[sage-support] Re: Coefficients of multivariate polynomials along with degrees
On Feb 19, 6:38 am, ObsessiveMathsFreak obsessivemathsfr...@gmail.com wrote: Basically, I want to restrict the variables of a multivariate polynomial to a certain set of symbols. B.variables() should return [x,y] instead of [a,x,y] How can this be done. Maybe I misunderstand you, but this approach works fine in sage 4.8, and probably earlier: sage: R.a = QQ[] sage: P.x,y = R[] sage: f = a*x^2 - 2*y sage: f.variables() (x, y) That said, I can't factor a^2*x^2-y^2 going this route, because this type of polynomial tries to interact with a specific (different) backend. (Incidentally, the Sage polynomial/ring documentation is absolute and utter bedlam. Is it not possible for ordinary mortals to work with polynomials without having to declare polynomials rings over integers. ) Again, maybe I misunderstand you, but the polynomial rings given above are not over the integers, and there are examples of this in the documentation: http://www.sagemath.org/doc/constructions/rings.html#polynomial-rings Which I accessed via clicking on Help/Documentation from the home page, then on View the online documentation, then on Constructions, then on Polynomial Rings. Could you be more specific as to where the bedlam lies? There's a doc days coming up, and I'm sure people working on documentation could use advice. regards john perry -- 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: Coefficients of multivariate polynomials along with degrees
Is there any way to get this code to deal with non integer coefficients. Specifically, can it return coefficients that are symbolic. For example I would like f(x,y)=a*x^10*y+3*x B=f(x,y).polynomial(SR) print B.coefficients() to return [a,3] but instead it returns [1,3] Is it possible to have this code consider 'a' not as a variable but as a constant? On Feb 9, 10:36 pm, ObsessiveMathsFreak obsessivemathsfr...@gmail.com wrote: Are you certain that these two functions return elements in the same order? On Feb 8, 11:40 pm, Mike Hansen mhan...@gmail.com wrote: On Wed, Feb 8, 2012 at 3:29 PM, ObsessiveMathsFreak obsessivemathsfr...@gmail.com wrote: Is there no way of getting sage to give back the degree's of the corresponding multivariate polynomials as well. That is to return something like [[10,[100,1]],[3,[1,0]]] exponents() is what you need: sage: zip(B.coefficients(), B.exponents()) [(10, (100, 1)), (3, (1, 0))] --Mike -- 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: Coefficients of multivariate polynomials along with degrees
Basically, I want to restrict the variables of a multivariate polynomial to a certain set of symbols. B.variables() should return [x,y] instead of [a,x,y] How can this be done. (Incidentally, the Sage polynomial/ring documentation is absolute and utter bedlam. Is it not possible for ordinary mortals to work with polynomials without having to declare polynomials rings over integers. ) On Feb 19, 12:12 pm, ObsessiveMathsFreak obsessivemathsfr...@gmail.com wrote: Is there any way to get this code to deal with non integer coefficients. Specifically, can it return coefficients that are symbolic. For example I would like f(x,y)=a*x^10*y+3*x B=f(x,y).polynomial(SR) print B.coefficients() to return [a,3] but instead it returns [1,3] Is it possible to have this code consider 'a' not as a variable but as a constant? On Feb 9, 10:36 pm, ObsessiveMathsFreak obsessivemathsfr...@gmail.com wrote: Are you certain that these two functions return elements in the same order? On Feb 8, 11:40 pm, Mike Hansen mhan...@gmail.com wrote: On Wed, Feb 8, 2012 at 3:29 PM, ObsessiveMathsFreak obsessivemathsfr...@gmail.com wrote: Is there no way of getting sage to give back the degree's of the corresponding multivariate polynomials as well. That is to return something like [[10,[100,1]],[3,[1,0]]] exponents() is what you need: sage: zip(B.coefficients(), B.exponents()) [(10, (100, 1)), (3, (1, 0))] --Mike -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Coefficients of multivariate polynomials along with degrees
On Sun, Feb 19, 2012 at 4:38 AM, ObsessiveMathsFreak
obsessivemathsfr...@gmail.com wrote:
Basically, I want to restrict the variables of a multivariate
polynomial to a certain set of symbols.
B.variables() should return
[x,y]
instead of
[a,x,y]
How can this be done.
I have a patch at http://trac.sagemath.org/sage_trac/ticket/12542
which provides a fix for this:
sage: var('a,x,y')
sage: f = a*x^10*y+3*x
sage: B = f.polynomial(ring=SR['x,y'])
sage: B.coefficients()
[a, 3]
The key is specifying that the resulting polynomial should live in the
ring SR['x,y'] instead of (by default) SR['a,x,y'].
--Mike
--
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URL: http://www.sagemath.org
[sage-support] Re: Coefficients of multivariate polynomials along with degrees
Are you certain that these two functions return elements in the same order? On Feb 8, 11:40 pm, Mike Hansen mhan...@gmail.com wrote: On Wed, Feb 8, 2012 at 3:29 PM, ObsessiveMathsFreak obsessivemathsfr...@gmail.com wrote: Is there no way of getting sage to give back the degree's of the corresponding multivariate polynomials as well. That is to return something like [[10,[100,1]],[3,[1,0]]] exponents() is what you need: sage: zip(B.coefficients(), B.exponents()) [(10, (100, 1)), (3, (1, 0))] --Mike -- 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
