Questions tagged [coefficients]

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1answer
47 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)+...
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0answers
28 views

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 ...
1
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0answers
110 views

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 ...
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1answer
43 views

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: ...
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2answers
53 views

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
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1answer
41 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 ...
1
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2answers
73 views

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{ ...
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1answer
44 views

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 ...
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0answers
45 views

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 ...
3
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1answer
39 views

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 $...
2
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1answer
46 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 ...
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0answers
82 views

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: $f(x)=\frac{\pi ^2}{\left(\frac{\pi }{2}-\tan ^{-1}(k (x-1))\right)^2}$ ...
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1answer
47 views

How can I add assumptions on the coefficients when using FindFit? [closed]

I have an equation of the following type: $$f(z) \overset{!}{=} a f_a(z) + \sum_{s=0}^\infty c(s) f_c(z,s)\tag{1}$$ where I know $f$ numerically and $f_a$ and $f_c$ analytically (they are long, ...
2
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1answer
70 views

Extracting coefficients from a sum of exponential functions

I'm dealing with a sum of exponential functions with different exponents ...
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0answers
57 views

Evaluate parameters before function uses them

I want to construct a power series: LP[s_] := With[{x = 1, R = 10, n = 1}, Sum[cc[i + n, n, x, R] s^i, {i, 0, 20}]] but it kinda takes a long time to compute the ...
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0answers
42 views

Solving a system of numerical equations from a truncated series

I have an equation of the following sort: $$\sum_{s=0}^\infty c(s)f(s,x) = g(x), \tag{1}$$ where everything is real and $s$ is an integer. I know $f(s,x)$ and $g(x)$ numerically for any $s$ and any $...
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1answer
40 views

Coefficient of expression that involves derivatives

I have a long expression, only representative terms are given below. As a first step, I want to collect terms in terms of u[x,t] and its derivatives. The second step is to make those coefficients ...
1
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1answer
92 views

Finding ODE series solution coefficients

I am trying to solve an ODE by subbing in a series form and then looking individually at the coefficients of different powers of the variable. I'm looking at a general form of equation: $$\frac{\...
1
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1answer
62 views

Polynomial transformation coefficients

Given a 3D polynomial of degree $m$ and coefficients $a_{ijk}^0$, $$p(x_0, y_0, x_0) = \sum_{i,j,k}^{m} a_{ijk}^0 x_0^i y_0^j z_0^k, \quad i + j + k \le m,$$ I want to make the transformation: $$x_0 =...
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2answers
74 views

Extract different part of a polynomial with square root $a(x)+b(x)\sqrt{c(x)}$

Say I have an expression like $a(x)+b(x)\sqrt{c(x)}+d(x)\sqrt{e(x)}+f(x)g(\sin(x))$, where a(x) to f(x) mean polynomials of $x, g(x)$ is a polynomial of $sin(x)$. I wonder how to extract the different ...
1
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2answers
111 views

Extract coefficients from ODE

I'm trying to extract the coefficients from an ODE $$y''''+y''+x^2 y'-6y+ 8\ cos(x)$$ and hoping the code will give a list with all the coefficients in, ranging from lower order to higher order, i.e. $...
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1answer
64 views

Find Unknown coefficient using Contour plot

I have I really complicated equation, but for simplicity lets assume my function is F(x,y,z)= ax+by+c*z, where a, b and c are some unknown constants. From experiments we know that at: x=3, y=2, z=1 ...
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3answers
109 views

Solving the issues related to the Coefficient command?

I am trying to extract coefficients of a complex expression which is a polynomial in two variables $x,y$ and has max order up to $x^{18},y^{18}$. I am trying to get the coefficient of say $x$ , $x^2$, ...
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0answers
35 views

Replacing factors that are only dependent on a single specific variable

I have expressions with terms that are products of factors. Some of the factors are expressions that depend on a single specific variable. I would like to replace those factors with constants and ...
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1answer
54 views

How the terms are arranged in `CoefficientList` command?

I have an expression containing various orders (powers) of F[r]. Using CoefficientList, the output is a blue box which is ...
1
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1answer
111 views

Coefficient Array from total derivative of expression

I have an expression $$\dot{r}\dot{\eta}+r^{2}\dot{\theta}\dot{\xi}=0$$ where $\eta$ and $\xi$ are both functions of $r,\theta$. In MM I wrote this as ...
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1answer
54 views

Generalize polynomial coefficients from multiple equations

I have following equations: $$\frac{1}{((a_1 - 1) f + 1)} + \frac{1}{((a_2 - 1) f + 1)} -k = 0$$ $$\frac{1}{((a_1 - 1) f + 1)} + \frac{1}{((a_1 - 1) f + 1)} + ... + \frac{1}{((a_n - 1) f + 1)} -k = 0$...
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2answers
113 views

Fast algorithm for finding all solutions of simple equation involving only addition of terms from list

I have a list $X=\{n_1,n_2,n_3,n_4, \dots, n_i\}$ with $n_i \in \mathbb{C}$, an integer $m \in \mathbb{N}$ and $S \in \mathbb{C}$. My question is how to find all solution to the equation $$\sum_{j=1}^...
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0answers
190 views

Non constant coefficient in heat equation

I have to solve the following heat equation over a cylindrical domain. In cylindrical coordinates the PDE Equation reads: ...
0
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1answer
110 views

Finding coefficient of exponent in an expression

I am trying to find coefficient of an exponent term in an expression. For example, consider tt = E^(I*T0*(ω+σ)); Doing ...
4
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1answer
67 views

Partial and semipartial correlation

I am interested to know if there are built-in Mathematica functions that performs partial and semipartial computations. If not, what would be a simple and efficient way to compute them from the ...
19
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3answers
470 views

Generate coefficient array from general formula of linear equation system

This is a problem coming out in the implementation of finite difference method (FDM). Here is a toy example. Suppose we want to solve the boundary value problem (BVP) $$y''(x)=\sin(x),\ y(0)=0,\ y(1)=...
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0answers
59 views

CoefficientRules for huge expressions

Is there some idea to get the coefficients for a very complicated, huge, and explicit polynomial expression to avoid insufficient memory problem? I am trying to use GroebnerBasis`DistributedTermsList ...
0
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1answer
135 views

How to create a list of undefined functions?

I have a undefined function $\phi[i,j]$ where $i=0,1,...,m$ and $i=0,1,...,n$. How can I generate this list: {$\phi[0,0],\phi[1,0],...,\phi[m,0],\phi[0,1],\phi[1,1],...\phi[m,1],\phi[0,2],...,\phi[m,...
3
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1answer
124 views

Collect Fourier series terms

Is there a way to make mathematica automatically collect terms like $\mathrm{Cos}[n\ x]$ with $n=1,2,3...$? I have a long expression coming out of a Fourier series where I see a lot of $Cos[x],Cos[2 x]...
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5answers
363 views

How to factor all coefficients of a multivariable into prime factors

I have several polynomials in 2 variables with integer coefficients, e.g., poly= -10 x - 10240 y^3 - 1520 x y^4; I'd like to convert all such polynomials into a ...
1
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1answer
79 views

Rearranging similar terms in an equation

In a piece of code I am writing, I run into an equation of the form ...
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0answers
248 views

Solving for coefficients of a polynomial ansatz in a rational function

(This is now a solved problem by my own alternative methods, and using some more physical arguments to limit the complexity of the problem. However more generally, any answers and strategies would be ...
1
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1answer
119 views

Plotting double series

I am new and hoping a warm welcome from this platform. I am trying to plot the graph of double series in one variable $$ \sum_{k=0}^{\infty} \sum_{j=0}^{\infty} C_{k,j} \exp(- 3^k 1.5^{j} x)$$ ...
0
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1answer
43 views

constructing Matrix from coefficients of solution & assigning 0 for empty Cells [closed]

i tried to construct a matrix from the coefficients of my solution, but problem that; 1; how can i get coefficients out of Solve 2; some Matrix elements are empty so i must assign 0 in those empty ...
1
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1answer
105 views

Constant term of Laurent polynomial in many variables

What is the quickest way to extract the constant term from a Laurent polynomial in two variables? For example $x+1 +x^{-2}y+x/y$ has constant term $+1$.
3
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3answers
280 views

How to using the method of undetermined coefficients in this equation?

I want to find the rational numbers $a$, $b$, $c$ satisfying the condition $$\displaystyle \int _ { 5 } ^ { 21 } \frac { \mathrm { d } x } { x \cdot \sqrt { x + 4 } } = a \ln 3 + b \ln 5 + c \ln 7.$$ ...
0
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1answer
57 views

Extract terms containing a specific symbol from an expression

I would like to be able to extract terms that contain either a symbol or a small expression from a larger one. Example (with a somewhat complicated function to give the idea of what I am after): <...
0
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0answers
431 views

Create a polynomial from a list of coefficients [duplicate]

First I have to extract coefficients from a polynomial.Then I have to make a polynomial from by given list and show that they are identical. So I tried like this: ...
2
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0answers
107 views

Coefficients of continuous wavelet transform

I am fiddling with wavelet coefficients in Mathematica, and for simplicty only a real valued Wavlet. Lets say we have the data: ...
3
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2answers
323 views

Solve PDE with complicated coefficient non-linearity [closed]

I wish to solve is the heat equation with solution-dependent coefficient. The equation along with BC's and IC's are as follows: $\begin{equation} \frac{\partial P[x,t]}{\partial t}-\alpha[x,t]\frac{\...
0
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3answers
506 views

how to get coefficient list from a polynomial with negative powers

Say a polynomial x^2-x^(-2), I need to extract its coefficient. I tried the command CoefficientList[x^2-x^(-2)], but no result ...
1
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1answer
63 views

Output of Apart as a list?

I have a rational funtion of one variable that I know will always have a simple partial fraction decomposition of the form $$\sum_{n=1}^N\frac{\alpha_n}{z- \beta_n},$$ but I do not know the values ...
3
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2answers
238 views

determining the coefficient matrix

We have a set of equations as a x + b y = c z + d w e x + f y = g z + h w We wish to have a matrix as below : How can we reach the ...
1
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1answer
41 views

How to choose elements of a matrix with internally generated variables and rank them with real coefficients

I have a Code (a long one), part of it is below. The following piece basically multiplies an adjacency matrix with a vector of equilibrium values. Then tries to pick non-zero elements to be used in ...