# Questions tagged [algebra]

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

144 questions
Filter by
Sorted by
Tagged with
34 views

### Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything

I think it is straightforward from the title, Simplify[Im[1/(x+I)], x > 0] spits out, Im[1/(x+I)] while I would have ...
16 views

### Expressing Numbers with Rational Denominators (Surd Form) [duplicate]

Is there a command which expresses given real numbers in surd form (when possible)? That is, a form where any rooted terms are placed in the numerator, and the denominator is rational. Here are some ...
42 views

### Grassman and Clifford algebras as quotients of the tensor algebra

I've been working with tensors in Mathematica; it's great to have something like TensorProduct built-in with linearity and everything. Maybe you can take advantage of these structures to work with ...
40 views

### Algebraic manipulation on removing common factor outside

d[i,j] and M[i,j] are elements of size arrays of size 2x2 After some manipulations I get this as Output ...
41 views

188 views

### Simplifying simple signed expression ( such as $-x(x-1) \to x(1-x)$ ) based on assumptions

Context I would like to simplify expression involving, say, (x-1) or (x^2-1) when I know that |x|<1 so that the global ...
91 views

### Finding the integer terms of a binomial expansion [closed]

What functions can I use to find how many integer terms the following expression has? $$\left (\sqrt{19}+\sqrt{95}\right )^{1995}$$ Edit 1 In the development of that binomial, at some point ...
44 views

### Function ellipticAdd to add points belonging to an elliptic curve $y^2 = x^3 + a\,x^2 + b\,x$ [duplicate]

In the EllipticLog WRI web page, there is a function called"ellipticMultiply defined as: ...
81 views

### Symmetrize a polynomial forgetting the commutativity property of multiplication

I need a script to authomatically symmetrize a given polynomial. For example, if the input is xy the output should be ...
235 views

### Solving an equation with vector coefficients

I want to solve $(ct)^2 = d(t)\cdot d(t)$ for $t$, where $d(t) = \frac{1}{2}at^2 + vt + r$ Where$a, v$, and $r$ are all 3-dimensional vectors in Cartesian coordinates. How can I do this?
62 views

197 views

### How to separate integers and radicals from a term?

If I have a variable such as r = 1 + Sqrt + Sqrt how can I separate that into two separate variables with the rational and irrational parts? i.e. ...
157 views

### Efficient implementation of the divided difference

Question. I am looking for more efficients ways to compute Newton's divided difference, i.e. the operator $$\partial : f(x,y) \mapsto \frac{f(x,y)-f(y,x)}{x-y} \ ,$$ for the case where $f$ is a ...
91 views

### Summation returns unevaluated

Please help me do this summation as Mathematica returns the same expression: ...
94 views

### Factoring expression with rational powers

To any great Mathematica-matician. Why Mathematica can’t factor this Factor[-1+x^(2/3)] I know that Factor mainly targets ...
29 views

### Computational discrepancy for plugging in equivalent forms into an expression

When the following 9th root of unity is raised to the 6th power a 3rd root of unity is returned. (Power[-(1/2) + (I Sqrt)/2, (3)^-1])^6 // N -0.5 - 0.866025 I ...
58 views

### Relabeling/matching variables of big data (in MultiplicationTable)

Let A and B be two sets of tables (from multiplication tables of a group, 24 by 24 as rows by columns), how can we effectively (and possibly also efficiently) find a way to map between them, if two ...
68 views

36 views

### Solving some constraints on a subgroup of a Lie group [closed]

Let $M$ be a rank-3 matrix, I am interested in searching all the group elements $g \in$ SU(3) Lie group, such that, $$g^T M g =M.$$ Example 1. Let  M= \left( \begin{array}{ccc} 0 & 1 &...
62 views

250 views

### Symbolic calculation with generators and relations

Is it possible to do the following in Mathematica: Define an algebra $A$ via generators and relations and multiply some tensors in $A\otimes A$ (and of course simplify the relations via the relations)...
so I have a bunch of equations $f_{abc} = f_{egd}m_{ae}m_{bg}m_{cd}$ (sum over repeated indices), where $f_{abc}$ are the structure constants of $su(N)$, for some $N$, and $m_{ab}$ are elements of ...