Questions tagged [algebra]

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

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1answer
60 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 ...
2
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1answer
70 views

Relabeling and matching variables (in MultiplicationTable)

Suppose we have a set of data given here as the multiplication table of 8 elements labeled {1,2,3,4,9,10,11,12}: $$ \begin{array}{cccccccc} 1 & 2 & 3 & 4 & 9 & 10 & 11 & ...
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47 views

Combinatorica and MultiplicationTable in Mathematica 11

I try to use <<Combinatorica` or call IntervalSlider; Needs["Combinatorica`"] or call ...
2
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0answers
35 views

Search the full group $G$ based on the partial list of its matrix representations

Suppose I have a list of matrices that may represent the partial list of the full group $G$. And here are the given set of 7 matrix elements. $$e =\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{...
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38 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[1]= \left( \begin{array}{ccc} 0 & 1 &...
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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 +...
2
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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 ...
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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 ...
2
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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 <...
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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. ...
2
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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 ...
4
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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)...
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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 <...
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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}^...
6
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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 ...
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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 ...
2
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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 ...
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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-...
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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 ...
3
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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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2answers
66 views

Algebra-Quadratics and Logarithms [closed]

If the two roots of the quadratic equation $x^2 - 6x + 1 = 0$ are $\log a$ and $\log b$. What is the value of $\log(a, a b^2) + log(b, a^2 b)$?
3
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2answers
174 views

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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0answers
419 views

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 ...
3
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1answer
67 views

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 ...
3
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1answer
432 views

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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2answers
258 views

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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1answer
65 views

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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0answers
178 views

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: ...
2
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1answer
116 views

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, ...
2
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0answers
114 views

Operations on ideals of polynomial rings

There is GroebnerBasis to compute a Gröbner basis of an ideal in a polynomial ring, but I am looking for a package to perform operations on ideals $I,J\subseteq\Bbb ...
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1answer
136 views

How do I define the distributive property for my operator?

I would like Simplify and Expand to work so that a^(b+c) <-> a^b + a^c I am ...
4
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1answer
364 views

How to cancel out denominator without expanding the numerator

I am trying to do algebra the way we do by hand. For example, ...
1
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1answer
75 views

How to pad periodically a cube to be compatible with ListInterpolation?

Context I would like to define a periodic interpolation function on a cube. It seems mathematica's ListInterpolation and the option ...
0
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1answer
68 views

What's the best strategy for finding the integers solutions of an hyperbola? [closed]

I have an hyperbola in this form $$y = \frac{ax+b}{cx+d}$$ (actually in my problem $c = -1$) and i have to find (at least)one of its integer solutions, I've seen that wolframalpha do it very quickly ...
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0answers
896 views

Algebra with Sums In Mathematica

I'm trying to perform basic algebra with summations and I haven't been able to find any information on whether it is possible in Mathematica. For instance, I took this rule about multiplying sums ...
4
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1answer
2k views

How to implement ladder operators for quantum harmonic oscillator?

I want to write the annihilation and creation operators for the harmonic oscillator, and see how they act on basis states of the form $\lvert n\rangle$. What's the best approach to implement this in ...
2
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1answer
392 views

Solve over Domains

Why do I get more real-valued solutions with Reals, than with Complexes: ...
-1
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2answers
325 views

Calculating the sum of a series of Lorentzian function

I understand the following result. Sum[1/((x + n)^2 + a^2), {n, -Infinity, Infinity}] ...
2
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1answer
102 views

How can I arrange linear equation in Mathematica?

How can I arrange linear equation in Mathematica When I define ...
1
vote
2answers
313 views

Defining a non-standard algebraic number

I need to perform matrix computations, where elements of matrices not only contain $i$ (imaginary unit), but also a specific "unit" number, let call it $c$, with non-standard algebraic properties: $c\...
3
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1answer
132 views

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 ...
3
votes
1answer
740 views

Hadamard Lemma and commutators algebra

I would like to implement the following formula, which goes under the name of Hadamard Lemma: $ e^A \, B \, e^{-A} = \sum_{k=0}^{+\infty} \frac{1}{k!} [A,B]_k $ where $ [A,B]_0 = B , \...
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2answers
349 views

Avoiding square and cubic root of complex number [closed]

I want to simplify following expression to avoid calculation of square and cubic root of complex numbers: $ \sqrt[3]{R + \sqrt{Q^3 + R^2)}} + \sqrt[3]{R - \sqrt{Q^3 + R^2})}$ where $ Q, R \in \...
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1answer
118 views

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 ...
11
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1answer
309 views

How to specify algebraic relations between objects?

so I'm wanting to screw around a bit with Geometric Algebra in Mathematica. To start, I want to create some basis objects: $e_1,~ e_2,~e_3$ and then specify the relations between them which are $$ ...
0
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1answer
59 views

Limit converges when I plug in numbers, but diverges when I leave in terms of variables [closed]

I have an expression such as the following $$\frac{ab+a^2c+bx-acx+2adx-(a-x)\sqrt{b^2+2abc+a^2c^2+4acdx}}{2ax}$$ which describes a physical system that I want to find the limit as $x$ goes to 0. If ...
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0answers
45 views

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: (...
0
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0answers
282 views

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. ...
3
votes
2answers
949 views

Factorization of a polynomial fraction to a certain combinations of other polynomial fractions

I currently am working on a project for to find some new algebra structures. But I faced with a factorization problem which I cannot come out of it! I could find the lower dimensional of it. But I ...
3
votes
1answer
94 views

Jordan product in Mathematica

Does anyone know how to best handle non-associative operations in Mathematica? I am specifically interested in finite commutative Jordan algebras. I would like to construct a product operator x such ...