Questions tagged [algebra]
Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.
255
questions
2
votes
2
answers
118
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 ...
- 23
0
votes
0
answers
48
views
Solving a system with Exponential equations [closed]
Given the following system
\begin{align*}
2\cdot 3^x-3 \cdot 2^y&=-22\\
5\cdot 3^x+\frac{1}{2}\cdot2^y&=9
\end{align*}
TThen let $w=3^x$ and $u=2^y$
\begin{aligned}
2\cdot w-3 \cdot ...
4
votes
1
answer
295
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:
$$e^{t(A+B)}= e^{tA}e^{tB}\prod_{n=2}^\infty e^{t^n ...
- 6,857
2
votes
2
answers
115
views
Series expansion using binomial theorem in Mathematica
The series expansion of $\displaystyle\left(1-\frac{a}{x}\right)^{1/3}$ using the Binomial theorem is given by
$$\displaystyle\left(1-\frac{a}{x}\right)^{1/3}=1-\frac{a}{3x}-\frac{a^{2}}{9x^{2}}-\...
- 159
3
votes
2
answers
140
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.
...
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1
vote
1
answer
55
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 ...
- 1,462
0
votes
1
answer
47
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.
0
votes
0
answers
43
views
Tropical Algebra (Min Plus or Max Plus) [duplicate]
How to make tropical calculations on Mathematica?, like tropical matrix addition, multiplication, powers and so on?
Tropical geometry is the study of polynomials and their geometric
properties when ...
0
votes
0
answers
24
views
Polynomial GCD over a ring with composite modulus [duplicate]
I need the gcd of two polynomials,
...
0
votes
0
answers
49
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.
...
- 15
0
votes
0
answers
31
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,
...
- 15
3
votes
2
answers
151
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^\...
0
votes
1
answer
62
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, \...
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.
...
2
votes
1
answer
173
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 ...
1
vote
2
answers
111
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 ...
1
vote
1
answer
76
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.
...
- 15
0
votes
0
answers
66
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 ...
2
votes
2
answers
175
views
How to define a new algebra using TagSet?
For example, I would like to define the algebra of quaternions. I coded something like
...
- 161
2
votes
1
answer
93
views
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
...
- 161
1
vote
1
answer
76
views
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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2
votes
1
answer
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views
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 ...
- 181
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votes
3
answers
137
views
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) $$x^5 + 6x^4 +x^3 + 1 \rightarrow x^2 ...
- 53
1
vote
0
answers
57
views
How to understand the very long confusing output of a command?
I have a complicated expression with many parameters
...
- 1,314
4
votes
2
answers
222
views
Tropical Operation Conversions: Multiple Operations
I apologize if my syntax is bad. I looked around, but didn't see anything on this in the stack exchange.
I would like to be able to transform a classical real-valued polynomial to a tropical ...
- 143
5
votes
1
answer
125
views
How to get the extension degree
The real number field cannot express $\sqrt{2}$, so we extend $2$ times to get $Q(\sqrt{2})=a+b\sqrt(2)$. But it cannot express $\sqrt{3}$ still. So we are going to extend it $2$ more times to get $Q(\...
- 25.3k
1
vote
0
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88
views
How to speed up Resultant?
I am experimenting with the polynomials Y and T:
i1 = 9; i2 = 4;
Y = Sum[ x^i y[i], {i, 0, i1}];
T = Sum[ x^i t[i], {i, 0, i2}];
Timing[Resultant[Y, T, x]]
Whith ...
- 161
0
votes
2
answers
172
views
Solving System of six Non-Linear Equations in Six Unknowns
I've been trying to solve the following system of equations using NSolve and the code has been running for close to 24 hours already. Is this normal? Is there a quicker way to solve these equations? ...
- 39
2
votes
0
answers
108
views
How to solve this equation analytically?
Why can't Mathematica 13 solve this equation in radicals?
Solve[x^5 - 5*x^4 - 10*x^3 - 10*x^2 - 5*x - 1 == 0, x] // ToRadicals
I also tried to use ...
user86117
2
votes
1
answer
189
views
Define a new rule for multiplication
I am trying to implement a new rule for noncommutative multiplication:
$$ x * q^n * y \to q^n * x * y, $$ where $\ast$ stands for noncommutative multiplication and x and y are random products in ...
- 45
1
vote
1
answer
76
views
Simple algebra question
Am I missing something here? This does not resolve to True.
Clear[x,y]
$Assumptions={x>0,y>0}
FullSimplify[(Sqrt[x] + Sqrt[y]) == Sqrt[x + y + 2 Sqrt[x y]]]
...
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1
vote
1
answer
103
views
Empty output {} for matrix solutions which I know graphically exist [closed]
I am new to Mathematica, so there's a good chance that I am missing something critical here but I tried to check the documentation and am still stuck.
...
- 111
-1
votes
1
answer
69
views
Factorize expression by specific term [closed]
I am new to Mathematica but I would like to know how to force Mathematica to factorize an expression by a specific term.
Exemple, imagine I have a term like this:
And I have an expression like this:
...
1
vote
0
answers
91
views
Mathematica doesn't simplify 1.` x
I'm debugging a program that uses polynomials with numerical coefficients and it turns out that mathematica does not simplify 1.` x[1]^2 x[2]^2 to ...
- 1,216
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votes
1
answer
123
views
How to get exact solution for determinant in mathematica? [closed]
I am currently trying to program in mathematica, my issue is that the program is not solving for the exact value of the determinant in comparison to matlab. Code given below, where a and x are ...
- 1
0
votes
0
answers
27
views
handling roots in mathematica [duplicate]
I am looking for the solution of:
$\text{Solve}\left[-\frac{\alpha }{\sqrt{1-L}}-\frac{L t}{2}=-\alpha -2,L,Reals,\text{Assumptions}\to 0\leq \alpha \&\& 0<t\right]$
Mathematica is giving ...
- 123
2
votes
3
answers
312
views
How to find constant term of binomial
There is supposed to be a command or set of commands to find the constant term of a binomial expression like
$$
\left(-2x^4 + \dfrac{-5}{x}\right)^{25}
$$
...
- 137
0
votes
1
answer
38
views
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 ...
- 155
0
votes
0
answers
36
views
Take a specific part of a matrix, excluding the external brackets [duplicate]
I have a little manipulation problem.
I have the following matrix:
...
1
vote
0
answers
59
views
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 ...
- 1,141
0
votes
0
answers
120
views
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 ...
- 41
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votes
0
answers
58
views
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
2
votes
0
answers
97
views
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 ...
- 133
1
vote
1
answer
112
views
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 ...
- 51
0
votes
0
answers
91
views
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 ...
- 3,623
0
votes
2
answers
74
views
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 ?
...
0
votes
0
answers
69
views
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 ...
- 347
0
votes
1
answer
94
views
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 ...
1
vote
1
answer
71
views
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 ...
- 2,185
1
vote
1
answer
394
views
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 ...
- 840