# Questions tagged [algebra]

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

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### Algebra deduction?

I was trying to use Mathematica for some simple algebra deduction, but it didnt work. code: TrueQ@(Sqrt[(e0 u0)/(e1 u1)] == Sqrt[e0 u0]/Sqrt[e1 u1]) Any ideas ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Finding the integer terms of a binomial expansion [closed]

What functions can I use to find how many integer terms the following expression has? $$\left (\sqrt[19]{19}+\sqrt[95]{95}\right )^{1995}$$ Edit 1 In the development of that binomial, at some point ...
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### 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: ...
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### 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 ...
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### 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?
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### How to separate integers and radicals from a term?

If I have a variable such as r = 1 + Sqrt[2] + Sqrt[13] how can I separate that into two separate variables with the rational and irrational parts? i.e. ...
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### 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 ...
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### 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 ...
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### 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[3])/2, (3)^-1])^6 // N -0.5 - 0.866025 I ...
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### 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 ...
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### 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[1]= \left( \begin{array}{ccc} 0 & 1 &...
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I am trying to figure out how to pick terms proportional to $x$ (or any other expression). I have the following problem: I want to pick out $(1+2y) x$ from a polynomial of the form $(1+2y)x + e^xx +... 1answer 98 views ### Simple tensor manipulations in mathematica I want to perform simple calculations involving kronecker deltas without specifying the dimension of the space I am in. For example, I would like to automatically calculate (note the implied Einstein ... 0answers 54 views ### Implement commutativity and associativity for custom operation Just to give context: I want to implement quantum mechanical ladder operators and for this I want Mathematica to realize when it can just commute my ladder operators with numbers or variables because ... 1answer 50 views ### Function definition interrupts pattern matching? I'm trying to redefine NonCommutativeMultiply (NCM) to behave like an anticommuting operator, based on the question here. This involves calling Unprotect on NCM and adding a definition that leaves <... 1answer 71 views ### Solving a system of inequalities I'm trying to solve a system of inequalities with$6$variables using Reduce but it's taking a long time (at least 30 mins) and has not yet finished. ... 1answer 41 views ### SeriesCoefficient returns unevaluated SeriesCoefficient[x^m, {x, 0, p}] This gives back the same thing. I tried Assumptions, FullSimplify etc. I keep getting back the same thing. The answer is ... 1answer 47 views ### Complex algebra I give Mathematica these commands:$Assumptions = Element[x, Reals] && Element[y, Reals] \[Theta] = ArcTan[x, y] z = Exp[I \[Theta]] Conjugate[z] I get <...
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)...