Questions tagged [coefficients]
The coefficients tag has no usage guidance.
137
questions
4
votes
2
answers
71
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Normalizing the output of Apart
My question is closely related to this one but the accepted answer does not meet my needs.
I have a rational function $f(x)$ in one variable which admits a partial fraction decomposition of the form
$$...
1
vote
1
answer
107
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Problem in getting coefficients list of power series solution of y''[x]*y'[InverseFunction[y][x]] - y'[x] == 0?
I have tried to get solution of the following ODE:
y''[x]*y'[InverseFunction[y][x]] - y'[x] == 0
Using the code given below, the solution is a formal power series ...
- 387
1
vote
1
answer
49
views
Coefficients of a multivariate polynomial
Let's say I have the polynomial $x+2y+3xy \in \mathbb Q[x,y]$ or $x_1+2x_2+3x_1x_2 \in \mathbb Q[x_1,x_2]$, that is x+2y+3xy or ...
- 335
1
vote
0
answers
43
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Nonlinear Model Fit - Force a Constrain
I am trying to achieve the best fit for a non linear model, yet I need to ensure that certain coefficients return as positive values. I have been looking for similar questions but I have found nothing ...
- 13
3
votes
3
answers
90
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Get coefficient of a symbolized symbol in a sum that involves other symbolized expressions
My mathematica notebook begins with symbolizing all expressions of the form $x$ subscript an integer, "$x_k$",
...
- 165
4
votes
2
answers
117
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Extracting the constant term
Finite difference problem
There are a large number of variables, interacting at most five at a time. A sample term is:
How to extract the constant term?
In this example, the constant term is -1/4.
- 956
1
vote
2
answers
109
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How to write code for SeriesCoefficient to work for non integral coefficients?
I have a function of $r$ which I expand at $\infty$ using Series. It is a complicated and messy function, with a parameter $0 \leq \epsilon < 1$. After expansion,...
- 71
1
vote
0
answers
127
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How to evaluate an Integral which has Interpolating functions
I am trying to evaluate an Integral which has products of Interpolating functions inside, using NIntegrate command. It gives a wrong answer. The code that I used for performing this task is given ...
- 313
4
votes
0
answers
222
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Finding Coefficients in a Perturbation Problem related to Chaotic Dynamics
I am trying to reproduce the results from this paper: Chaotic dynamics of a suspended string
in a gravitational background with magnetic field
I am currently stuck with finding the coefficients.
First ...
- 313
11
votes
2
answers
632
views
2
votes
1
answer
75
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Plotting of a polynomial function via two approaches
I am trying to plot a polynomial via two approaches:
Take CoefficientList of the polynomial and then take Internal`FromCoefficientList, and finally replacing the value of the free parameter with a ...
- 53
0
votes
1
answer
71
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Series development of laurent in a defined domain
I am trying to correct some bills for laurent series with mathematica, but the output I am getting at the moment is not the best.
For example, I have this function
$$\frac{1}{z^2 + 9}$$
to develop at ...
- 121
0
votes
1
answer
52
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Create a general polynomial function [duplicate]
I search for a simple procedure to create a polynomial function with unknown coefficients.
For example if I asked for the most general polynomial of two variables 'x' and 'y', of second degree, it ...
1
vote
1
answer
74
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Replace coefficients in a polynomial
I want to replace the coefficients of a polynomial by new coefficients.
For example, my polynomial of variable 'r' is in the picture
I want to replace the coefficients with 'a subscripts' similar to
...
- 11
1
vote
0
answers
78
views
Coefficient works on $\pi$, $x$ and $x^2$, but not on $\pi ^2$
Consider
(\[Pi] + 2 \[Pi]^2 + 3 x + 4 x^2)
Executing
...
- 1,185
1
vote
2
answers
98
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Finding coefficients where part of the coefficient may appear in the terms
A minimal example is given below. My goal is that given a algebraic expression such as:
expr = a^2 + a b + a^3 b + 2 a^2 b^2 + a b^3
I'm trying to find a command, ...
- 707
0
votes
1
answer
82
views
Collecting coefficients of non-commutative products from an expression
I am trying to manipulate a Hamiltonian with non-commutative operators, $a_j,a_j^\dagger$. After some algebra using NCAlgebra package in Mathematica, I have an expression like, $$H = C_1 (b**a) + C_2 (...
- 1
2
votes
1
answer
197
views
How to expand a function as a linear combination of other functions?
I would like to be able to expand certain functions as linear combinations of other specified functions when I know that the original function can be represented in such a way e.g. we know that $\sin^{...
- 837
0
votes
1
answer
79
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The list of coefficients of the "polynomial", which has the order of derivatives instead of degrees
I have some equation
eqn = (A + B).x''[t] + Transpose[x'[t]].(2 A - 3 B + 1).x'[t] +(СС - 5).y'[t]+ Sin[x[t]+y[t]]
I need to collect all the coefficients at ...
- 1,847
0
votes
2
answers
76
views
Kernel dies when trying to compute coefficients in a linear sum involving expressions like b[1,2][3,4]
The following happens on 11.0.1.0:
Have
...
- 2,067
1
vote
0
answers
44
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How to extract the coefficient all the monomials of an arbitrary polynomial efficiently?
At present I know 3 efficient function to generate a list of all the monomials and the corresponding coefficients of an arbitrary polynomial. They are CoefficientRule, MonomialList and GroebnerBasis`...
- 63
1
vote
0
answers
54
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Problem using KarhunenLoeveDecomposition
I have a matrix called stochasticData.mat which size is 211302*50 and I need to perform the Karhunen-Loève decomposition on it to calculate the uncorrelated random variables. Note that stochasticData....
- 115
3
votes
0
answers
32
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Unexpected behaviour with Coefficient
If I run
expr = (CF G[0, zb])/(1 - zb) + (CF zb^2 G[0, zb])/(1 - zb) + (2 CF G[1, zb])/(1 - zb) + (2 CF zb^2 G[1, zb])/(1 - zb);
Coefficient[expr, zb, -1]
in ...
- 31
0
votes
1
answer
35
views
Is it possible to automatically check a polynomial to determine whether it has integer coefficients?
Given a polynomial f, I want to determine whether f has integer coefficients. More specifically, define
M[f_]:=MonomialList[f].
Is it possible to determine ...
- 1
0
votes
1
answer
56
views
Extract coefficients and terms in polynomial expansion [closed]
I have a polynomial in $a$ and $b$:
$$(Aa^2 + Bb^2 + Ca + Db + E)^m$$
How can I construct a table of coefficients corresponding to all different products $a^i b^j$ in the expansion for a defined $m$, ...
- 883
3
votes
2
answers
133
views
1
vote
0
answers
54
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Defining general recurrence expression and extracting coefficient
I'm new to Mathematica and I wish to solve a difference equation which is defined by the relation:
$y_{i-1}-2y_{i} +y_{i+1} = f(x_i,y_i),\\y_0 = a, y_n = b.$.
Where $x_i$ is given for all $i$.
I want ...
1
vote
1
answer
99
views
Series expansion with criteria on the coefficients
I will first do an illustrative example. Suppose I have the following function:
$ f(\vec{x},\vec{t})=\frac{x_1x_2}{(1-x_1 x_2^{-1} t_1)(1-x_2x_1^{-1} t_2)}$
I want to expand it with respect to $(t_1,...
3
votes
2
answers
108
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Comparison of Coefficients involving complex exponentials
I'm trying to solve a couple (independently) of equations of the following type
$ a_0 x + 3 a_1 y(1 + xe^{i3q} + e^{-iq + 2ip}) + ... = 0, \forall x, y, q, p$.
Using SolveAlways doesn't work well. So ...
- 133
2
votes
1
answer
63
views
LogicalExpand to find coefficients in power series
I am attempting to use the LogicalExpand command to find an equation for each coefficient in a power series. The documentation gives the following example of this usage:
...
- 193
2
votes
1
answer
82
views
Collecting coefficient list of arbitrary polynomial
Say I have a polynomial like:
1+x^(n)+3x^(n+1)+3nx^(3n+4)
I want to extract the coefficient list {1,1,3,3n}.
I've been toying ...
- 197
1
vote
0
answers
53
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Series coefficient not working for abstract powers
I'm trying to extract coefficients of some complicated polynomials.
If I try to write
SeriesCoefficient[1/(x-1)^4,{x,0,m}], this works fine, everything as expected.
...
- 197
0
votes
1
answer
120
views
Dft to evaluate Fourier coefficients
Use the DFT to evaluate the N Fourier coefficients cs of fp(t), derived by sampling the
following periodic functions: (a) fp(t) = cos^2(t) and (b) fp(t) with unit cell φ(t) = rect(t) and
period ∆t = 3....
- 69
2
votes
1
answer
193
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Easy way to extract coefficients of functions in an ODE/PDE? [closed]
Suppose I have an ODE like
$$ \epsilon y''(x)y(x) + xy'(x) + \epsilon^2 y(x)=0$$
or a PDE like
$$ \dfrac{{\cal U}}{{\cal T}}\dfrac{\partial u}{\partial t}+\dfrac{{\cal U}^{2}}{{\cal L}}u\dfrac{\...
- 155
5
votes
2
answers
91
views
Take coefficients of the variable from a Matrix
I have a question how can I take coefficients of the variable from a matrix? for example;
I have a matrix such as:
A={{2a,3b,4c},{4d},{1a,1e}} variable is {a,b,c,d,...
- 143
0
votes
2
answers
93
views
How to collect coefficients that has summation in ODE
I have the following equation,
equation= x''[t]+a*x'[t]+b*x[t]+c*y[t]+d*u[t]+e*v[t]+Sum[f[i]*x[t]+g[i]*u[t]+h[i],{i,1,n}]+k
When I collect the coefficient of each ...
- 755
5
votes
1
answer
124
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Behaviour of Coefficient[] for negative exponents in rational expressions
I've observed a puzzling behaviour of Coefficient[] for negative exponents and I'm wondering if I was always just relying on undefined behaviour or if there is a ...
- 695
1
vote
5
answers
192
views
Finding polynomial coefficients returns Tag Plus is Protected [closed]
I'm trying to find the coefficients of a polynomial $P(x)$. Please see following equation.
$$P(x+2)+P(x-2)=2x+8$$
CoefficientList[P(x+2)+P(x-2)=2x+8,P(x)]
However ...
- 13
1
vote
1
answer
75
views
Collect a multivariate polynomial with 26 variables
I have a polynomial like this:
$(wz+h+j-q)^2+((gk+2g+k+1)\cdot(h+j)+h-z)^2+(2n+p+q+z-e)^2+(16(k+1)^3\cdot(k+2)\cdot(n+1)^2+1-f^2)^2+(e^3\cdot(e+2)(a+1)^2+1-o^2)^2+((a^2-1)y^2+1-x^2)^2+(16r^2y^4(a^2-1)+...
- 121
1
vote
0
answers
43
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Calculating the coefficients in a double Laurent series
I am interested in calculating the coefficients in the Laurent series of the following Hankel function
$H_{0}^{(1)}(\sqrt{(3+x-y)(3+1/x-1/y)})$
I am familiar with the Coefficient command and its ...
- 837
1
vote
0
answers
137
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Find coefficients of a periodic function with non-linear fit [closed]
Description of the problem:
I'm studying a signal that is the sum of two exponentials at two different frequencies:
$z(n) = A_1*e^{2\pi i\nu_1n } + A_2*e^{2\pi i\nu_2 n } + noise$
The signal itself is ...
- 11
3
votes
1
answer
91
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Extension of Coefficient to variable exponents
Say I have an expression that is a polynomial in a variable, for example in the variable $x$, in which terms appear for which the exponent of $x$ also includes variables. For example:
...
- 545
0
votes
2
answers
71
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Computing the coefficients of series
I am trying to fully expand the following
$$\sum_{n=0}^{\infty} \frac{q^{\frac{n(n+1)}{2}}}{(q;q)_n}$$
Which when expressed in Mathematic is: q^(n*(n + 1)/2)/QPochhammer[q, q, n]
I would like to be ...
1
vote
1
answer
61
views
Parse coefficients from a Resolve output
I have a huge output from Resolve (quantifier elimination) that I must parse to extract the coefficients as numbers. Take for instance something that looks like ...
- 85
1
vote
2
answers
79
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List manipulation with special requirements
Let $N$ be the ground set.
I want to express the coefficients of following linear inequalities with a matrix (actually a list):
$$a_{S,i}-a_{T,i}\geq 0 \text{ for any }S\subseteq T\subseteq N \text{ ...
- 827
0
votes
1
answer
74
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How to find expansion coefficients in Fourier-Legendre
I am trying to find the coefficients for the Fourier-Legendre expansion of a potential. My goal was to obtain the coefficients as expressions in terms of x and y. I followed the example given on the ...
- 61
0
votes
0
answers
105
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How to join the lhs and rhs of the rows of a matrix equation and solve for one of the variables?
The matrix equation m.{x,y}==b results in an awkward disjointed looking presentation but correct construction of a system of linear equations ...
- 1,861
3
votes
1
answer
45
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How can I separate the coefficients of $x^k$ and $x^k \log x$ in a function?
I have a function of the following form:
$$f(x) = a_0 + a_1 x + a_2 x^2 + ... + b_1 x \log x + b_2 x^2 \log x + b_3 x^3 \log x + ..., \tag{1}$$
and I would like to collect the coefficient $a_k$ and $...
- 641
2
votes
1
answer
59
views
Fancy Indexing of a 4D array (tensor)
I'm trying to mimic the CoefficientArrays function, which I can't get to work for my symbolic equations. The CoefficientList ...
- 127
1
vote
0
answers
130
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Approximation of a function by a polynomial (Chebyshev First Kind, Bernstein, etc...) containing only even degrees and constants in a given Range[a,b]
In Mathematica, how can I create a polynomial function containing only even degrees and constants?
That is, I have a function:
$f(x)=\frac{\pi ^2}{\left(\frac{\pi }{2}-\tan ^{-1}(k (x-1))\right)^2}$
...
- 1,847