# Questions tagged [algebra]

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

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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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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 &... 1answer 63 views ### Picking out terms according to proportionality in expressions 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 101 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 57 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 52 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 98 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 275 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)... 1answer 48 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 <... 1answer 72 views ### Hochschild complex differential For a finite-dimensional \mathbb{C}-algebra A with basis \{e_1,...,e_n\} (structure of algebra encoded by structural constants \{c_{ij}^k\}_{i,j,k=1}^n such that e_ie_j = \sum_{k=1}^n c_{ij}^... 2answers 229 views ### Turn single fraction into multiple fraction expression I would like to find a way to take an algebraic fraction, where there is only a single numerator and denominator, and to turn it into multiple fractions multiplied by each other. I would like to ... 0answers 25 views ### Finding trivial solutions, of the type 0 = 0, of an equation involving su(N) structure constants 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 ... 1answer 222 views ### Linear operator algebra: How to distinguish scalars and operators? In the book "A Physicist' s Guide to Mathematica" Patrick Tam introduces symbolic rules for an algebra of linear operators. Mathematically the rules are as follows, where upper (lower) case letters ... 2answers 225 views ### How to make D apply chain rule on user-defined symbols as it does on Dot and NonCommutativeMultiply I have my own version of Dot called mydot, and it behaves quite similar to the built-in version in that it represents the non-... 0answers 74 views ### How can I test that an expression is a member of a field extension of Q Are there functions in Mathematica that I can use to define a field extension of Q? I want to be able to check if an element a \in Q(\sqrt2). So far I've tried to bypass this with with ... 1answer 575 views ### Normal ordering in Mathematica I want to create a function which normally orders a string of field operators. Consider the following:$$\langle0\vert\hat{a}(k_n) \cdots \hat{a}(k_2)\hat{a}(k_1)\hat{a}^\dagger(k_1)\hat{a}^\dagger(...
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If the two roots of the quadratic equation $x^2 - 6x + 1 = 0$ are $\log a$ and $\log b$. What is the value of $\log(a, a b^2) + log(b, a^2 b)$?
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### Non-commutative Algebra $LM=t^2 ML$, using NCAlgebra/Mathematica

I am currently using the NCAlgebra package, and am working with the algebra where $LM=t^2 ML$, where t is commutative. ...
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### Normalize a complex matrix

I have a complex matrix say, M={{a+bi,c,c,d},{0,a-di,c,d},{d,c,a-di,0},{d,c,c,a+bi}}; Normalize[M] I attempted to normalize this symbolic matrix with Mathematica ...
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### Algebra, Local variables and the Module function

Algebra is so much fun but I'm struggling to understand how MMA executes local variables within Module. Reading the Module ...
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### Rewriting a polynomial product into sums and differences of squares (a type of Lagrange reduction)

Say I have a product of two polynomials and I need to rewrite it into as many squares as possible using similar sums and differences. Is there a way to achieve this in Mathematica ? E.g. ...
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### Operator satisfies Leibniz rule

Suppose I have some symbols $a[-i]$ and $b[-j]$, where $i,j=1,\cdots,7$. The relation between them are $$a[-i]a[-j]=a[-j]a[-i],$$ $$a[-i]b[-j]=b[-j]a[-i],$$ $$b[-i]b[-j]=b[-j]b[-i],$$ I want to ...
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### Expand a differentiation-like product

Suppose I have some symbols $\tau$, $a[-i]$ and $b[-j]$, where $i,j=1,\cdots,7$. The relation between them are $$a[-i]a[-j]=a[-j]a[-i],$$ $$a[-i]b[-j]=b[-j]a[-i],$$ $$b[-i]b[-j]=b[-j]b[-i],$$ ...
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### collecting terms with different order

I am using homotopy perturbation method to solve nonlinear ODE. The first step is to introduce P parameter and collect different order of P. The code is like this: ...
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### How can I find properties of conic section (center, vertices, foci, etc.)?

Is there a built-in function that can compute properties of conic section from its equation? For example, provided the equation $\ (x-3)^2/25+(y-4)^2/16=1$ is it possible to find its center, foci, ...
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### KroneckerDelta does not automatically simplify

R[a_, b_] := FullSimplify[ KroneckerDelta[a, b] KroneckerDelta[a, b]] R[a, b] (* KroneckerDelta[a, b]^2 *) Should the the full simplified answer not be just ...
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### Expansion on sums of NonCommutativeMultiply

Following the MMa's documentations, the ExpandNCM[] function expands a**(b+c) without efforts (although I don't have very good ...
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### Find rectangle boundries with any angle

I have a rectangle that has an angle and i need to find its boundaries in an equality form ( less than, greater than). so i guess the best way to start is to tell you what i know CENTER: (...
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### Manipulations with complex numbers, phasors

I am trying to implement phasor arithmetic, but cannot get it to work well. The key is that the arguments to the phasor function are Reals, but I cannot get Mathematica to deal with that efficiently. ...