# Questions tagged [algebra]

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

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### How can I check whether a long rational expression contains a minus?

I have some monster expressions, but for simplicity, consider m = -(-3 + a+3 b-5 c)/(-d -5); How can I check if "undisplayable" expressions contain ...
• 1,982
1 vote
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### How to find the solutions to simulteneous linear equations in mathematica, in case if the solution to them is not unique? [closed]

I have these three simultaneous equations b+c-a-d=0; 2b-a+c=0 and c-e=0 I entered the command Solve[{b+c-a-d==0, 2b-a+c==0, c-e==0},{b,d}] But I got {}
• 223
361 views

### PolynomialQ behaviour

I am crafting some functions on polynomials that must be in x. But I checked that it is always True whatever variable I use: ...
152 views

### Evaluating square roots of quartic powers

I wonder why Mathematica does not act on the powers inside square roots. See the following example: Sqrt[a^4 b^4 c^4 d^4] does not give ...
• 575
384 views

### 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 ...
• 433
1 vote
60 views

### 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 ...
• 193
1 vote
116 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 ...
1 vote
71 views

### 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 ...
1 vote
145 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 ...
59 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) ...
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49 views

### 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: ...
• 133
104 views

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 ...
119 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: ...
• 75
824 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 ...
• 1,235
1 vote
97 views

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### 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, \...
1 vote