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# Questions tagged [algebra]

Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.

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### Update: Calculate Tensor products and traces with Mathematica

My goal is to algebraically simplify expressions involving tensor products and taking the trace. That is, I would like to compute $\operatorname{Tr}\left( \prod_i(id+a_i \otimes b_i) \right)$, using ...
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### Identity Matrix in symbolic Tensor Product [closed]

I am trying to simplify symbolic tensor products. E.g. ...
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### Simplifying polynomials in non-commutative variables

I would like to be able to simplify a polynomial in two non commuting variables, the desired result being that in every term one variable occurs to the left of the other variable. An example would be ...
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### How to define custom operators

I am currently running Mathematica 8 and I would like to know how to define custom operators. Let's say I define an operator called $\times$ where: $$a\times b = a+a\cdot b+b$$ I also want to know ...
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### How can I convert a list to an expression? [duplicate]

For example, I have the following list: {x1,op1,x2,op2,x3,op3,...} And I would like to convert the list to the following expression: x1 op1 x2 op2 x3 op3 ...
Let $N$ be a prime, and $q$ be a positive integer. Given a polynomial $f(x)$ in $R = \mathbb Z[x]/(x^N-1)$, I want to find another polynomial $f_q(x)$ in $R_q = \mathbb Z_q[x]/(x^N-1)$, such that f(...