Yes I wanted the splitting field. I didn't know exactly the terminology of
all this things as I'm still learning most of it.
One more question. Would you happen to know any source that I can look into
it to see how or at least the vague idea of how the splitting field and the
factors are calcul
On Tuesday, November 19, 2019 at 1:35:24 AM UTC-5, Pedro Vinícius Ferreira
Baptista wrote:
>
> Given an irreducible polynomial P from Q[x] I want to find the primitive
> element A of the extension field defined by it.
> Moreover I want to know how to write the roots of P in terms of A(per
> exa
On Tuesday, August 15, 2017 at 4:21:03 PM UTC+2, chandra chowdhury wrote:
>
> x = var('x')
> factor(x^5-x, IntegerModRing(25)['x'])
>
Look at the output of `factor??`. A ring argument is not supported. So you
have to create the ring first (var gives you only the symbolic ring). Then
create the
On 15 August 2017 at 18:42, Nils Bruin wrote:
> On Tuesday, August 15, 2017 at 7:21:03 AM UTC-7, chandra chowdhury wrote:
>>
>> Is it possible to factor polynomials completely over modular ring?
>>
>> Like
>> x = var('x')
>> factor(x^5-x, IntegerModRing(25)['x'])
>> gives
>>
>> (x-1)(x+1)(x^2+1)*x
On Tuesday, August 15, 2017 at 7:21:03 AM UTC-7, chandra chowdhury wrote:
>
> Is it possible to factor polynomials completely over modular ring?
>
> Like
> x = var('x')
> factor(x^5-x, IntegerModRing(25)['x'])
> gives
>
> (x-1)*(x+1)*(x^2+1)*x
>
The second argument is simply ignored here, by the
On Monday, March 24, 2014 7:56:33 AM UTC-7, martin@gmx.net wrote:
>
> Working in a stack of multivariate polynomial rings, how can I compute the
> quotient of two polynomials in those cases where I know the remainder to be
> zero?
>
> Reading the docs I found two likely approaches, but neithe
Hi Peter,
Thanks for your suggestion, it's something I hadn't considered specifying
for all of my variables. I managed to avoid the '_first_ngens' by
restructuring the code, and your comment about making sure that everything
is actually an integer saved me a lot of time fixing the next error.
Hello Tristan,
> n = 100; d=3
> load DATA+'my_functions.py'
> coefficients = poly_expand(n,int(n**(1/d)),d)
> R. = ZZ[]
> f = 0
> for c in coefficients:
> f += c*t^d
> d -= 1
> g = f.homogenize('s')
>
> Running this returns "AttributeError: 'GlobalPolynomialRing' object has no
> attribu
On 12/11/2013 08:40 PM, Thierry Dumont wrote:
Hello, all,
I am going to manipulate Legendre (P) polynomials.
So I do something like this:
sage: P.=QQ[]
sage: #generate de first Lagrange polynomial
sage: s=[legendre_P(i,x) for i in [0..2]]
sage: print s
[1, x, 3/2*x^2 - 1/2]
sage: #now, look a
2013/4/18 Simon King
> A symbolic expression is something fairly general---so general that many
> methods won't make sense in this generality. A symbolic expression may
> contain all "strange" stuff like sin(x^2), exp(pi), x^x, etc.
>
> From computer science point of view, the mathematical algo
Hi Andrea,
On 2013-04-17, Andrea Lazzarotto wrote:
>> Note that by saying
>> S(x) = ...
>> you define S as a symbolic function on a symbolic variable x, and if you
>> re-define x later, then the variable of S will still be symbolic, and
>> not belong to a polynomial ring.
>>
>
> Ok, my bad
Hi,
> The problem is that in fact you are *not* considering two polynomials:
> [...]
>
> Note that by saying
> S(x) = ...
> you define S as a symbolic function on a symbolic variable x, and if you
> re-define x later, then the variable of S will still be symbolic, and
> not belong to a p
Hi Andrea,
On 2013-04-17, Andrea Lazzarotto wrote:
> Hi, I am trying to work with polynomials in Finite Fields. We have to
> implement the Extended Euclidean Algorithm for using it with Reed Solomon
> Codes.
> ...
> Now my problem is that I would like to divide a by b and get bot the quotient
Sage hangs on the following input:
sage: K. = FractionField(PolynomialRing(QQ,4,'pdeN'))
sage: R. = K[]
sage: a = x-x^-1
sage: b = x^6-x^-6
sage: c = x^7-x^-7
sage: X = p*a + d*b + e*c
sage: F = N*a*b*c - X^2*(x-x^-1)
and also on this closely related input
sage: K. = FractionField(PolynomialRing
Easy, you just need to define the ring Q(a)[x] like this:
sage: K. = FractionField(PolynomialRing(QQ,'a'))
sage: R. = K[]
sage: f = x^2+1
sage: g = a*x
sage: f.quo_rem(g)
(1/a*x, 1)
On Sunday, April 22, 2012 9:23:53 PM UTC+1, Michael Beeson wrote:
>
> Sage version 4.6.1 (I know it's old, new on
I want to take, for example, x^2 + 1 mod a*x and get quotient (1/a)*x
and remainder 1.It doesn't work if I work in PolynomialRing because
then you can't have 1/a.
It doesn't work in the quotient field because then you always get remainder
0.To have f.quo_rem(g) work, I must a
Can't help with Sage, but Mathematica 8.0 has no function SymmetricReduce.
It does have SymmetricReduction:
SymmetricReduction[f,{Subscript[x, 1],...,Subscript[x, n]}]
gives a pair of polynomials {p,q} in Subscript[x, 1],...,Subscript[x, n]
such that f==p+q, where p is the symmetric part and q
On Wednesday 13 Jun 2012, Oleksandr Kazymyrov wrote:
> 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
>
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 fi
I found the error. The following one is correct now:
F.=GF(16)
for b, c in F^2 :
print "x=",b,"y=",c, "T:",b*custom_divide((custom_divide(b,c))^4+a*(
custom_divide(b,c))^2+1,a*((custom_divide(b,c))^3+1)+(a^3+a^2)*((
custom_divide(b,c))^2+custom_divide(b,c)))+(b*c).nth_root(2)
W dniu wto
Simple explanation of my problem (if the previous one was too complicated):
Let
GF(2^4)={0, 1, a, a+1, a^2, a^2+1, a^2+a, a^2+a+1, a^3, a^3+1, a^3+a, a^3+a+
1, a^3+a^2, a^3+a^2+1, a^3+a^2+a, a^3+a^2+a+1} and a^4+a+1=0.
Let
T:= x*([c^2((y/x)^4+(y/x))+c^2(1+c+c^2)((y/x)^3+(y/x))]/[(y/x)^4+c(y/x
Because you divided by x in your computation, the polynomial f was coerced
into the fraction field. In the fraction field, quotient is always possible
without reminder:
sage: f.parent()
Fraction Field of Multivariate Polynomial Ring in x, N, p, r, m, l over
Rational Field
You want to convert f
The Deprecation warning was absent in 4.3.3 but is there in 4.6.2. Does
this mean consecutive brackets are treated as Lamda expressions scoping to
the right?
Like:
sage : y=1/((x-1)(x-3)(x-5))
sage : y
1/(x-9)
sage : y=1/((x-1)(x-3)(x^2-5))
sage : y
1/(x^2-9)
sage : y=1/((x-1)
On Friday, March 25, 2011 9:35:13 PM UTC-7, Surendran Karippadath wrote:
>
> If the multiplication sign * is absent ( say by mistake!) what is SAGE
> evaluating?
> For example:
> x=var('x');f=1/((x-1)(x-3));
> f.limit(x=1) returns -1/3
> diff(f,x) returns -1/(x - 4)^2
> plot(f,(x,0,10)) plo
On 12/24/10 5:40 AM, lainme wrote:
Hi, I want to do polynomial interpolation with sage, such as the
Lagrange Interpolation
I searched the group and reference manual of sage, but only found the
complex interpolation.
I made this for my numerical analysis class:
http://demo.sagenb.org/home/pub
Yes, exactly 12xy= 24x+36y.
On 5 December 2010 00:22, JamesHDavenport wrote:
>
>
> On Dec 4, 5:14 pm, Santanu Sarkar
> wrote:
> > Consider a collection of polynomials over three variables x, y, z.
> > Suppose, we replace monomial xy by 2x+3y for each polynomial.
> > And also each multiple of xy
On Dec 4, 5:14 pm, Santanu Sarkar
wrote:
> Consider a collection of polynomials over three variables x, y, z.
> Suppose, we replace monomial xy by 2x+3y for each polynomial.
> And also each multiple of xy say xyz will be replaced by z(2x+3y).
Therefore (xy)*(xy) will be (2x+3y)*(2x+3y) which has
Hi Simon!
On 11/17/2010 08:33 AM, Simon King wrote:
On 16 Nov., 23:48, Johannes Huisman
wrote:
Does sage have a command for polynomial division by increasing powers? I
could not find such a command. Of course, one may use power series
division in order to compute the quotient, but it would be n
Hi Johannes!
On 16 Nov., 23:48, Johannes Huisman
wrote:
> Does sage have a command for polynomial division by increasing powers? I
> could not find such a command. Of course, one may use power series
> division in order to compute the quotient, but it would be neat if one
> could avoid all that.
Andrew,
Read up on resultants:
sage: R.=QQ[]
sage: f=x^2+a1*x+a2
sage: g=x^2+b1*x+b2
sage: f(x=y).resultant(g(x=x-y),variable=y)
a1^2*b1*x + a1*b1^2*x + a1^2*x^2 + 3*a1*b1*x^2 + b1^2*x^2 + 2*a1*x^3 +
2*b1*x^3 + x^4 + a1*a2*b1 + a2*b1^2 + a1^2*b2 + a1*b1*b2 + 2*a1*a2*x +
2*a2*b1*x + 2*a1*b2*x + 2*
is there a way of doing what uve done except considering the pair of
polynomials
x^2+a1*x+a0
x^2+b1*x+b0
where a0,a1,b0,b1 lie in QQ but their exact values r not known
and al is a root of the first and be is a root of the second?
On Sun, Oct 24, 2010 at 5:22 PM, Yann wrote:
> On Oct 23, 9:39
On Oct 23, 9:39 pm, andrew ewart wrote:
> if alpha is a root of x^2+a_1*x+a_0 and beta is a root of x^2+b_1*x
> +b_0 (both polynomials r in QQ), then how do i construct code such
> that it can tell me the minimum polynomials of the following roots
> alpha+beta
> and
> alpha*beta
Hi, I'm not sure
On Apr 28, 2010, at 6:04 AM, Yann wrote:
This at least documented:
sage: R.=ZZ[]
sage: f = x^3+x+1
sage: f.mod?
...
When little is implemented about a given ring, then mod may
return
simply return f. For example, reduction is not implemented for
ZZ[x] yet. (TODO!)
s
This at least documented:
sage: R.=ZZ[]
sage: f = x^3+x+1
sage: f.mod?
...
When little is implemented about a given ring, then mod may
return
simply return f. For example, reduction is not implemented for
ZZ[x] yet. (TODO!)
sage: R. = PolynomialRing(ZZ)
sage: f = x
Thank you very much for your kind help.
On 25 April 2010 17:00, Simon King wrote:
> On 25 Apr., 12:50, Santanu Sarkar
> wrote:
> > Sorry again. Dependency needs over integer.
>
> Probably there is a better way of doing it, but the following works:
>
> Transform the problem into a matrix: One ro
On 25 Apr., 12:50, Santanu Sarkar
wrote:
> Sorry again. Dependency needs over integer.
Probably there is a better way of doing it, but the following works:
Transform the problem into a matrix: One row for each polynomial, one
column for each monomial that occurs in one of the polynomials, and
th
Sorry again. Dependency needs over integer.
On 25 April 2010 16:06, Simon King wrote:
> Hi!
>
> On 25 Apr., 12:26, Santanu Sarkar
> wrote:
> > I want to find linear dependence of the set polynomials {f1,f2,f1*f2,
> > x1*f2,x2*f2}
>
> 'Linear over ZZ' or 'linear over R'?
>
> If it is the latter,
Hi!
On 25 Apr., 12:26, Santanu Sarkar
wrote:
> I want to find linear dependence of the set polynomials {f1,f2,f1*f2,
> x1*f2,x2*f2}
'Linear over ZZ' or 'linear over R'?
If it is the latter, the following might help (but is only implemented
if you have polynomials over a field, not over ZZ):
sa
Hi,
No, my polynomials are not homogeneous and are of different degree. Suppose:
R.=ZZ[]
f1=1+x1+x2+x1*x2
f2=1+x1+x3+x1*x3
I want to find linear dependence of the set polynomials {f1,f2,f1*f2,
x1*f2,x2*f2}
With regards,
Santanu
On 25 April 2010 15:33, Simon King wrote:
> Hi!
>
> On 25 Apr.,
Hi!
On 25 Apr., 11:41, Santanu Sarkar
wrote:
> Suppose f1, f2,,f10 are polynomials over 20 variables over integers.
> How one can check weather they are linearly independent or not in Sage?
When you talk about linear indepence of polynomials, you probably
assume that they are all homogeneou
Hi Zach!
On Feb 11, 2:37 pm, zsharon wrote:
> This should also work:
>
> R. = PowerSeriesRing(ZZ)
> z+1
> #1+z
I am a bit surprised that it works, because I thought that
PowerSeriesRing comes with a default precision of 20. So, I thought
that any polynomial would be cut off in degree 20.
But in
> How about this:
This should also work:
R. = PowerSeriesRing(ZZ)
z+1
#1+z
See http://www.sagemath.org/doc/tutorial/tour_polynomial.html for
other examples.
Zach
--
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to
sage-support+
>
> But there are people who would (at least if the context is formal
> power series) prefer
> 1 + 6*t + 4*t^2
>
> Is there a way to switch between these to conventions?
>
How about this:
R. = LaurentSeriesRing(QQ)
x^3+x+1
#1 + x + x^3
Zach
--
To post to this group, send email to sage-suppor
On Tue, Jan 5, 2010 at 12:37 AM, Michael Beeson wrote:
> Thanks, that's a start, but my polynomials have some parameters
> a,b,c,...
> in the coefficients. In Mathematica you say PolyomialRemainder[f,g,x]
> where the
> last 'x' names the polynomial variable, so all other variables are
> parame
On 5 jan, 09:37, Michael Beeson wrote:
> Thanks, that's a start, but my polynomials have some parameters
> a,b,c,...
> in the coefficients. In Mathematica you say PolyomialRemainder[f,g,x]
> where the
> last 'x' names the polynomial variable, so all other variables are
> parameters. When
>
Thanks, that's a start, but my polynomials have some parameters
a,b,c,...
in the coefficients. In Mathematica you say PolyomialRemainder[f,g,x]
where the
last 'x' names the polynomial variable, so all other variables are
parameters. When
I tried to modify your code by inserting a=var('a') an
bump wrote:
>
> On Jan 3, 10:59 am, Michael Beeson wrote:
>> I am just learning Sage. I tried to define a polynomial and then
>> find the polynomial remainder upon division by the
>> cyclotomic_polynomial(18), which is 1-x^3+x^6.This is easily
>> accomplished in Mathematica using the Polyno
On Jan 3, 10:59 am, Michael Beeson wrote:
> I am just learning Sage. I tried to define a polynomial and then
> find the polynomial remainder upon division by the
> cyclotomic_polynomial(18), which is 1-x^3+x^6. This is easily
> accomplished in Mathematica using the PolynomialRemainder funct
Thank you for your answers !!
I was thinking about some multidimensional linear approximation, where
the basis you use is ( for points of coordinates (x_i, y_i ) ) the
vectors
The family of x_i, x_i
The family of x_i, x_i^2
The family of x_i, x_i^3
The family of x_i, x_i^4
...
But it turns out S
Robert Bradshaw wrote:
> On Nov 2, 2009, at 8:41 AM, Nathann Cohen wrote:
>
>> Hello !!!
>>
>> I remember there is an easy way ( through matrices ) to get the
>> "best" approximation of a function by a polynomial of bounded degree
>> ( and not only the usual approximation by a line ) I lo
On Nov 2, 2009, at 8:41 AM, Nathann Cohen wrote:
> Hello !!!
>
> I remember there is an easy way ( through matrices ) to get the
> "best" approximation of a function by a polynomial of bounded degree
> ( and not only the usual approximation by a line ) I looked for
> such functions in S
Nathalie Cohen ha scritto:
> Hello !!!
>
> I remember there is an easy way ( through matrices ) to get the "best"
> approximation of a function by a polynomial of bounded degree ( and not only
> the usual approximation by a line )
Are you speaking about the Taylor expansion ?
If so, it is impl
Hi!
On 22 Sep., 20:08, Shing Hing Man wrote:
> Thanks for the reply!
> Just one more question.
> In general, if k is a finite field, what is k(i), where i is an
> integer, suppose to be ?
Apart from the autocompletion, another useful way to get
information is to look into the documentation. T
Thanks for the reply!
Just one more question.
In general, if k is a finite field, what is k(i), where i is an
integer, suppose to be ?
The following example suggests k(i) will be the elements in the base
field as i varies.
sage: k. = GF(9)
sage: for i in [0..8]: print k(i)
:
0
1
2
0
1
2
0
Hi Shing!
Two possibilities:
sage: k. = GF(9)
sage: t=a^2+1
Now, you can learn about all possible methods for elements of k by
doing
sage: t.
(you type t, dot, and hit the tab key).
This will show you a list of possible methods.
One of the methods is called int_repr:
sage: t.int_repr()
On Wed, 15 Jul 2009 11:29:37 -0700
William Stein wrote:
>
> On Wed, Jul 15, 2009 at 11:23 AM, Martin
> Albrecht wrote:
> >
> >> That's not surprising given what power_mod does. Do power_mod?? to
> >> see. It's generic code that does the arithmetic in the parent
> >> ring, then calls mod after
On Wed, Jul 15, 2009 at 11:23 AM, Martin
Albrecht wrote:
>
>> That's not surprising given what power_mod does. Do power_mod?? to
>> see. It's generic code that does the arithmetic in the parent ring,
>> then calls mod after each multiply. so in the above first example,
>> zmod_poly is never us
> That's not surprising given what power_mod does. Do power_mod?? to
> see. It's generic code that does the arithmetic in the parent ring,
> then calls mod after each multiply. so in the above first example,
> zmod_poly is never used.
This reminds me: Why do we have power_mod() when pow() doe
On Wed, Jul 15, 2009 at 5:03 AM, Martin
Albrecht wrote:
>
>> For the ring of polynomials with coefficients over ZZ:
>>
>> --
>>
>> | Sage Version 4.1, Release Date: 2009-07-09 |
>> | Type notebook() for the
> For the ring of polynomials with coefficients over ZZ:
>
> --
>
> | Sage Version 4.1, Release Date: 2009-07-09 |
> | Type notebook() for the GUI, and license() for information.|
>
> --
On Jul 15, 1:46 pm, Santanu Sarkar
wrote:
> Suppose f=2*x^2+3*x+1 is a polynomial in x. How efficiently we
> can calculate f^10 modulo 24?
quite fast i think:
sage: R. = PolynomialRing(Integers(24), x)
sage: R
Univariate Polynomial Ring in x over Ring of integers modulo 24
sage: f = 2*x^2+3*x
On Wednesday 15 July 2009, Santanu Sarkar wrote:
> Suppose f=2*x^2+3*x+1 is a polynomial in x. How efficiently we
> can calculate f^10 modulo 24?
sage: P. = PolynomialRing(Zmod(24))
sage: f = 2*x^2+3*x+1
sage: type(f)
sage: %timeit f**10
10 loops, best of 3: 19 µs per loop
Hi Santanu,
On Wed, Jul 15, 2009 at 9:46 PM, Santanu
Sarkar wrote:
> Suppose f=2*x^2+3*x+1 is a polynomial in x. How efficiently we
> can calculate f^10 modulo 24?
For the ring of polynomials with coefficients over ZZ:
--
| Sa
Thanks for your clarification and help, Carl.
Alex
On Feb 24, 5:15 pm, Carl Witty wrote:
> On Feb 23, 7:57 pm, Carl Witty wrote:
>
> > On Feb 23, 6:54 pm, Alex Raichev wrote:
>
> > > Carl, regarding the parenthetical remark of your first reply, are you
> > > saying the coercion error for plai
On Feb 23, 7:57 pm, Carl Witty wrote:
> On Feb 23, 6:54 pm, Alex Raichev wrote:
>
> > Carl, regarding the parenthetical remark of your first reply, are you
> > saying the coercion error for plain old monomials below is supposed to
> > happen?
>
> Well, I wouldn't say "supposed to happen" because
On Feb 23, 6:54 pm, Alex Raichev wrote:
> Carl, regarding the parenthetical remark of your first reply, are you
> saying the coercion error for plain old monomials below is supposed to
> happen?
Well, I wouldn't say "supposed to happen" because I don't think this
is the way it should stay long-t
Carl, regarding the parenthetical remark of your first reply, are you
saying the coercion error for plain old monomials below is supposed to
happen?
If so, then what's the simplest way to take an element f of a
polynomial ring R over a number field F and compute its embedded image
in RR= R.change
Sweet! Thanks, Carl.
Alex
On Feb 20, 8:08 pm, Carl Witty wrote:
> On Feb 19, 10:16 pm, Carl Witty wrote:
>
> > There's a bug. And, now that you've pointed out the bug, I figured
> > out how to crash Sage with a segmentation fault; so it's a serious
> > bug. Thanks for reporting it! This bu
On Feb 19, 10:16 pm, Carl Witty wrote:
> There's a bug. And, now that you've pointed out the bug, I figured
> out how to crash Sage with a segmentation fault; so it's a serious
> bug. Thanks for reporting it! This bug is now being tracked at
> http://trac.sagemath.org/sage_trac/ticket/5316
OK
On Feb 19, 7:59 pm, Alex Raichev wrote:
> Hi all:
>
> I get an error when i try to coerce monomials of a multivariate
> polynomial ring over a number field to the corresponding polynomial
> ring over QQbar. Shouldn't this work? They're monomials; no
> coefficients. Here's an example.
>
> Alex
Robert Bradshaw wrote:
> On Dec 29, 2008, at 4:47 PM, William Stein wrote:
>
>> On Mon, Dec 29, 2008 at 4:34 PM, Robert Bradshaw
>> wrote:
>>> +1 to (deprecating then removing) removing X.list(), and replacing it
>>> with X.entries().
>> Very good point. We *must* remember to make X.list() use
On Dec 29, 2008, at 4:47 PM, William Stein wrote:
>
> On Mon, Dec 29, 2008 at 4:34 PM, Robert Bradshaw
> wrote:
>>
>> +1 to (deprecating then removing) removing X.list(), and replacing it
>> with X.entries().
>
> Very good point. We *must* remember to make X.list() use the
> deprecation warning
On Mon, Dec 29, 2008 at 4:34 PM, Robert Bradshaw
wrote:
>
> +1 to (deprecating then removing) removing X.list(), and replacing it
> with X.entries().
Very good point. We *must* remember to make X.list() use the
deprecation warning system, and only remove it after 6 months. Could
you make a tra
On Dec 29, 2008, at 4:15 PM, William Stein wrote:
> On Mon, Dec 29, 2008 at 2:43 PM, Justin Walker wrote:
>>
>> On Dec 29, 2008, at 5:23 PM, John Cremona wrote:
>>
>>>
>>> Maybe I missed the point here but after
>>
>> The point was a minor one...
>>
>>> R.=QQ[]
>>> M=matrix(R,1,2,[x1+x2,x1*x2])
On Mon, Dec 29, 2008 at 2:43 PM, Justin Walker wrote:
>
>
> On Dec 29, 2008, at 5:23 PM, John Cremona wrote:
>
>>
>> Maybe I missed the point here but after
>
> The point was a minor one...
>
>> R.=QQ[]
>> M=matrix(R,1,2,[x1+x2,x1*x2])
>>
>> you can get at the entries like this:
>> sage: M[0,0]
>
On Dec 29, 2008, at 5:23 PM, John Cremona wrote:
>
> Maybe I missed the point here but after
The point was a minor one...
> R.=QQ[]
> M=matrix(R,1,2,[x1+x2,x1*x2])
>
> you can get at the entries like this:
> sage: M[0,0]
> x1 + x2
> sage: M[0,1]
> x1*x2
For the OP, it was surprising that "lis
Maybe I missed the point here but after
R.=QQ[]
M=matrix(R,1,2,[x1+x2,x1*x2])
you can get at the entries like this:
sage: M[0,0]
x1 + x2
sage: M[0,1]
x1*x2
where the only non-obvious thing to a mathematician is that the
row/col indices start at at 0.
The list() discussion seems separate to me.
On Dec 29, 2008, at 4:53 PM, Robert Bradshaw wrote:
>
> On Dec 29, 2008, at 1:38 PM, Justin Walker wrote:
>
>> On Dec 29, 2008, at 3:32 PM, Santanu Sarkar wrote:
>>
>>> I write a program in SAGE as follows:
>>> R.=QQ[]
>>> M=matrix(R,1,2,[x1+x2,x1*x2])
>>> may i do following steps to extract poly
On Dec 29, 2008, at 1:38 PM, Justin Walker wrote:
> On Dec 29, 2008, at 3:32 PM, Santanu Sarkar wrote:
>
>> I write a program in SAGE as follows:
>> R.=QQ[]
>> M=matrix(R,1,2,[x1+x2,x1*x2])
>> may i do following steps to extract polynomials from matrix?
>> 1) x = list(M)
>> 2) f1 = x[0]
>> 3) f2
On Dec 29, 2008, at 3:32 PM, Santanu Sarkar wrote:
> I write a program in SAGE as follows:
> R.=QQ[]
> M=matrix(R,1,2,[x1+x2,x1*x2])
> may i do following steps to extract polynomials from matrix?
> 1) x = list(M)
> 2) f1 = x[0]
> 3) f2 = x[1]
> is f1 & f2 are polynomials?
> if not how i can get
On Mar 25, 2:18 am, continuum121 <[EMAIL PROTECTED]> wrote:
> Hi!
>
> I have a problem. Here is its formulation. I work in some polynomial
> ring - lets say
> R,(x,y) = PolynomialRing(QQ, 2, 'xy', order='lex').objgens()
> and consider ideal in R
> I = ideal(x+y^3-2,y+x^3-2)
> then I calculate grob
If getting numerical roots is sufficient, then you might want to check
out the optional phcpack package. I am working on a more full-
featured interface for sage-2.11 that classifies roots of
multivariable polynomial systems.
Phcpack is be able to compute roots for systems where Groebner bases
It might work if you try coercing f = B[0] first into
R2. = PolynomialRing(CC, 2, 'xy')
then applying factor or whatever to R2(f). I haven't tried it with your
problem but that general idea has worked for me in similar situations.
On Tue, Mar 25, 2008 at 5:18 AM, continuum121 <[EMAIL PROTECTED
Dear Sage team,
sorry, i have a follow up question:
sage: F=FractionField(PolynomialRing(QQ,'A'))
sage: R=PolynomialRing(F,'x0,x1,x2,x3')
sage: x0=R.gen(0);x1=R.gen(1);x2=R.gen(2);x3=R.gen(3)
sage: A=F('A')
sage: I=R.ideal((-1)*x0^2 + (-1)*x1*x2 + 1, (-1)*x0*x2 + (-1)*x2*x3,
(-1)*x0*x1 + (-1)*x1
Dear John,
On Feb 13, 1:17 pm, "John Cremona" <[EMAIL PROTECTED]> wrote:
> I would say
> F=FractionField(PolynomialRing(QQ,'A'))
> A-F.gen()
> and then
> 1/A
> F(1/A)
> are all fine.
My main question was how to do 1/A in a polynomial ring over F (not
over F itself), but in fact your suggestion w
Your problem is too many quotes! You are giving strings to F().
I would say
F=FractionField(PolynomialRing(QQ,'A'))
A-F.gen()
and then
1/A
F(1/A)
are all fine.
John
On 13/02/2008, Simon King <[EMAIL PROTECTED]> wrote:
>
> Dear Sage team,
>
> i tried the following:
> sage: F=FractionField(Po
On Jan 1, 2008 1:31 PM, [EMAIL PROTECTED]
<[EMAIL PROTECTED]> wrote:
>
> After executing the following commands in Sage:
>
> QQi.=QQ.extension([x^2+1]);
> R.=MPolynomialRing(QQi,order='lex')
> T1_Pxxx=3*a^2*b+(1-a)^2*(1-b)-f0
> T1_Pxxy=3*(1-a)^2*b+3*a^2*(1-b)+6*a^2*b-f2
> T1_Pxyz=6*(1-a)*a*b+6*a*(
On 3/8/07, Kyle Schalm <[EMAIL PROTECTED]> wrote:
> > That said, I would love to add a function that basically does the above
> > to SAGE, but it's unclear what the notation would even be. One idea
> > is this:
> >sage: f(w=3)
>
> in my actual situation, i have something like
>
> R1. = QQ
>
> The above code is a good idea, but there would be efficiency
> issues. It would be better to do this (see the ev function below).
>
> sage: R1. = QQ['w']
> sage: R2. = R1['z']
> sage: f = w*z + (1-w)*z^3 + 3
> sage: def ev(f, a):
> ...return f.parent()([c(a) for c in f.list()])
> sage: e
On 3/7/07, Kyle Schalm <[EMAIL PROTECTED]> wrote:
> > On 3/7/07, Kyle Schalm <[EMAIL PROTECTED]> wrote:
> >> . the question is: how do i evaluate w while leaving z untouched?
> >> (i actually want to do this when R1 is a multivariable ring, but i imagine
> >> it works the same way.)
> >>
> >
> > C
>
> On 3/7/07, Kyle Schalm <[EMAIL PROTECTED]> wrote:
>
>> . the question is: how do i evaluate w while leaving z untouched?
>> (i actually want to do this when R1 is a multivariable ring, but i imagine
>> it works the same way.)
>>
>
> Can't you just work with all the variables together, like:
On 3/7/07, Kyle Schalm <[EMAIL PROTECTED]> wrote:
> . the question is: how do i evaluate w while leaving z untouched?
> (i actually want to do this when R1 is a multivariable ring, but i imagine
> it works the same way.)
>
Can't you just work with all the variables together, like:
sage: P.=QQ['
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