Questions tagged [coefficients]
The coefficients tag has no usage guidance.
156
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Finding the coefficients of a decomposition of complicated expression into products of special functions
I have the following expression which arises while studying minimal models in CFT. The 4-point amplitude of scalars is given by
$$G(z,\overline{z}) = ((1-z)(1-\overline{z}))^{\frac{m-1}{m+1}}\mathcal{...
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how to get the set of coefficient of a trig function in terms of the sines and cosines of a given angle
Say I have an expression like this
a Sin[\[Theta]]^4 + b Cos[\[Theta]]^4 +
c Sin[\[Theta]]^3 Cos[\[Theta]] + d Sin[\[Theta]]^2 + e=0
My ultimate goal is to solve ...
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Inversion in Fourier coefficients estimation problems
Let us suppose we have a coefficient vetor:
coeff = {a0, a1, b1, a2, b2, ..., an, bn}
with a total of (2*n + 1) elements. Those coefficients are applied in a ...
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67
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Comparing two power series and extracting their coefficients
I have a standard mathematical problem that I was wondering how to solve efficiently by mathematica. Here is the problem.
I have two power series expansions of a function ...
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49
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Replace coefficients with RootApproximant of themselves
I have an expression, not necessarily a polynomial, and want to take all the coefficients on whatever terms there are and replace them with the RootApproximant ...
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91
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Extracting the coefficient of a certain term from a polynomial
I want to take out the coefficient of z1^a1 z2^a2 ... zn^an from a polynomial function expr,where ...
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2
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87
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How to get the coefficient list of their product from the coefficient list of two polynomials?
If I have the coefficient list of two polynomials
...
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35
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Calculating minimal unknown coefficients of a sum
I have a problem, where I have to find the minimum of a function with a sum in it (coefficients are unknown):
psi[x_] := 1 + a*x + b*x^2 + c*x^3 + d*x^4 + ...
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58
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Can't use Coefficient properly
I could successfully solve an ODE (Ordinary Differential Equation) with this:
...
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89
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Extract system of linear equations from the linearly independent vectors
Dear StackExchange Community,
I have a lot of linearly independent vectors, e[i]e[j], e[i]e[j]h[i], f[i]e[j], etc, and I have an equation for example
...
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113
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54
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SolveAlways with functions as fixed variables
I have an expression that looks like this:
c1*dot[p[1],p[2]]+c2*dot[eps[1],p[2]]+c3*dot[p[1],S,p[2]]+...==dot[p[1],p[2]]+...
i.e. an equation where in the left ...
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69
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Putting everything with the same power together
I'm doing some computations wich involves a lot of big polynomials, for example:
...
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79
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Simplifying the function for the common factors; and showing that it contains a multiplicative factor $i e^{i (6 x + 3 b + t)}$
I have the given long function for $\{x>0,b,t\}\in\mathbb{R}$ and $\{m,n\}\in\mathbb{N}$. I have two questions:
This function contains many common factors in polynomial form (as can be seen in the ...
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CoefficientList for unbounded list of variables
Consider a polynomial: expr = Sum[x[k] a[k] + x[k], {k, 0, K}];
I want to determine the coefficients for variables x[k] for each ...
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How to ask Mathematica to extract all $y$-dependent terms in the given function $f(x,y,z)$?
I have a very large three-variable function $f(x,y,z)$ for real variables $\{x,y,z\}$ (I had to put only part of my original function because of the limit of $30000$ characters).
Is it possible to ...
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Is there any hope to compute the determinant of $56\times 56$ parametric matrix and simplify the result?
I have this $56\times 56$ parametric matrix $M$ and I want to compute its determinant where $\{t,y,z\}$ are some real parameters. I use Det[M] but it takes a lot ...
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Finding the coefficients that equate two sides of an equation
I have the following equation : $f(x)p(x)=g(x)p(\frac{x}{q}) + g(\frac{1}{xq})p(xq)$
q is a constant and $f(x)$ is a polynomial whose expression I have. Similarly $g(x)$ is also a known function.
$p(x)...
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2
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87
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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
$$...
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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 ...
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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 ...
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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 ...
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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$",
...
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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.
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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,...
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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 ...
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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 ...
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668
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2
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91
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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 ...
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84
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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 ...
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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 ...
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157
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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
...
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Coefficient works on $\pi$, $x$ and $x^2$, but not on $\pi ^2$
Consider
(\[Pi] + 2 \[Pi]^2 + 3 x + 4 x^2)
Executing
...
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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, ...
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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 (...
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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^{...
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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 ...
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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
...
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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`...
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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....
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Unexpected behaviour with Coefficient
Bug introduced in version 12.2 or earlier. Fixed in 13.2.0 or earlier
If I run
...
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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 ...
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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 $m$, ...
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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 ...
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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,...
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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 ...
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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:
...
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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 ...
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