4 + a^3 + a)^79', '(a^4 + a^3 + a)^101']
If I have one program then the above method suits me. But if two, i.e. one
program represents polynomial in the form b^(i1)*x^5 ... and returns b and
another program tries to restore it, then I worry about the phrase
The docs for multiplicative_generator() say: return a generator of
the multiplicative group, then add Warning: This generator might
change from one version of Sage to another.
2. So the question is how to uniquely reconstruct the original *pol*, if
I have *modulus*, *multiplicative generator *and* representation of pol
as *b^(i1)*x^5...?
Regards,
Oleksandr
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[sage-support] Isomorphism of Linear Codes
Hi all, I have next code for checking CCZ-equivalence of two vectorial Boolean functions in magma: n:=7; GF:= FiniteField(2,n); a:=PrimitiveElement(GF); // returns the linear Code with columns (1,x,f(x)) function CF(f) M:=Matrix( 2*n+1, 2^n, [1: x in GF] cat [Trace(a^i * x): x in GF, i in [1..n ]] cat [Trace(a^i * f(x)): x in GF, i in [1..n]]); return LinearCode( M ); end function; f:=funcx | x^3 ; g:=funcx | x^5 ; if IsIsomorphic(CF(f),CF(g)) eq false then f and g are NOT equivalent; else f and g are equivalent ; end if; I can't find analogue of IsIsomorphic in sage.It is the main problem of converting code to sage. Is sage has similar function? Or how to implement it? Best regards, Oleksandr -- 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] Isomorphism of Linear Codes
It seems to be true. But are your sure that functions are equivalent? On Thursday, June 7, 2012 5:05:11 PM UTC+2, David Joyner wrote: On Thu, Jun 7, 2012 at 10:13 AM, Oleksandr Kazymyrov Hi all, I have next code for checking CCZ-equivalence of two vectorial Boolean functions in magma: n:=7; GF:= FiniteField(2,n); a:=PrimitiveElement(GF); // returns the linear Code with columns (1,x,f(x)) function CF(f) M:=Matrix( 2*n+1, 2^n, [1: x in GF] cat [Trace(a^i * x): x in GF, i in [1..n]] cat [Trace(a^i * f(x)): x in GF, i in [1..n]]); return LinearCode( M ); end function; f:=funcx | x^3 ; g:=funcx | x^5 ; if IsIsomorphic(CF(f),CF(g)) eq false then f and g are NOT equivalent; else f and g are equivalent ; end if; I can't find analogue of IsIsomorphic in sage.It is the main problem of converting code to sage. Is sage has similar function? Or how to implement it? Do you want something like the LinearCode method is_permutation_equivalent? Best regards, Oleksandr -- 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 -- 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: Crash report: integral of ln(1+4/5*sin(x)) crashes Maxima and Sage
I have the same problem on: sage: version() 'Sage Version 5.0, Release Date: 2012-05-14' hamsin@hamsin-PC:~$ uname -a Linux hamsin-PC 3.2.0-24-generic #39-Ubuntu SMP Mon May 21 16:52:17 UTC 2012 x86_64 x86_64 x86_64 GNU/Linux On Thursday, June 7, 2012 11:13:44 PM UTC+2, Benjamin Jones wrote: On Mac OS X 10.6.8 intel core i7 and sage-5.0 (also sage-5.1.beta2) I can crash sage (and Maxima) by evaluating: sage: integrate(ln(1+4/5*sin(x)), x, -3.1415, 3.1415) ;;; ;;; Binding stack overflow. ;;; Jumping to the outermost toplevel prompt ;;; ... ;;; ;;; Binding stack overflow. ;;; Jumping to the outermost toplevel prompt ;;; /Users/jonesbe/sage/sage-5.1.beta2/spkg/bin/sage: line 335: 86594 Illegalinstruction sage -ipython $@ -i The same happens with the indefinite integral and the exact definite integral from -pi to pi. Has anyone seen similar crashes using sage-5.0 or earlier? -- 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] Generator of Finite Field
I have used log_repr() and expect that it return y of equation x^y = z. I also believed hat k.gen() return generator of the field. Now I must use following construction for solving my problem sage: R.x=ZZ[] sage: k=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1) sage: a = k.multiplicative_generator() sage: a^ZZ(k(ZZ(3).digits(2)).log(a)) == k(ZZ(3).digits(2)) By the way, any of next functions don't return the value y of equation x^y=z sage: b=K(ZZ(3).digits(2)) sage: b a + 1 sage: b.log_repr() '1' sage: b.log_to_int() 3 I think that log_repr() should has the same logic as int_repr() or integer_representation(), i.e. sage: a=K.multiplicative_generator() sage: ZZ(K(ZZ(3).digits(2)).log(a)) 164 What do you think? Kind regards, Oleksandr On Tuesday, May 29, 2012 12:52:16 PM UTC+3, AlexGhitza wrote: Hi, On Mon, May 21, 2012 at 9:29 AM, Oleksandr Kazymyrov vrona.aka.ham...@gmail.com wrote: I have encountered the following problem In Sage 5.0: sage: R.x=ZZ[] sage: k=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1) sage: k(ZZ(3).digits(2)) a + 1 sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr()) a sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2)) False sage: k(a+1)^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2)) True It easy see that k.gen() or k.multiplicative_generator() is not a generator of the finite field: sage: k.multiplicative_generator() a^4 + a + 1 Why is it clear that a^4+a+1 is not a multiplicative generator? I think it is: sage: k.a = GF(2^8, names='a', name='a', modulus=x^8+x^4+x^3+x+1) sage: (a^4+a+1).multiplicative_order() 255 Indeed, so is a+1: sage: (a+1).multiplicative_order() 255 The docs for multiplicative_generator() say: return a generator of the multiplicative group, then add Warning: This generator might change from one version of Sage to another. -- Best, Alex -- Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne http://aghitza.org -- 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: Methods in GF
Hi, I agree with Martin, especially about private methods. sage: k.some_elements ? ... Returns a collection of elements of this finite field *for use in unit testing.* The function is indeed used in unitests as confirmed by search_src(some_elements). Perhaps it should start with an underscore? In my opinion it must start with an underscore. The method k.random_element() return a random element and it is enough for users. 2. Also a few misunderstanding functions - sage: *k.cardinality* ? Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method cardinality of FiniteField_givaro_with_category object at 0xbb0eaac Namespace: Interactive Definition: k.cardinality(self) Docstring: Return the order of this finite field (*same as self.order()*). Why is this confusing? I can't understand the confusion either. Some people say order and some people say cardinality when they refer to the number of elements of a group or field. Personally, I'd tend to say cardinality in the case of a set (but a field *is* as set!), and order in the case of a field or group. But why shouldn't one offer both, if both is used by people? In most of books Finite Fields you can find definition order (imho). But if some use it, then it's no problem. In general I can't understand why it is important to have two (or more) functions with the same functionality in user space. If some of them are used for compatibility, then maybe they should be private? - sage: *k.ngens* *?* Docstring: The number of generators of the finite field. * Always 1.* This is a generic function provided for compatibility with other parents in Sage. At that point one should mention duck typing, I guess. Sometimes one writes generic code, that is supposed to work with various kinds of objects, and the type of these objects does not (and should not) matter. In some cases, all what one wants to know is whether the object is defined in terms of generators (e.g., a polynomial ring is, but a set is not), and how many generators there are. ngens() answers both questions. Ok, but the finite field has a set of generators. I'm a bit confused. sage: R.x=ZZ[] sage: K=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1) sage: m=[i.multiplicative_order() for i in K if i != 0] sage: m.count(255) 128 Anyway, do you want to provide (documentation) patches for the issues you discovered? My English is not so good for documentation, but I can provide some code (logic and programming) patches after my registration at trac.sagemath.org. -- 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: Generator of Finite Field
Hi again, A try to use *log* function and got error: sage: R.x=ZZ[] sage: k.a=GF(2^8,modulus=x^8+x^4+x^3+x+1) sage: b=k.random_element() sage: b.log(a) --- ValueErrorTraceback (most recent call last) /home/hamsin/ipython console in module() /home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/rings/finite_rings/element_givaro.so in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement.log (sage/rings/finite_rings/element_givaro.cpp:11248)() /home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/groups/generic.pyc in discrete_log(a, base, ord, bounds, operation, identity, inverse, op) 814 return CRT_list(l,[pi**ri for pi,ri in f]) 815 except ValueError: -- 816 raise ValueError, No discrete log of %s found to base %s%(a,base) 817 818 def discrete_log_generic(a, base, ord=None, bounds=None, operation='*', identity=None, inverse=None, op=None): ValueError: No discrete log of a^7 + a^6 + a^5 + a^4 + a^2 + 1 found to base a I also found some strangeness: sage: m=[a^i for i in xrange(255)] sage: m.append(0) sage: len(set(m)) 52 But last value must be 256, if *a *is a generator. So *k.gens() *returns wrong value. P.S. sage: version() 'Sage Version 5.0, Release Date: 2012-05-14' On Monday, May 21, 2012 1:29:29 AM UTC+2, Oleksandr Kazymyrov wrote: Hello all. I have encountered the following problem In Sage 5.0: sage: R.x=ZZ[] sage: k=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1) sage: k(ZZ(3).digits(2)) a + 1 sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr()) a sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2)) False sage: *k(a+1)*^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2)) True It easy see that k.gen() or k.multiplicative_generator() is not a generator of the finite field: sage: k.multiplicative_generator() a^4 + a + 1 sage: k.gen() a sage: k.list() [0, a + 1, a^2 + 1, a^3 + a^2 + a + 1, a^4 + 1, a^5 + a^4 + a + 1, a^6 + a^4 + a^2 + 1, ... ] Generator is a+1! How to get generator of Finite Field? It was fine in Sage 4.8. Ubuntu 12.04 Linux hamsin 3.2.0-24-generic #37-Ubuntu SMP Wed Apr 25 08:43:52 UTC 2012 i686 i686 i386 GNU/Linux Best regards, Oleksandr -- 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] Generator of Finite Field
Hello all. I have encountered the following problem In Sage 5.0: sage: R.x=ZZ[] sage: k=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1) sage: k(ZZ(3).digits(2)) a + 1 sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr()) a sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2)) False sage: *k(a+1)*^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2)) True It easy see that k.gen() or k.multiplicative_generator() is not a generator of the finite field: sage: k.multiplicative_generator() a^4 + a + 1 sage: k.gen() a sage: k.list() [0, a + 1, a^2 + 1, a^3 + a^2 + a + 1, a^4 + 1, a^5 + a^4 + a + 1, a^6 + a^4 + a^2 + 1, ... ] Generator is a+1! How to get generator of Finite Field? It was fine in Sage 4.8. Ubuntu 12.04 Linux hamsin 3.2.0-24-generic #37-Ubuntu SMP Wed Apr 25 08:43:52 UTC 2012 i686 i686 i386 GNU/Linux Best regards, Oleksandr -- 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] Methods in GF
Dear all, 1. Why important next functions? k.a_times_b_minus_c k.a_times_b_plus_c k.c_minus_a_times_b sage: k.some_elements ? ... Returns a collection of elements of this finite field *for use in unit testing.* Why this function are defined as public? 2. Also a few misunderstanding functions - sage: *k.cardinality* ? Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method cardinality of FiniteField_givaro_with_category object at 0xbb0eaac Namespace: Interactive Definition: k.cardinality(self) Docstring: Return the order of this finite field (*same as self.order()*). - sage: *k.cayley_graph() * --- AttributeErrorTraceback (most recent call last) /home/hamsin/ipython console in module() /home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/categories/semigroups.pyc in cayley_graph(self, side, simple, elements, generators, connecting_set) 284 generators = connecting_set 285 if generators is None: -- 286 generators = self.semigroup_generators() 287 if isinstance(generators, (list, tuple)): 288 generators = dict((self(g), self(g)) for g in generators) /home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__getattr__ (sage/structure/parent.c:6805)() /home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.getattr_from_other_class (sage/structure/parent.c:3248)() AttributeError: 'FiniteField_givaro_with_category' object has no attribute 'semigroup_generators' - sage: *k.has_base()* *True* sage: *k.has_base* ? Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method has_base of FiniteField_givaro_with_category object at 0xbb0eaac Namespace: Interactive Definition: k.has_base(self, category=None) *??* * * - sage: *k.ngens* *?* Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method ngens of FiniteField_givaro_with_category object at 0xbb0eaac Namespace: Interactive Definition: k.ngens(self) Docstring: The number of generators of the finite field. * Always 1.* * * - sage: *k.normalize_names ?* Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method normalize_names of FiniteField_givaro_with_category object at 0xbb0eaac Namespace: Interactive Definition: k.normalize_names(self, ngens, names=None) sage: k.normalize_names() --- TypeError Traceback (most recent call last) /home/hamsin/ipython console in module() /home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/structure/category_object.so in sage.structure.category_object.CategoryObject.normalize_names (sage/structure/category_object.c:3939)() TypeError: normalize_names() takes at least 1 positional argument (0 given) sage: k.normalize_names(1) *??* * * - sage: *k.on* k.one k.one_element sage: k.one ? Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method one_element of FiniteField_givaro_with_category object at 0xbb0eaac Namespace: Interactive Definition: k.one(self) Docstring: Return the one element of this ring (cached), if it exists. EXAMPLES: sage: ZZ.*one_element()* 1 sage: QQ.*one_element()* 1 sage: QQ['x'].*one_element()* 1 The result is cached: sage: ZZ.*one_element() *is *ZZ.one_element()* True - sage: *k.zero ? * Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method zero_element of FiniteField_givaro_with_category object at 0xbb0eaac Namespace: Interactive Definition: k.zero(self) Docstring: Return the zero element of this ring (cached). EXAMPLES: sage: *ZZ.zero_element()* 0 sage: *QQ.zero_element()* 0 sage: QQ['x'].*zero_element()* 0 The result is cached: sage: ZZ.*zero_element()* is ZZ.*zero_element()* True Definition of the field: sage: R.x=ZZ[] sage: k=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1) --
[sage-support] Re: Reserved words (Sage + Cython)
Hi Simon, Rename it, if that solves the problem. I have done it. But I wonder why has that happened after upgrade from 4.7.2 to 4.8 (5.0beta4)? Best regards, Oleksandr -- 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: Modular operation in multivariate polynomials
Hi Simon,
Do you have a trac account, or shall I open a trac ticket myself?
No, I havn't. If this is not a problem for you then open.
At the moment I use the following code:
pol=sum([g.mod(P(y^{0}+y.format(1bits))) for g in pol.monomials()])
Maybe it will help.
Best regards,
Oleksandr
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[sage-support] Re: Modular operation in multivariate polynomials
Hi Simon, I agree with you. My previous message is true only for GF(2^n). Best regards, Oleksandr -- 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] Reserved words (Sage + Cython)
Hi All, After upgrading from version 4.7.2 to 4.8, one function of dozen is stopped working. I use a combination of Sage + Cython. You can find examples in the attachments. The main problem is: when you use PC as the function name in *.c file sage gives an error /home/hamsin/bin/sage/local/lib/libcsage.so(print_backtrace+0x31)[0x7f3c8b89e3a3] /home/hamsin/bin/sage/local/lib/libcsage.so(sigdie+0x14)[0x7f3c8b89e3d5] /home/hamsin/bin/sage/local/lib/libcsage.so(sage_signal_handler+0x20e)[0x7f3c8b89e000] /lib/x86_64-linux-gnu/libpthread.so.0(+0x10060)[0x7f3c8dc93060] /home/hamsin/bin/sage/local/lib/libreadline.so.6(PC+0x0)[0x7f3c861f83cc] Unhandled SIGSEGV: A segmentation fault occurred in Sage. This probably occurred because a *compiled* component of Sage has a bug in it and is not properly wrapped with sig_on(), sig_off(). You might want to run Sage under gdb with 'sage -gdb' to debug this. Sage will now terminate. local/bin/sage-sage: line 460: 10163 Segmentation fault python $@ If I use PCc or PC_1, then there are no problems. So this is a bug, feature or Cython has limitations on function names. If the last point, then where I can see this limitations. Best regards, Oleksandr Machine: linux: Linux pcen 3.0.0-16-generic #28-Ubuntu SMP Fri Jan 27 17:44:39 UTC 2012 x86_64 x86_64 x86_64 GNU/Linux sage: 'Sage Version 4.8, Release Date: 2012-01-20' -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org Cython_bad.tar.gz Description: Binary data Cython_good.tar.gz Description: Binary data
[sage-support] Re: Reserved words (Sage + Cython)
Dear Simon, But the only difference between the good and the bad version is that some function is called PC in the bad file and PCc in the good file Yes, exactly. However, Oleksandr: What is one supposed to do in order to reproduce the error? When I start a sage session and attach Main.sage, then it fails with both the bad and the good version. You should replace: if __name__ == __main__: sys.exit(main()) by main() Or just run Main.sage from a shell (in this case, variable PATH should has a path to the sage directory, like this one PATH=/home/user/bin/sage/:$PATH). Best regards, Oleksandr -- 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: Modular operation in multivariate polynomials
Dear Simon, There is a difference between a polynomial (i.e., an element of a polynomial ring) and a polynomial function. Polynomials can be of arbitrary degree, over any coefficient field. Yes I know this. But I think there is no difference between defining of PolynomialRing and PolynomialQuotientRing, assuming that you independently perform the operation by modulus. I am forcing the call of a function pol.mod(P(y^8+y)) to obtain the remainder by modulus. And I expect that monomial y^10*a2*b1^10*p5^2 will has degree 3 (y^3*a2*b1^10*p5^2) after operation pol.mod(P(y^8+y)) in the polynomial. KInd regards, Oleksandr -- 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
