Hi,
On Wednesday 05 Aug 2015 23:35:26 Kwankyu wrote:
> Hi,
>
> I am learning to use the libSingular interface to use Singular functions in
> Sage. I have two questions.
>
> (1) My Singular procedures return multiple values, but my Sage function
> wrapping the procedure (via "singular_function")
Hi,
see here:
http://doc.sagemath.org/html/en/reference/sat/index.html#solvers
sage: from sage.sat.solvers.dimacs import DIMACS
sage: fn = tmp_filename()
sage: solver = DIMACS(filename=fn)
sage: solver.add_clause( ( 1, 2, 3) )
sage: solver.add_clause( ( 1, 2, -3) )
sage: _ = solver.write()
sa
Hi Peter,
variety() calls triangular_decomposition() which indeed changes the term
ordering for you if required:
# make sure to work w.r.t. 'lex'
if P.term_order() != 'lex':
Q = P.change_ring(order='lex')
else:
Q = P
So the documentation should be
Hi,
$ sage -i cryptominisat && sage -b
should do the trick.
Cheers,
Martin
On Monday 20 Apr 2015 07:01:00 Dibyendu Roy wrote:
> Dear Members,
>
> I want to install CryptoMiniSat 2.9.9. I have downloaded the latest file
> from https://gforge.inria.fr/frs/?group_id=1992. Could you please tell me
abf7158809cf4f3c'
>
> On Monday, March 16, 2015 at 11:59:52 PM UTC+1, Martin Albrecht wrote:
> > On Monday 16 Mar 2015 12:45:07 Joe Ouni wrote:
> > > Hello ,
> > >
> > > The following SR (2,1,1,4) worked fine.
> > >
> > >
On Monday 16 Mar 2015 12:45:07 Joe Ouni wrote:
> Hello ,
>
> The following SR (2,1,1,4) worked fine.
>
> sage: sr = SR(2,1,1,4,star=True,aes_mode=True,
> gf2=True,allow_zero_inversions = True)
> sage: P = sr.vector([0, 0, 1, 0])
>
> sage: K = sr.vector([1, 0, 0, 1])
> sage: C = sr(P,K)
> sage: l
Hi,
it seems you're running into a compiler bug:
libtool: compile: gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I./m4rie -I/home/alwi-
wheezy/sage-6.5/local/include -I/include -mmmx -msse -msse2 -msse3 -O2 -fPIC -
Wall -pedantic -g -I/home/alwi-wheezy/sage-6.5/local/include -MT
m4rie/conversion_cling16.
Hi,
try:
http://www.sagemath.org/doc/reference/sat/
Cheers,
Martin
PS: it's the first hit on Google when you search for "PolynomialSequence
DIMACS Sage". Just saying.
On Wednesday 28 Jan 2015 12:57:21 Juan Grados wrote:
> Dears members,
> I have a object PolynomialSequence in ANF.
>
> PF = P
sage: gp.qflll?
Type: GpFunction
String form:qflll
File: /opt/sage-devel/local/lib/python2.7/site-
packages/sage/interfaces/gp.py
Definition: gp.qflll(self, *args, **kwds)
Docstring:
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x
(gives the unimodul
Works for me:
sage: sr = mq.SR(1,1,1,4, gf2=True, polybori=True)
sage: K = sr.base_ring()
sage: a = K.gen()
sage: K = [a]
sage: P = [1]
sage: F,s = sr.polynomial_system(P=P, K=K)
sage: F.groebner_basis()
[k100, k101 + 1, k102, k103 + k003, x100 + 1, x101 + k003 + 1, x102 + k003 +
1, x103 + k003,
Your matrix is over GF(2) not over the symbolic ring SR:
sage: m1 = SR(GF(2)(1)) * var("m1")
sage: m2 = SR(GF(2)(1)) * var("m2")
sage: m3 = SR(GF(2)(1)) * var("m3")
sage: m4 = SR(GF(2)(1)) * var("m4")
sage: q = Matrix(SR, [
[m1, m2],
[m3, m4],
])
sage: q^2
[ m1^2 + m2*m3 m1*m2 + m2*m4]
[
This is a bug in Sage's finite field via NTL's GF2E implementation which is
triggered by M4RIE:
sage: K. = GF(2^15)
sage: type(K), type(matrix(K))
(sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro_with_category,
sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense)
sage: K. = GF(2^16
It means that the system is believed to be unsolvable.
On Wednesday 27 Aug 2014 13:54:47 Juan Grados wrote:
> Dear members,
>
> I'm trying to solve the attach formulas but I get FALSE, anyone know what
> means that, or Why I get FALSE?
>
> sage: solve_sat(PolynomialSequence(F,RR),n=infinity)
> F
This is a bug. In particular:
sage: S.solve(eliminate_linear_variables=False)
[{w: 0, z: 0, y: 0, x: 0}]
Does the trick. The bug is that eliminating linear variables already solves
the problem and the logic in solve() doesn't handle this case. Please open a
ticket and CC me.
On Tuesday 12 Aug
Why? These are different errors. One is (probably) an integer overflow, the
other a failure to allocate 2^30 something.
On Sunday 10 Aug 2014 04:38:52 pp wrote:
> Hi all,
>
> Consider the following code:
>
> NUM = 2
> R = BooleanPolynomialRing(NUM, ['x%d'%(i) for i in range(NUM)])
> expr = R('x
> this?
>
> On Saturday, December 22, 2012 9:16:31 AM UTC-8, Martin Albrecht wrote:
> > Pass a list of numbers instead of independent numbers. SBox( [1,2,3]) not
> > SBox(1,2,3)
> >
> > sent from a telephone.
> >
> > On 19 Dec 2012 08:17, "sea21&qu
On Saturday 07 Jun 2014 13:34:18 Volker Braun wrote:
> Afaik its only used in the openid module. And exploiting a timing attack
> over network is most likely not possible.
they are practical at least over LAN:
https://crypto.stanford.edu/~dabo/papers/ssl-timing.pdf
> On Saturday, June 7, 2014 8
ction is L.closest_vector(t) which uses
> Miccianchio-Voulgaris algorithm. Is there also another algorithm from
> fplll?
> thanks
>
> On Tuesday, May 13, 2014 8:37:25 PM UTC+3, Martin Albrecht wrote:
> > On Tuesday 13 May 2014 09:51:27 J.A. Ketch wrote:
> > > are the fo
Looks like a bug, can you open a ticket?
On Monday 19 May 2014 19:13:55 Grégory Landais wrote:
> Hello,
>
> evaluating a polynomial on a finite field does not work if the finite
> field was created with a 'repr' argument in the constructor different
> than the default one (poly).
>
> Curently us
On Tuesday 13 May 2014 09:51:27 J.A. Ketch wrote:
> are the following algorithms implemented in sage?
> enum algorithm (for svp and cvp)
fpLLL has enumeration for finding the shortest vector (the code for CVP is
experimental according to the docs). There's a ticket on trac implementing an
interf
Why not:
%time A = random_matrix(GF(4,'a'), 36, 10^6)
CPU times: user 568 ms, sys: 12 ms, total: 580 ms
Wall time: 578 ms
However, getting the rows out takes ages. The reason is that vectors over
GF(4) are generic, i.e. noone sat down and wrote up a simple class which
implements these vectors a
Hi Nils,
On Wednesday 07 May 2014 16:43:03 Nils Bruin wrote:
> On Wednesday, May 7, 2014 9:58:48 AM UTC-7, François Colas wrote:
> > What I want to do is a way to evaluate polynomials of K in a power of a
> > primitive square root of unity:
> >
> > omega = CC(e^(2*I*pi/m))
> > F = Hom(K, CC)
> >
Here's how to find out:
sage: P. = GF(2)[]
sage: f = P.random_element()
sage: f.is_irreducible??
if 0 == GF2X_IterIrredTest(self.x):
return False
else:
return True
Okay, what's GF2X_IterIrredTest?
sage: search_src("GF2X_IterIrredTest")
libs/ntl/ntl_GF2X_d
Hi,
just doing
sage: A = matrix(GF(2), 52751923, 39)
sage: A[i,j] = your entry
doesn't do the trick?
In this case: with extremely high probability this matrix has full rank, so
imply extract a, say, 1000 x 39 submatrix, compute Gaussian elimination on
that. The rest will be zero anyway.
On T
You'd write it like this:
sage: sage.rings.polynomial.toy_buchberger.buchberger??
G = set(F.gens())
B = set(filter(lambda (x,y): x!=y, [(g1,g2) for g1 in G for g2 in G]))
while B!=set():
g1,g2 = select(B)
B.remove( (g1,g2) )
h = spol(g1,g2).reduce(G)
attribute 'clauses'? If so, how may
> I go about doing it?
>
> Also, is there a possibility for multi-threading for CryptoMiniSat in Sage?
>
>
> Valerie
Cheers,
Martin
--
name: Martin Albrecht
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_otr: 47
age(package, force)
> 169 if not force:
> 170 if is_package_installed(package):
> --> 171 raise ValueError, "Package is already installed.
> Try install_package('%s',force=True)"%(package)
> 172 raise Value
fix it?
>
> It should be set to $SAGE_LOCAL/share/terminfo
--
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_www: http://martinralbrecht.wordpress.com/
_jab: martinralbre...@jabber.ccc.de
signature.a
Maybe there is some permission problem?
>
> On Thursday, August 22, 2013 10:32:46 PM UTC+1, Martin Albrecht wrote:
> > Hi Volker,
> >
> > here you go. Grepping through it nothing stood out ... I am not sure what
> > I am
> > looking for, though.
> >
>
perhaps note that I am on zsh if that makes a difference (?)
Cheers,
Martin
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signature.asc
Description: This is a digitally signed message part.
L. -lpanelw
> -lncursesw -lpython2.7 -o build/lib.linux-x86_64-2.7/_curses_panel.so ***
> WARNING: renaming "_curses_panel" since importing it failed:
> /lib64/libncursesw.so.5: undefined symbol: _nc_putchar
>
> On Thursday, August 22, 2013 2:22:50 PM UTC+1, Martin Albrec
/p/iterm2/issues/detail?id=1956
>
> On Thursday, August 22, 2013 1:56:09 PM UTC+1, Martin Albrecht wrote:
> > Hi all,
> >
> > with Sage 5.12.beta3 I get:
> >
> > sage: os.environ["TERM"]
> > 'xterm'
> > sage: ZZ?
> >
> >
wn"),
---> 33 fd=_sys.__stdout__.fileno())
34 stdscr = _curses.initscr()
35 for key, value in _curses.__dict__.items():
error: setupterm: could not find terminal
sage:
This is in konsole (KDE's console). Any ideas?
Cheers,
Martin
--
name: Martin Al
upport+unsubscr...@googlegroups.com.
To post to this group, send email to sage-support@googlegroups.com.
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-
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name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/loo
Hi all,
do we have n-dimensional numerical integration in Sage? All I can find is 3D,
but what about higher dimensions?
Cheers,
Martin
--
name: Martin Albrecht
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_www:
be input to the converter, along with the ANF expression).
>
> Please help if anybody can come up with a solution.
>
> Thanks a lot.
Cheers,
Martin
--
name: Martin Albrecht
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_otr: 47F43D1A 5D68C36F 468BAEBA 640E
leanPolynomialRing()
> f=a+b*c
Cheers,
Martin
--
name: Martin Albrecht
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_www: http://martinralbrecht.wordpress.com/
_jab: martinralbre...@jabber.ccc.de
--
You received thi
y^2 + z, z^3 + y^2])
>
> (z^3 + y^2, x^6 - y^2 + z) => 0
> G: set([x^6 - y^2 + z, z^3 + y^2])
>
> 2 reductions to zero.
> [x^6 - y^2 + z, z^3 + y^2]
> I just want to know what is "set_verbose(3)" command in this? also "toy:"
> ... that I just
e.sat.boolean_polynomials
> B= sage.sat.boolean_polynomials.solve(I.gens())
Cheers,
Martin
--
name: Martin Albrecht
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_jab: martinralbre...@jabber.c
he monomial a*b. On multiplying these clauses, the
> answer comes as a' + b', and not a*b as required.
>
> Can anybody please help?
Cheers,
Martin
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_otr: 47F43D1A 5D68C36F 468BAEBA 640E
t; zero-based, but Permutations(50) permutes the numbers from 1 to 50, not
> from 0 to 49.
>
> Best regards,
> Simon
Cheers,
Martin
--
name: Martin Albrecht
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_ww
shows the variables, which I
> do not want.
> Is there any way to tackle this?
Cheers,
Martin
--
name: Martin Albrecht
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_jab:
infinity import PlusInfinity
>
> from sage.sat.solvers import SatSolver
> from sage.sat.converters import ANF2CNFConverter
>
>
>
> Traceback (click to the left of this block for traceback)
> ...
> ImportError: No module named sat.solvers
Cheers,
Martin
--
name: Marti
> * Unable to download cryptominisat-2.9.5
> * Please see http://www.sagemath.org//packages for a list of valid
> * packages or check the package name.
> **
> Error:
Pass a list of numbers instead of independent numbers. SBox( [1,2,3]) not
SBox(1,2,3)
sent from a telephone.
On 19 Dec 2012 08:17, "sea21" wrote:
> Why is it that when I try to input an 8-bit Sbox into the argument of S =
> mq.SBox(.), I get the error: "SyntaxError: more than 255 arguments"? Doe
> "sage-support" group.
> > 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.
> > Visit this group at http://groups.google.com/group/sage-support?hl=
lean_polynomials.solve(I.gens())
[{x7: 1, x8: 0, x9: 1, x6: 0, x5: 0, x4: 1, x3: 1, x1: 1, x2: 1, x0: 1}]
sage: I.groebner_basis()
[x0 + 1, x1 + 1, x2 + 1, x3 + 1, x4 + 1, x5, x6, x7 + 1, x8, x9 + 1]
Cheers,
Martin
--
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e you can download it in the paper.
>
> All that said, when I look at your system, I wonder if something's wrong
> with the formatting, because it looks to me as if it's either linear or
> univariate. Is that the case?
>
> regards
> john perry
Cheers,
Martin
fineSpace(GF(2),2)
> sage: S = AA.subscheme(x^2+y^2)
> sage: S.point_set().points()
> [(0, 0), (1, 1)]
>
> On Saturday, December 8, 2012 6:14:19 AM UTC, Santanu wrote:
> > I have a system of non linear equations over GF(2). How to solve
> >
> > them in Sage?
Che
don-Curtis/5046185>
> <https://plus.google.com/u/0/105858766264293200612/about>
> <http://brandoncurtis.net>
> <http://jbei.org>
> *
Cheers,
Martin
--
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x(2, 3, [1, 0, 2, 0, 1, 2])
> [1 0 2]
> [0 1 2]
>
> #rows, #columns and a function to supply elements
> sage: matrix(6, 4, lambda i, j: i+j)
> [0 1 2 3]
> [1 2 3 4]
> [2 3 4 5]
> [3 4 5 6]
> [4 5 6 7]
> [5 6 7 8]
>
>
> Hope it helps,
>
> jo
n n unknowns, how do I use SAGE to give
> me the coefficient matrix* A*(size m *n) and column vector *b*(size m*1)
> such that Ax = b; where *x*(size n*1) is the vector of unknowns ?
>
> Thanks a lot.
Cheers,
Martin
--
name: Martin Albrecht
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and Q over the
> course of several days and don't quite understand what happened.
>
> Thanks!
>
> Robert
Cheers,
Martin
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_www: htt
m
> f chosen at the time this function is yz. What does the call f(*G) mean?
sage: f(x,y,z) calls f on x,y,z. G is a list of length three and * turns that
into three different arguments for f's call. This is not a Sage feature but a
feature of the Python language.
Cheers,
Martin
--
d similarly, how do I compute f(g())
> composition?
>
> Can someone help please?
>
> Thanks in advance.
> Virendra
Cheers,
Martin
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>
> R.=GF(2)['t,x']
> g=t^16*x + t^10*x + t^9*x + t^6*x + t^5 + t*x + x^2
> g.factor(proof=False)
Cheers,
Martin
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store 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 qu
ckages (LinBox, NTL,
IML, M4RI, M4RIE, Pari, ...) or implements its own highly efficient linear
algebra. The only case when Singular is called is when linear algebra over
multivariate polynomial rings is performed.
See http://wiki.sagemath.org/DenseLinearAlgebra
Cheers,
Martin
--
name: Martin
trix and perform the algorithm
> on that part of it, and just re-join it to the rest of the matrix, but I
> was wondering if there is some built-in function for this.
>
> Thanks,
> Tom
Cheers,
Martin
--
name: Martin Albrecht
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PARI doesn't have a log_repr() to begin with, so I don't see how that's
relevant.
On Sunday 03 Jun 2012, Jeroen Demeyer wrote:
> On 2012-06-03 12:14, Martin Albrecht wrote:
> > 2) K.multiplicative_generator() currently returns a random generator, but
> > for t
> > Why is it clear that a^4+a+1 is not a multiplicative generator? I think
> > it is:
> >
> > sage: k. = GF(2^8, names='a', name='a', modulus=x^8+x^4+x^3+x+1)
> > sage: (a^4+a+1).multiplicative_order()
> > 255
> >
&g
gh the
> > MILP class.
> >
> > 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, vi
sage: *ZZ.zero_element()*
> 0
> sage: *QQ.zero_element()*
> 0
> sage: QQ['x'].*zero_element()*
> 0
>
> The result is cached:
>
> sage: ZZ.*zero_ele
us a patch ;) On a more serious note, it
seems you found a bug and your code above is the right fix. So it would be
great if you could open a ticket and provide a patch which falls back to the
generic code above if the base is >= 2^64.
Cheers,
Martin
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you switch to multiplicative_generator() or
does that present problems for you?
Cheers,
Martin
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y sat down and implemented the correct formula (i.e., is it
known)?
If an exact formula is not know, does anyone know an upper bound (somewhat
tight :))?
Cheers,
Martin
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her. The idea
> is similar to polynomial system construction in mq.SR for AES and *ctc.py*
> for Courtois Toy Cipher by Martin Albrecht. And I'm wondering what is the
> best way to test correctness of the system.
>
> What I've implemented so far:
>
>1. replacing ev
mod2_dense.Matrix_mod2_dense.submatrix
> (sage/matrix/matrix_mod2_dense.c:9696) TypeError: submatrix() takes
> exactly 4 positional arguments (2 given)
>
>
> When I looked at the code, it seemed that "Matrix Mod2" submatrix doesn't
> have the parameters "nrow
Try
sage: sage_eval?
which preparses it's input while eval does not.
On Thursday 19 Apr 2012, Graham Gerrard wrote:
> z="1/2*x"
> x=3
> eval(z)
> 0
> z="x*1/2"
> eval(z)
> 3/2
>
> ??
>
> Graham
Cheers,
Martin
--
name: Martin Albrec
w it can be used. I would appreciate any help and hints on using
> SAT solvers in Sage.
>
> Thanks.
Cheers,
Martin
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rict or not, as I feel free to replace
> < 1 by <= 0.9.
>
> Would you know of any way to solve this type of equations, or to
> ensure that no solution exists ?
>
> Thank yo ! :-)
>
> Nathann
Cheers,
Martin
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gt; clinton
Cheers,
Martin
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F is a Galois Field. In sage i
> have a roots() function, I want know please, What is a algorithm used
> for implement this function?.
>
> thanks.
Cheers,
Martin
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ts).
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Martin
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s?
How soon do you need it? I'm asking because I don't know how soon I could make
this happen, but I'm sure we can make this much much faster by doing this in
the M4RI library itself, i.e., in C. Do you know a bit of C?
Cheers,
Martin
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ear much slower than it should (it's my fault btw.).
Someone should implement it and send us a patch :) cf. solve.h in M4RI:
http://m4ri.sagemath.org/doxygen/solve_8h.html
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Martin
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n('minbase')
sage: minbase(J)
[x^2, x*y*z, x*z^2, y^2, y*z^2, z^3]
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Martin
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reply; I looked at the solution a long time ago &
> it seems to work. A natural question, naturally :-) is there an easier
> way to specify the include directory? after all, this changes by
> machine & version.
>
> john
>
> On Jul 25, 8:34 am, Martin Albrecht
> wrote:
; > For more options, visit this group at
> > http://groups.google.com/group/sage-support
> > URL: http://www.sagemath.org
Cheers,
Martin
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t; That seems to fix it for me!
Indeed, I can confirm this. I don't know which change in M4RI triggered the
fix (i.e., we didn't explicitly work on kernels since 2009).
Cheers,
Martin
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_otr:
Hi John,
see attachment. You'll have to change the cinclude path for it to work on your
machine.
On Monday 25 July 2011, john_perry_usm wrote:
> On Jul 25, 6:46 am, Martin Albrecht
>
> wrote:
> > You'll need to compile your extension module (i.e. your pyx file) with
ore ‘<’ token
> -
>
> then more of other types.
You'll need to compile your extension module (i.e. your pyx file) with C++
instead of C. See
http://sagemath.org/doc/developer/coding_in_cython.html#special-pragmas
Cheers,
Martin
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hg qpush # it will print the same error as above, ignore it
5) ./sage -b
Essentially, you do the same thing as the Sage command you quote above, but
you ignore the error (since it isn't really that important in this particular
case)
For more details check:
http://sagemath.org/doc/develope
of the Sage community have invested in this tool. A lot of my
> research has come out of what I've been able to write in Sage.
Cheers,
Martin
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_
ever, it might be the case that the patch
at #11316 fixes this issue as well.
Cheers,
Martin
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//www.mpir.org/
Cheers,
Martin
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irectly in
Sage, by writing singular.eval("foo") to send the command foo.
Cheers,
Martin
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I started changing that (only RR so far) in:
http://trac.sagemath.org/sage_trac/ticket/7577
but the ticket got stuck because we need to decide whether it's okay to use
MPF instead of MPFR for multivariate polynomials.
Cheers,
Martin
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On Monday 28 February 2011, dmharvey wrote:
> On Feb 27, 5:29 pm, Martin Albrecht
>
> wrote:
> > sage: R. = PolynomialRing(QQ)
> > sage: f = x0^2*x1 + x1^2*x2 + x2^2*x3 + x3^2*x0
> > sage: (f0, f1, f2, f3) = [f.derivative(v) for v in [x0, x1, x2, x3]]
> >
^5
Cheers,
Martin
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Hi, I know of no elegant way of doing that. There are a few ANF
(polynomials) to CNF (ORs and ANFs) strategies which are used for example in
cryptography. Those might be of interrest to you. I have a few pointers in
my thesis.
Cheers,
Martin
On Feb 4, 2011 6:12 PM, "Francois Maltey" wrote:
--
T
the quotient P/ is precisely the right one to use since x_i^2 - x_i has the
roots 0, 1 and no root in the extension. Thus, the only possible solutions to
the common system have components in GF(2).
More details for example in my thesis (Section 3.6):
http://martinralbrecht.files.wordpress.com/2010/10/
hat happens in the latter. In sage
you should construct
B. = BooleanPolynomialRing()
Cheers,
Martin
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?
sage: K = GF(32003)
sage: P. = K[]
sage: P.lagrange_polynomial([(K.random_element(),K.random_element()) for _ in
range(10)])
25484*x^9 + 16230*x^8 + 21258*x^7 + 5369*x^6 + 5329*x^5 + 26390*x^4 +
18568*x^3 + 24278*x^2 + 26684*x + 4684
Cheers,
Martin
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ng)c);
+ res->data = (char *)((long)cc);
return jjPLUSMINUS_Gen(res,u,v);
}
"""
It seems with the new patch the overflow would at least be detected? Can you
give it a try?
Cheers,
Martin
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On Wednesday 13 October 2010, Simon King wrote:
> Hi Martin!
>
> On 13 Okt., 15:12, Martin Albrecht
>
> wrote:
> > > sage: I.radical().vector_space_dimension()
> > > 6
> > > which would raise a TypeError if the ideal was not zero dimensional.
>
> sage: I.radical().vector_space_dimension()
> 6
> which would raise a TypeError if the ideal was not zero dimensional.
We should probably change that to be a ValueError, since the "value" of the
ideal is wrong, not the type?
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ate Polynomial Ring in x, y, z over
Rational Field
Is that what you want?
Martin
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Q,order='neglex')
sage: I = Ideal(x^5 + y^4 +z^3, x^3 + y^2 + z^2 -1)
sage: I.groebner_basis()
[1]
See
http://sagemath.org/doc/reference/sage/rings/polynomial/multi_polynomial_ideal.html
Martin
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le.com/group/sage-support
> URL: http://www.sagemath.org
>
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