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Questions tagged [algebra]

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

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5 votes
3 answers
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How to get the analytical form of a solution to an algebraic equation?

The real analytical solution of the algebraic equation $x^5 + 10 x^3 + 20 x == 4$ is $x=-2^{2/5} + 2^{3/5}$, how to get it with Mathematica? I've tried with ...
SHBooKP's user avatar
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1 vote
1 answer
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Solving algebraic equations perturbatively (using function series)

I have linearised some equations and trying to solve them perturbatively in powers of small parameter $e$. Here is my script ...
Marco's user avatar
  • 163
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2 answers
86 views

Simplification of quantum ladder operators (ideally using Using NCAlgebra)

I want to do math that involves a series of ladder operators. In the past I've tried to get it working with a 20 year old Mathematica package. But my feeling is that this is a very unused package and ...
Steven Sagona's user avatar
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Modern way of simplifying non-commutative algebraic expressions in 2022

I have been asking about how to do modern quantum optics calculations in 2022, and one potential solution is to use a package that uses noncommutative algebra. There are currently very old questions ...
Steven Sagona's user avatar
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0 answers
95 views

Modern way to do quantum optics calculations in 2024?

Quantum Optics can often require messy algebraic simplifications of noncommuting operators (usually ladder operators and commutators). I've asked here about how to do it before. What are some modern ...
Steven Sagona's user avatar
0 votes
1 answer
55 views

Solving high dimensional nonlinear algebraic equation numerically

I would like to solve an algebraic equation A=f(A) whose argument A is a large 3D matrix. Ideally, I would not like to flatten the system of equations, before feeding into FindRoot because f(A) ...
Tamaghna's user avatar
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0 answers
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Finding coefficient of vector expression when using SuperLie package

I'm using the SuperLie package and using that have defined a Lie superalgebra with an ordered basis: ...
AXidenT's user avatar
  • 133
2 votes
2 answers
94 views

Graded commutativity

As we all know, Mathematica has extensive built-in support for computations in free commutative algebras, AKA polynomials algebras. It's also not that hard to make computations in exterior algebras ...
Najib Idrissi's user avatar
-1 votes
1 answer
109 views

Expression for an integral

I am facing a problem obtaining an expression for my integral. My code goes in a time-consuming loop whenever I execute this integral. The code is: ...
Jpmg's user avatar
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4 votes
3 answers
777 views

Why is the result of TrueQ[(x^n)^m == x^(n*m)] False?

Why is the result of the code below False ? TrueQ[(x^n)^m == x^(n*m)] How can I get it to be ...
vasili111's user avatar
  • 1,215
1 vote
1 answer
95 views

Rearranging a simple algebraic expression

I have a polynomial of variables $x,y$, where $|x|<1$ and $|y|<1$. When I apply the Simplify function to this expression, I get an expression of the form $(x-...
akr's user avatar
  • 177
4 votes
5 answers
215 views

A script for finding a basis of positive vectors in the kernel of a matrix which is minimal in some sense?

The kernel to the left of the matrix ...
florin's user avatar
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0 votes
1 answer
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Transform a list of delayed rules with conditions to a new list of delayed rules

I have a list of rules that implement some abstract algebras, for instance, that of the Pauli matrices, ...
Lelouch's user avatar
  • 533
-1 votes
2 answers
84 views

If x^x^x=y^y, express y in terms of x [closed]

This question is one of my friend think out suddenly and asked me how to do, but I have no idea how to do it, anyone have ideas? (even my friend don't know how to do it, he just think up the question) ...
teeeshj dabest's user avatar
5 votes
1 answer
437 views

Present a logarithm in terms of two logarithms

If $\log _8 3=p$ and $\log _3 5=q$ then, in terms of $p$ and $q$, what does $\log _{10} 5$ equal? I tried by my hand, I get the answer is $\dfrac{3pq}{1+3pq}$. How can I tell Mathematica solve ...
Laurenso's user avatar
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0 votes
1 answer
130 views

Solve[] isn't producing a correct result

I want to find the exact algebraic roots of the following function in terms of Z, P, Q, <...
Lawton's user avatar
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1 vote
0 answers
60 views

How do I efficiently define rules for non-commutative algebras, (like differential forms)?

Defining rules seems to be quite troublesome, because whatever rule I make has to have the exact syntax ordering of the expression I want to modify. For example, take this differential form ...
ions me's user avatar
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1 vote
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How to solve quartic equation modulo a composite? [closed]

I have an univariate polynomial equation over a composite moduli. Namely the composite is of for $q=(2p)^{2}-1$ where $p$ is odd and $2p-1$ and $2p+1$ are distinct primes. The modular equation is $$ax^...
Turbo's user avatar
  • 145
7 votes
4 answers
256 views

Move variables to one side of equation

I have a bunch of linear equations of the form x[1] == 5012 - 5x[3] - 2x[4] + 5x[7] etc. Specifically there is one linear variable on the left, and the right-hand ...
Facieod's user avatar
  • 175
1 vote
2 answers
140 views

How to determine the shape of real quadric surfaces? Use discriminants?

Let $a x^2+2 b x y+c y^2+2 d x+2 e y+f=0$ be the implicit equation that defines a conic section , where $a,b,c,d,e,f$ are real numbers. I have known from wikipedia how to use 2 discriminants to ...
138 Aspen's user avatar
  • 1,371
0 votes
2 answers
72 views

How to define an infinite dimensional algebra with a known basis and multiplication rule?

My goal is to do symbolic calculations in the noncommutative associative algebra generated by two elements $x,y$ satisfying the relation $x.y=q~y.x$. This infinite dimensional algebra has the basis $...
Lagrenge's user avatar
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4 votes
3 answers
131 views

Odd behavior of GroebnerBasis

I have a parametric equation like following: ...
yode's user avatar
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1 vote
1 answer
32 views

Validate equalities among Square roots for a simple expression

I am trying to validate this property: $\sqrt{1-z}=\sqrt{-(-1+z)}=(\text{}\pm i) \sqrt{-1+z}$ FullSimplify[Sqrt[1 - z] == I Sqrt[(-1 + z)]] I have seen how we need ...
Jmtz's user avatar
  • 113
1 vote
1 answer
54 views

ParallelTable and NC polynomial simplification

I use NC algebra to apply simplification rules on non commutative polynomials. I would like to treat a huge number of polynomials, ~200, so I would like to run these computations in parallel. However, ...
Goupildz's user avatar
1 vote
0 answers
79 views

NoncommutativeMultiply, wedge product and exterior algebra

I would like want to automate some calculations involving wedge products of differential form of different order. Is it possible to define a NoncommutativeMultiply function that has the properties of ...
Spinoro's user avatar
  • 11
1 vote
3 answers
157 views

Product involving Kronecker Deltas

I am trying to do some products involving some objects made out of Kronecker deltas. For example, taking an object like $x_{abcd}=\delta_{ab}\delta_{cd}$, where all the indices run from $1$ to $N$, I ...
dorrel's user avatar
  • 49
3 votes
0 answers
46 views

Can we ask Mathematica if a reduction of a system to one scalar equation in one variable+ rational representations of the other variables exists?

Nonlinear determined systems have typically several solutions involving square or higher order roots. Instead of solving them, it may be more profitable to reduce them to smaller systems with fewer ...
florin's user avatar
  • 1,798
1 vote
1 answer
91 views

How can I solve/verify the following matrix?

Given $ZFZ’ = C$, I have the following set of symbolic matrices: $Z$ of order $m\times q$ $Z’$ is the transpose of matrix $Z$ of order $q\times m$ $F$ of order $q\times q$ $C$ of order $m\times m$ ...
EVC's user avatar
  • 13
0 votes
1 answer
48 views

Resubstituting variables back into the calculated

I have lengthy second order derivative of a function that is defined with multiple lines of variables. When I compute the derivative how can I put back into the computed result the auxilary variables ...
Al Guy's user avatar
  • 1,610
0 votes
0 answers
95 views

Plug in values in symbolic expressions

With the help of answers on this post: new rule for noncommutative multiplication, defined new noncommutative multiplication: ...
skipi's user avatar
  • 45
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0 answers
84 views

Standard Monomials

I'm trying to find the number of standard monomials of an ideal. The footprint bound says (1) that the number of solutions to a system of polynomials is bounded by the number of standard monomials of ...
atat's user avatar
  • 95
1 vote
0 answers
52 views

Mathematica reacts to a wrong condition in a weird way

With apologies, I evaluated the eigenvalues of a matrix under a condition which included wrongly some Falses. The weird result was a failure to obtain the eigenvalues? ...
florin's user avatar
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1 vote
1 answer
89 views

Reducing roots of power sums

Often I encounter expressions like for example Root[ 1 - # + #^2 - #^3 + #^4 - #^5 + #^6 &, 3 ] or ...
Gert's user avatar
  • 1,530
2 votes
2 answers
126 views

ReplaceAll for expressions involving negative power [closed]

I have an expression: $exp=1+\frac{1}{x}+\frac{2}{x^{2}}-\frac{3}{x^{3}}$ I am trying to make the following replacement: $\frac{1}{x^{i}}\rightarrow f(i)$, where f is any arbitrary function. The ...
Utsab Dey's user avatar
4 votes
1 answer
354 views

Zassenhaus formula in Mathematica

I'm looking for Mathematica implementation of Zassenhaus formula -- given two matrices $A,B$, truncate the expansion of $\exp(A+B)$ from this paper: $$e^{t(A+B)}= e^{tA}e^{tB}\prod_{n=2}^\infty e^{t^n ...
Yaroslav Bulatov's user avatar
2 votes
2 answers
260 views

Series expansion using binomial theorem in Mathematica

The series expansion of $\displaystyle\left(1-\frac{a}{x}\right)^{1/3}$ using the Binomial theorem is given by $$\displaystyle\left(1-\frac{a}{x}\right)^{1/3}=1-\frac{a}{3x}-\frac{a^{2}}{9x^{2}}-\...
VH84's user avatar
  • 179
3 votes
2 answers
166 views

Precise control of fraction expression

It seems that expression for fraction differs when the number of terms in the numerator is more than 2. ...
imida k's user avatar
  • 4,295
1 vote
1 answer
57 views

How to Simplify expression into partial Trignometric form?

I have an expression with thousands of terms each of them has the form (1- Exp[-2 a x]) . I want to be able to write it as 2 Exp[- a x] Sinh[ a x] . How do I do this without doing it for each term ...
Quasar Supernova's user avatar
0 votes
1 answer
48 views

Expressing n in terms of x, given x in terms of n [closed]

Using Wolfram Alpha, I tried finding solution of this: If n(n - 1)/2 = x,then find value of n. Unfortunately, not getting value for n.
Splendid Digital Solutions's user avatar
0 votes
0 answers
28 views

Polynomial GCD over a ring with composite modulus [duplicate]

I need the gcd of two polynomials, ...
PorkyPhoenix091's user avatar
0 votes
0 answers
57 views

Cells stuck at running after running after finding symbolic eigenvalues of a 4x4 matrix

I used the code below to calculate the eigenvalues of a 4x4 matrix symbolically. ...
Anik's user avatar
  • 15
0 votes
0 answers
32 views

Expanding a large dynamic expression involving roots of a degree 4 polynomial

I am trying to find the eigenvalues of a 4x4 Matrix symbolically. Below is the code I am using, ...
Anik's user avatar
  • 15
3 votes
2 answers
263 views

Function to write an algebraic expression in terms of another

So I'm working on a physics problem. I have two functions: $\rho = \frac{F}{(\beta F^\alpha+1)^\frac{1}{\alpha}}$, $p = - \frac{F}{(\beta F^\alpha+1)^\frac{1}{\alpha}} + \frac{4}{3}\frac{F}{(\beta F^\...
Vicente Sierra Rosas's user avatar
0 votes
1 answer
75 views

Conditional Expectation of an autoregressive (AR1) Process

Suppose X is a time series that follows the process: $X[t]=\rho X[t-1] + \varepsilon[t]$ where $\varepsilon[t] \sim \mathcal{N}(0.0, \sigma)$, $\varepsilon[t]$ is IID and $X[0] \sim \mathcal{N}(0.0, \...
Baba Yara Fahiz's user avatar
1 vote
1 answer
76 views

Simple Algebra (solving for an unknown)

I am trying to solve this equation for kss with mathematical but the system is failing and so I am hoping to get some pointers here. ...
Baba Yara Fahiz's user avatar
2 votes
1 answer
227 views

How to get the real part of a complex function with some real coefficients?

I want to get the real part of the function n3[t] (see below) which is the solution to a differential equation. Solve the differential equation. (Suppose ...
Ryoko Asakura's user avatar
1 vote
2 answers
182 views

How to get the algebraic form of cellular automata

In atlas.wolfram.com (see here http://atlas.wolfram.com/01/01/views/173/TableView.html, for example) we can get the algebraic form of any given elementary cellular automaton in 1D. Is there a way to ...
Kostas's user avatar
  • 65
1 vote
1 answer
83 views

FullSimplify not working when simplifying a complex number

Here is a snippet of the code I am working on, which requires me to get the Real part of the Harmonic Oscillator wavefunction. ...
Anik's user avatar
  • 15
0 votes
0 answers
74 views

FullSimplify command not showing any output

I am trying to FullSimplify an expression and in the end I am not getting any output displayed. The process runs for sometime and stops after making a sound. The ...
Dumbledore Albus's user avatar
2 votes
2 answers
202 views

How to define a new algebra using TagSet?

For example, I would like to define the algebra of quaternions. I coded something like ...
Curious Cat's user avatar

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