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.Sun, 02 Jan 2022 17:22:35 +0100Constructing a non-commutative algebra over Z[q, q^-1] given some relationshttps://ask.sagemath.org/question/60516/constructing-a-non-commutative-algebra-over-zq-q-1-given-some-relations/
I would like to construct a non-commutative alegebra over Z[q, q^-1] generated by the variables u1, u2, u3 with the relations:
u2*u1 = q*u1*u2
u3*u2 = (q^2)*u2*u3
u3*u1 = u1*u3
but I am having some trouble getting this to work. I have primarily been trying to do this using the FreeAlgebra structure. Here is what I have tried:
----------
Zq.<q> = LaurentPolynomialRing(ZZ)
A.<u1,u2, u3> = FreeAlgebra(Zq, 3)
G = A.g_algebra({u2*u1: q*u1*u2, u3*u2: (q**2)*u2*u3})
G
but I get the errors:
AttributeError: 'FreeAlgebra_generic_with_category.element_class' object has no attribute 'lift'
TypeError: unable to coerce <class 'sage.algebras.free_algebra.FreeAlgebra_generic_with_category.element_class'> to `an integer`
----------
Zqring.<q, qinv> = ZZ[]
qideal = Zqring.ideal(q*qinv - 1)
Zq.<q, qinv> = Zqring.quotient(qideal)
A.<u1,u2,u3> = FreeAlgebra(Zq, 3)
I = A.ideal(u2*u1-q*u1*u2, u3*u2-(q**2)*u2*u3, side = "twosided")
W.<u1, u2, u3> = quotient(A,I)
u2*u1-q*u1*u2
but this outputs "(-q)*u1*u2 + u2*u1" and not "0"
----------
Zqring.<q, qinv> = ZZ[]
qideal = Zqring.ideal(q*qinv - 1)
Zq.<q, qinv> = Zqring.quotient(qideal)
A.<u1,u2,u3> = FreeAlgebra(Zq, 3)
I = A*[u2*u1-q*u1*u2]*A
W.<u1,u2,u3> = A.quo(I)
W(u2*u1-q*u1*u2)
and, again, the output is not "0".
Is there a better way I can construct such a non-commutative algebra?
Thanks!kAllenMathSun, 02 Jan 2022 17:22:35 +0100https://ask.sagemath.org/question/60516/Saturated chainshttps://ask.sagemath.org/question/43545/saturated-chains/ I know there is a command to take all maximal chains and all cover relations of a poset. I am working with a ranked poset and I am wondering if there is a command for all saturated chains in a poset. I appreciate any help given.StivenSat, 01 Sep 2018 02:16:47 +0200https://ask.sagemath.org/question/43545/Noncommuting variableshttps://ask.sagemath.org/question/7784/noncommuting-variables/I am extremely new to Sage, and even newer to this site, so I apologize if anything is not up to standards.
I am dealing with a multivariable polynomial ring over $\mathbb{Z}$ with noncommuting variables. Is there a way to implement this with Sage? The closest thing I have found is FreeAlgebra, where the variables are noncommutative, but I have not found any way to impose relations that I want.
As stated before, I am extremely new to all of this so don't assume that I know anything, and don't hesitate to give any and all suggestions.Eric A BunchMon, 06 Dec 2010 21:53:32 +0100https://ask.sagemath.org/question/7784/How do I define a piecewise function?https://ask.sagemath.org/question/7709/how-do-i-define-a-piecewise-function/[http://en.wikipedia.org/wiki/Piecewise][1]
[1]: http://en.wikipedia.org/wiki/PiecewiseccanoncSat, 25 Sep 2010 15:04:52 +0200https://ask.sagemath.org/question/7709/How does sage deal with choosing branches? Examples?https://ask.sagemath.org/question/7710/how-does-sage-deal-with-choosing-branches-examples/[http://en.wikipedia.org/wiki/Principal\_branch][1]
[http://en.wikipedia.org/wiki/Exponentiation#Failure\_of\_power\_and\_logarithm\_identities][2]
[1]: http://en.wikipedia.org/wiki/Principal_branch
[2]: http://en.wikipedia.org/wiki/Exponentiation#Failure_of_power_and_logarithm_identitiesccanoncSat, 25 Sep 2010 15:34:50 +0200https://ask.sagemath.org/question/7710/