Questions tagged [algebra]
Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.
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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 ...
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1
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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.
...
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0
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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 ...
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2
answers
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How to define a new algebra using TagSet?
For example, I would like to define the algebra of quaternions. I coded something like
...
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How to define an operator like ⊕？
For example, I define the circle plus as
a_\[CirclePlus]b_ := a + b^2;
a__\[CirclePlus]b_ := (a[[1 ;;-2]]\[CirclePlus]a[[-1]])\[CirclePlus]b;
But when I try
...
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How to define functions using $Z_2$ coefficients and $Z_N$ variables, e.g, realizing $1+1=0$?
A minimal example is to realize the following:
$x+x = (1+1)x = 0$, and $x^{N+1}y^{N+1}=xy$,
where $N$ is a given positive integer.
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Separating the Numerator & Denominator
It's been years since I last programmed in Wolfram & for the first few days, I felt like I've been feeling around the dark; now that I've mostly forgotten how to code it.
Again, I could be ...
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Reducing Polynomial Functions over a Finite Field
Over $\mathbb{F}_{4}$, for example, I am looking for a function that will, for example, reduce the polynomial function (not an element of the finite field itself) $$x^5 + 6x^4 +x^3 + 1 \rightarrow x^2 ...
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How to understand the very long confusing output of a command?
I have a complicated expression with many parameters
...
- 1,250
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Tropical Operation Conversions: Multiple Operations
I apologize if my syntax is bad. I looked around, but didn't see anything on this in the stack exchange.
I would like to be able to transform a classical real-valued polynomial to a tropical ...
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How to get the extension degree
The real number field cannot express $\sqrt{2}$, so we extend $2$ times to get $Q(\sqrt{2})=a+b\sqrt(2)$. But it cannot express $\sqrt{3}$ still. So we are going to extend it $2$ more times to get $Q(\...
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How to speed up Resultant?
I am experimenting with the polynomials Y and T:
i1 = 9; i2 = 4;
Y = Sum[ x^i y[i], {i, 0, i1}];
T = Sum[ x^i t[i], {i, 0, i2}];
Timing[Resultant[Y, T, x]]
Whith ...
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Solving System of six Non-Linear Equations in Six Unknowns
I've been trying to solve the following system of equations using NSolve and the code has been running for close to 24 hours already. Is this normal? Is there a quicker way to solve these equations? ...
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How to solve this equation analytically?
Why can't Mathematica 13 solve this equation in radicals?
Solve[x^5 - 5*x^4 - 10*x^3 - 10*x^2 - 5*x - 1 == 0, x] // ToRadicals
I also tried to use ...
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Define a new rule for multiplication
I am trying to implement a new rule for noncommutative multiplication:
$$ x * q^n * y \to q^n * x * y, $$ where $\ast$ stands for noncommutative multiplication and x and y are random products in ...
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Simple algebra question
Am I missing something here? This does not resolve to True.
Clear[x,y]
$Assumptions={x>0,y>0}
FullSimplify[(Sqrt[x] + Sqrt[y]) == Sqrt[x + y + 2 Sqrt[x y]]]
...
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Empty output {} for matrix solutions which I know graphically exist [closed]
I am new to Mathematica, so there's a good chance that I am missing something critical here but I tried to check the documentation and am still stuck.
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Factorize expression by specific term [closed]
I am new to Mathematica but I would like to know how to force Mathematica to factorize an expression by a specific term.
Exemple, imagine I have a term like this:
And I have an expression like this:
...
1
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0
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Mathematica doesn't simplify 1.` x
I'm debugging a program that uses polynomials with numerical coefficients and it turns out that mathematica does not simplify 1.` x[1]^2 x[2]^2 to ...
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How to get exact solution for determinant in mathematica? [closed]
I am currently trying to program in mathematica, my issue is that the program is not solving for the exact value of the determinant in comparison to matlab. Code given below, where a and x are ...
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handling roots in mathematica [duplicate]
I am looking for the solution of:
$\text{Solve}\left[-\frac{\alpha }{\sqrt{1-L}}-\frac{L t}{2}=-\alpha -2,L,Reals,\text{Assumptions}\to 0\leq \alpha \&\& 0<t\right]$
Mathematica is giving ...
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3
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How to find constant term of binomial
There is supposed to be a command or set of commands to find the constant term of a binomial expression like
$$
\left(-2x^4 + \dfrac{-5}{x}\right)^{25}
$$
...
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Spotting and condensing expressions in output
I am running some symbolic scripts to generate a model problem. One of my outputs is
This is generated by the Mathematica code
or, in Mathematica format (owing to the fancy lettering and formatting ...
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Take a specific part of a matrix, excluding the external brackets [duplicate]
I have a little manipulation problem.
I have the following matrix:
...
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56
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How to use only real values in a notebook?
I am wondering how to make Mathematica only evaluate real numbers by creating an initialization line in the beginning of a notebook.
I would like to prevent the following:
complex trigonometric ...
- 1,117
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109
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Algorithms or Mathematica definition for functions ideals of polynomial Rings
This question was well posed four years ago without answer at Operations on ideals of polynomial rings. I asked again in Nov 2021 and posted possible function defininitions. Lichtblau commented ...
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57
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apply a change of variable to an expression
What would be the simplest way in which we can write
y[x1_, x2_, x3_] = x1 + x2*x3
then
x4 = x2*x3;
to get to the form:
...
- 575
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0
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Mathematica package for computing Macdonald polynomials
I want to implement computation of Macdonald polynomials in mathematica. A similar question was raised in another question 5 years ago (Macdonald-Koornwinder polynomials?), but received no clear ...
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How to apply this function? [closed]
I have defined functions f[x], g[x]. How can I let them act on variable x (I want to put the ...
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Inverse/Division in finite field?
Think of multiplictavie group of finite field F[p,n], where p is a prime number and n is a positive integer.
The whole elements of F[p,n] can be represented as
p^n-p^(n-1) positive integers in the ...
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How can I multiply two 2-dim. matrices? [closed]
If I have the given below matrix d1[7,7], how can I multiply d1 by d1 to get the square matrix d2=d1.d1 ?
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Simplify simple symbolic expression with KroneckerDelta
In short, my question is about finding a method for performing an automatic substitution f[a]/.{a->b}, where b depends on the ...
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No solution to the equation even though it has one
I was trying out Mathematica with a simple equation. I tried this one out, but it outputted nothing and when I went on WolframAlpha to test it, there was a result (c = 3 btw). Please let me know if ...
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generate quadratic functions to evaluate membership of points
How can I make a printable list with different quadratic functions and with points that belong or not to them so that a young person can check whether or not the point belongs to the parabola? my code ...
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Simplifying quantum operators (ladder operators with multiple modes)
Similar to this question, I am interested in working with an implementation of quantum ladder operators.
I've been trying to use this "Quantum Mathematica Package" to solve some lengthy ...
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Using Curl and Grad in cylindrical coordinates gives different result than in Cartesian
I am doing a quite elementary calculation to verify
$$
\vec \nabla\cdot V = \vec\nabla \times \vec A
$$
Where $V$ is just some scalar function in $\rho$, $\phi$ and $z$ and $A$ is defined as
$$
...
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Substitution of sequences to derive recursive mean
I would have the following derivation to calculate the recursive moving average and I'd like to follow it as closely as possible in Mathematica.
For the sequence where $y(i)$ is considered as an ...
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How to solve these type : If $a + b + c + d = 63$ then find the Maximum of $(a b+ b c+ c d)$
If a + b + c + d == 63 then find the Maximum of a b + b c + c d.
I tried using If, ...
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Group terms in a large expression based on their minimum variable dependencies
Suppose I have a very large expression, myEq[x1,x2,x3,x4] in four variables, x1, x2, ...
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How to simplify for a ratio of two variables
Say I have an equation like
$$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$
...
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How to solve these algebraic identities?
I need help in finding/solving these types of algebraic equations using Mathematica.
here is the problem/code. I tried using 'With' command but no use. Thanks in advance.
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Solving from previous results
I require in this program to use only all the value of “p” form “solution 1” in “solution 2”.
Instead of copy and paste each value of “p” individually in solution 2, I am trying to write a function to ...
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How to generate multiplication tables up to nxn?
I'm doing a simple multiplication table and I have this that I'm having a hard time with.
I imagine that there must be a shorter way to do it, what I can't get is that it paints black the first column ...
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Simplifying cross product expressions
Suppose I want to calculate:
Cross[A1 + B1, A2 - B2] + Cross[A1 - B1, A2 + B2]
which is equal to 2 A1xA2 - 2 B1xB2
Using ...
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Check if polynomial is in factored form, without factoring
I have a large list list of integer polynomials, all of which are the output of Factor. So my list looks something like this: <...
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1
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52
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Sorting terms in a huge equation by grouping specific products
I have a boundary condition for a problem, which contains around 100 terms! I have no trouble getting Mathematica to compute it, but the terms are sorted in a seemingly random order and I would like ...
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Can I implement a constant in such a way that every function of it gets redirected?
Basically, I want to implement split-complex numbers and tessarines.
They can be easily implemented as 2x2 matrices with complex elements.
But I want them to work in general expressions.
So I want a ...
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Perform Eliminate, Solve and Format at once in Mathematica
I have a series of equations where I use eliminate to get a new equation with desired variables. This equation is then solved for a specific variable and then the result is presented in a specific ...
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numerical values of coefficients
Consider the following output:
x= (Sqrt[3/(2 (1 + Sqrt[11]/4))] b[0, π/3] - (1 + Sqrt[7/3]) b[(2 π)/3, (2 π)/3])/(4 Sqrt[2] 7^(1/4) Sqrt[1 + Sqrt[7]/4])
If i do <...
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