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 ...
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 ...
45 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 ...
241 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?
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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. ...
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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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Summation returns unevaluated

Please help me do this summation as Mathematica returns the same expression: ...
95 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 ...
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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)/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= \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)...