ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 10 Jul 2021 01:31:47 +0200How to computation primary decomposition in complex ring?https://ask.sagemath.org/question/57945/how-to-computation-primary-decomposition-in-complex-ring/ Help me! I am noob to use sagemathJose FigueroaSat, 10 Jul 2021 01:31:47 +0200https://ask.sagemath.org/question/57945/how to computation primary decomposition in quotient polynomial ring?https://ask.sagemath.org/question/57944/how-to-computation-primary-decomposition-in-quotient-polynomial-ring/Help me! I am noob to use sagemath Jose FigueroaSat, 10 Jul 2021 01:30:03 +0200https://ask.sagemath.org/question/57944/Derivative in infinite polynomial ringhttps://ask.sagemath.org/question/53319/derivative-in-infinite-polynomial-ring/ I am defining my ring as R.<x>=InfinitePolynomialRing(QQ), and this should give me ring with variables x[1],x[2],... etc. right? Now I want to differentiate a polynomial with respect to x[1] variable. So I defined f=x[1]^3 (for example). I am trying f.derivative(x[1]) but that does not work. It shows " 'typeerror': argument 'var' has incorrect type (expected sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular, got InfinitePolynomial_dense)."
Can someone please explain what is wrong and what I should do to fix it?
mathstudentSat, 05 Sep 2020 18:32:15 +0200https://ask.sagemath.org/question/53319/a basis for quotient module/vector spacehttps://ask.sagemath.org/question/50521/a-basis-for-quotient-modulevector-space/I have a ring (field) $R$, a polynomial ring $R[x_1,x_2,...,x_n]$ and a quotient module (vector space) $R[x_1,x_2,...,x_n]/I$ where $I$ is an ideal of $R[x_1,x_2,...,x_n]$ . For the case, when $R$ is a field, the basis of the quotient vector space can be found to consist of the cosets of monomials which are not divisible by leading monomials of grobner basis of $I$. A similar theorem exists for the case when $R$ is a ring with effective coset representatives. For example, the ring of integers. Can I find these coset representatives that form the basis for the quotient module/vector space in sage?arpitSat, 04 Apr 2020 19:23:39 +0200https://ask.sagemath.org/question/50521/How do I retrieve the variables that appear in a polynomial?https://ask.sagemath.org/question/50250/how-do-i-retrieve-the-variables-that-appear-in-a-polynomial/Hello, I'd like to know I can retrieve the list of variables that appear in $g$ in the following example.
A.<x,y> = InfinitePolynomialRing(QQ)
g=x_[0]+x_[1]+y_[0]
Thanks in advance!mcmugSun, 15 Mar 2020 14:28:15 +0100https://ask.sagemath.org/question/50250/Change degree in InfinitePolynomialRinghttps://ask.sagemath.org/question/44059/change-degree-in-infinitepolynomialring/If I use
<pre><code> P.<x,y,z> = InfinitePolynomialRing(QQ)</code></pre>
Assuming any of the orderings 'lex, deglex, degrevlex' I will have
$z_0 < z_1 < z_2 < ... < y_0 < y_1 < ... < x_0 < x_1 < ...$
And each variable having degree 1. I would like to obtain something like 'deglex' but assigning degree $n$ to $x_n,y_n,z_n$ so that in particular I would obtain
$z_0 < y_0 < x_0 < z_1 < y_1 < x_1 < ... $
Is there a way to implement this. It seems that in order to compute Grobner bases on arc schemes these orderings are much more natural that the ones implemented, but I just started looking at Sage so I may have missed the right implementation of polynomial rings in infinitely many variables to work. heluaniWed, 24 Oct 2018 19:38:41 +0200https://ask.sagemath.org/question/44059/Infinite polynomial ring with several indexhttps://ask.sagemath.org/question/46487/infinite-polynomial-ring-with-several-index/I know it's easy to create a infinite polynomial ring:
R.<y>=InfinitePolynomialRing(ZZ)
But how can I make a infinite polynomial ring with variables indexed by pairs, like x_(a,b)?
ianncunhaFri, 10 May 2019 20:54:43 +0200https://ask.sagemath.org/question/46487/parametric solution for a system of polynomial equationshttps://ask.sagemath.org/question/46043/parametric-solution-for-a-system-of-polynomial-equations/I have the following system of equations,
1+x+y+z==0, 1+xy+yz+xz==0
which I want to solve in the extension field of GF(2) for example. There is a parametric solution of these equations in terms of the parameter s as x=1+s, y=1+$\omega$ s, z=1+$\omega^2$s where $s$ is the parameter and $\omega^2+\omega+1=0$. How can I modify the following for Sage to be able to output parametric solutions like this one?
R.<x,y,z> = PolynomialRing(GF(4))
I = R.ideal([1 + x + y + z, 1 + x*y + y*z + x*z])
I.variety()arpitSun, 07 Apr 2019 22:40:40 +0200https://ask.sagemath.org/question/46043/formal series over InfinitePolynomialRinghttps://ask.sagemath.org/question/44056/formal-series-over-infinitepolynomialring/ I apologize if the question does not belong here. This is my first try to using sage and I find the documentation hard to read/search. I am trying to work with symbolic power series over a non-Noetherian ring. So for example I have:
sage: P.<x> = InfinitePolynomialRing(QQ)
sage: R.<t> = PowerSeriesRing(P)
And I'd like to consider the series $f(t) = \sum x_n t^n$ as an element of R. But my first try
<pre><code>
sage: sum(x[n]*t^n,(n,0,oo))
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-27-d7d20df9d062> in <module>()
----> 1 sum(x[n]*t**n,(n,Integer(0),oo))
/usr/lib64/python2.7/site-packages/sage/rings/polynomial/infinite_polynomial_ring.pyc in __getitem__(self, i)
1433 alpha_1
1434 """
-> 1435 if int(i) != i:
1436 raise ValueError("The index (= %s) must be an integer" % i)
1437 i = int(i)
TypeError: int() argument must be a string or a number, not 'function'
</code></pre>
I'll appreciate any help or if you can point me to the documentation where to read about this. heluaniWed, 24 Oct 2018 17:31:33 +0200https://ask.sagemath.org/question/44056/