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.Mon, 28 Mar 2022 12:48:28 +0200Define a polynomial subalgebra generated by given polynomialshttps://ask.sagemath.org/question/61717/define-a-polynomial-subalgebra-generated-by-given-polynomials/Given a polynomial algebra in some variables, say $\mathbb{Q}[x_1,x_2,x_3,x_4]$, I'd like to define certain subalgebras that are generated by elements, e.g. $x_4$, $x_3^2-x_2x_4$. So I'd like to define $\mathbb{Q}[x_4,x_3^2-x_2x_4]$. As this uses the variables of the bigger space, I assume it needs to be defined as a subalgebra. But I could not seem to find a way of doing so.
I'm actually just interested in the dimensions of the degree-graded spaces of the subalgebra if that makes it easier.NicconMon, 28 Mar 2022 12:48:28 +0200https://ask.sagemath.org/question/61717/How can I construct graded algebras?https://ask.sagemath.org/question/8622/how-can-i-construct-graded-algebras/I am trying to create a graded algebra using generators and relations. I found that sage has a category for such things:
[http://www.sagemath.org/doc/reference/sage/categories/graded_modules_with_basis.html](http://www.sagemath.org/doc/reference/sage/categories/graded_modules_with_basis.html)
but there are no constructors or examples of how to create these things. Does anyone know where I can find examples of how to construct graded algebras, or more generally how to construct non-commutative algebras?StarxThu, 12 Jan 2012 19:49:07 +0100https://ask.sagemath.org/question/8622/