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Questions tagged [coefficients]

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votes
3answers
58 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 $x$ , $x^2$, ...
1
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0answers
32 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 ...
2
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1answer
37 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
38 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 ...
0
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1answer
43 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$...
5
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2answers
92 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}^...
2
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0answers
80 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
73 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
46 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 ...
18
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3answers
358 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(...
0
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0answers
29 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
78 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,...
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0answers
30 views

What is the coefficient of E^(k t) in this moment generating function?

nn = 10; Range[0, nn]! CoefficientList[ Series[Product[Cosh[k t], {k, 1, 3}], {t, 0, nn}], t] returns the first 10 moments of the Wilcoxon signed rank statistic ...
-1
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1answer
44 views

Quadratic equation with integral coefficients [closed]

Let $a,b,c $ be Natural Numbers, such that roots of the equation $ax^2+bx+c=0$ are distinct and both lie in the interval (0,1) (1,2) (2,3) (Brackets signify open interval, roots are $IN BETWEEN $ ...
1
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2answers
55 views

Matrix whose coefficients are functions

What is the right way to declare of matrix whose coefficients are functions of a variable $x$ ? I tried : Table[Table[a[i,j][x_],{j,1,NN}],{i,1,NN}]
3
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1answer
96 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]...
5
votes
5answers
294 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
47 views

Rearranging similar terms in an equation

In a piece of code I am writing, I run into an equation of the form ...
1
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0answers
161 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
79 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
37 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 ...
0
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1answer
55 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
241 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
votes
1answer
48 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
167 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
75 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: ...
2
votes
2answers
261 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{\...
-1
votes
1answer
128 views

How to extract a coefficient from a sum

Let us consider a sum of specified functions multiplied by coefficients, for example f[x_]:= Sum[Exp[j*x]*p[j],{j,1,n}] I want to extract the coefficient ...
0
votes
3answers
209 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
vote
1answer
38 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 ...
2
votes
2answers
56 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
vote
1answer
40 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 ...
5
votes
2answers
219 views

Extracting coefficients from sum

I'm having the hardest time working if I have a sum of products, with coefficients out the front, like expr = 1 + 2 a[0] b[1] + 2 a[0] b[1] c[3] + c[6] + 5 d[3, 4] ...
3
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2answers
234 views

How to get vector a from known inner product?

Assuming that a.b=z,where b={b1,b2,b3} and z=x b1+y b2+z b3, obviously ...
0
votes
1answer
96 views

Get Polynominal Coefficient of non linear equation [closed]

I have a non linear equation and want to create a polynomial of that. For this I have to calculate the coefficients. The problem is that the equation is a little bit long. So I wanted to do it with ...
0
votes
1answer
68 views

Collect terms in Fourier Transform

I want to collect terms in x from a product of polynomials and Fourier transform. So I try following code: ...
5
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4answers
133 views

Replace with partial match

I have some issues with expressions like the following A^3B^4/b + A^3B^4C/d in that I want to substitute A^3B^4 and ...
1
vote
1answer
228 views

Get coefficients of specified variables of polynomial, including zeros

In general I want to extract coefficients of specific variables of a polynomial (even of variables whose coefficients are zero). I try to explain it step by step: 1) I have a first polynomial. ...
6
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4answers
777 views

Given $ax^2+bxy+cy^2+dx+ey+f$, what is the best way to get {a,b,c,d,e,f}?

Test cases: ...
8
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4answers
735 views

How to locate a list within a list?

for example f[{1,2,3,4},{2,3}]=True, f[{1,2,3,4},{2,3,4}]=True but f[{1,2,3,4},{2,4}]=False. ...
2
votes
1answer
210 views

Solving for coefficients in a polynominal

I've the following problem: how can I solve for the coefficients in a polynominal? So, I mean the following: I've the following expression: $$\left(56-85689\cdot x\right)^2-3136\tag1$$ And I ...
1
vote
2answers
137 views

Collect terms with same-kind coefficients and factor exponential based on that

In the following expression, how can I group apart the terms in the exponential with a and b coefficients so that I can express ...
1
vote
3answers
89 views

Replace coefficient list with new coefficient list

I would like to replace all the coefficients with new conditions in a list that I specify. For example, suppose I have the polynomial $a_1 x + a_2 x^2$. ...
1
vote
1answer
50 views

About the Coefficient command after double Taylor Series

First, let me give the code. These are the matrices. ...
1
vote
2answers
473 views

How to solve for all coefficients in a sum

The statement of the problem: In the following formula, $$g(u,v) - \sum_{\Delta,l} c_{\Delta,l} u^{\frac{1}{2}} G^{(l)}\Bigg(\frac{1}{2} (\Delta-l),\frac{1}{2} (\Delta-l),\Delta,u,v \Bigg) = 0$$ ...
2
votes
1answer
51 views

Advanced Trivariate Polynomial With Integer Coefficients Manipulation

Suppose $$f(a,b,c)=\left(a+b+c \right)^{2}-2 \left(a^{2}+b^{2}+c^{2}\right)-4abc$$ and $g(a,b,c)$ is some polynomial of total degree 6 with integer coeffients. I want to find a polynomial $h(x)$ with ...
3
votes
1answer
95 views

LogitModelFit function

I have a problem with LogitModelFit function in Wolfram Mathematica. Specifically, I am not sure how to include Nominal variables. This is my approach: ...
0
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1answer
74 views

Getting errors when trying to solve an integral equation

I am getting the final integrate value with x range, I need to find the only one real parametera,but I receive an error: This ...
6
votes
3answers
186 views

SeriesCoefficient is broken in Mathematica 11.1, but works in 11.0

Consider the following implementation of the complex square root: f[z_]:=Sqrt[(z - I)/(z + I)]*(z + I); This implementation has branch points at $\lambda=\pm i$ ...
0
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1answer
35 views

Finding the value of some coefficients such that an equation is true [closed]

I have some expression that is a function of some variables $q_i$ and some coefficients $\gamma_j$, which is equal to zero, $$ f(q_i, \gamma_i) = 0$$ I want to find the value of the coefficients, ...