ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 23 Nov 2017 11:18:11 -0600Characteristic polynomial wont be used in solvehttp://ask.sagemath.org/question/39746/characteristic-polynomial-wont-be-used-in-solve/ When I try to find roots in a characteristic polynomial it gives me errors:
sage: #Diagonalmatrix
....:
....:
....: A=matrix([[1,-1,2],
....: [-1,1,2],
....: [2,2,-2]])
....: var('x')
....: poly=A.characteristic_polynomial()
....: eq1=solve(poly==0,x)
....:
x
--------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-86-fee7a7de2ea1> in <module>()
7 var('x')
8 poly=A.characteristic_polynomial()
----> 9 eq1=solve(poly==Integer(0),x)
/usr/lib/python2.7/site-packages/sage/symbolic/relation.pyc in solve(f, *args, **kwds)
816
817 if not isinstance(f, (list, tuple)):
--> 818 raise TypeError("The first argument must be a symbolic expression or a list of symbolic expressions.")
819
820 if len(f)==1:
TypeError: The first argument must be a symbolic expression or a list of symbolic expressions.
sage:
What can I do in order to use the polynomial in an equation I wish to solve?PoetastropheThu, 23 Nov 2017 11:18:11 -0600http://ask.sagemath.org/question/39746/How to pick out the largest root of an equation?http://ask.sagemath.org/question/25568/how-to-pick-out-the-largest-root-of-an-equation/ I tried the following but it didn't work,
p = x^2 - 7*a*x + 5;
a=5;
m = max((p == 0).solve([x]))
PhoenixMon, 19 Jan 2015 22:22:48 -0600http://ask.sagemath.org/question/25568/Ideals of non-commutative polynomialshttp://ask.sagemath.org/question/9748/ideals-of-non-commutative-polynomials/Basically I have the same question as [here](http://ask.sagemath.org/question/1267/find-specific-linear-combination-in-multivariate), but in the non-commutative case: Given non-commutative polynomials $f_1,\dotsc,f_s \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$, how can I test (with sage, or any other program which can do this) that some $g \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$ satisfies $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal), and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?
In trac ticket [#11068](http://trac.sagemath.org/sage_trac/ticket/11068) non-commutative quotient rings were implemented. However, according to the reference manual on [quotient rings](http://www.sagemath.org/doc/reference/sage/rings/quotient_ring.html), this assumes that one defines a reduce method by hand. But in my example , it is not clear how to do this.Martin BrandenburgSun, 27 Jan 2013 13:23:38 -0600http://ask.sagemath.org/question/9748/Find specific linear combination in multivariate polynomial ringhttp://ask.sagemath.org/question/8827/find-specific-linear-combination-in-multivariate-polynomial-ring/Assume that I have given a sequence of polynomials $f_1,\dotsc,f_s$ in a multivariate polynomial ring (over $\mathbb{Z}$, if that matters) and want to decide whether a given polynomial $g$ can be written as $g = \lambda_1 f_1 + \dotsc + \lambda_s f_s$. Then in Sage I just let
I = Ideal([f_1,...,f_s])
and test with
g in I
If this returns True, how can I get Sage to display some possible $\lambda_1,\dotsc,\lambda_s$?
As for my specific problem, I have already tried it by hand, but this is hard: My polynomial ring has $15$ indeterminates and there are $s = 250$ polynomials.Martin BrandenburgSun, 25 Mar 2012 01:53:55 -0500http://ask.sagemath.org/question/8827/Polynomial.http://ask.sagemath.org/question/8743/polynomial/I've a question. Is in Sage a function, method, whatever, what can show me step by step, how solve, for example: polynomial "n" grade?
Thanks for answers, Ani.AniMon, 27 Feb 2012 04:44:43 -0600http://ask.sagemath.org/question/8743/Factorization of non-commutative Laurent polynomialshttp://ask.sagemath.org/question/8417/factorization-of-non-commutative-laurent-polynomials/Hi, can Sage factorize non-commutative Laurent polynomials in several variables?
By those polynomials I mean elements in the group algebra Z[F(n)], where Z is the integers and F(n) is the free group on n letters.
(The case with Z/2- instead of Z-coefficients would also be interesting.)
Thank you!bmTue, 25 Oct 2011 19:37:53 -0500http://ask.sagemath.org/question/8417/