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Questions tagged [coefficients]

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0
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1answer
40 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,...
0
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0answers
25 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
39 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
49 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
votes
1answer
92 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
218 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
vote
1answer
43 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
154 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
67 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
votes
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
32 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
votes
3answers
231 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
30 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
votes
0answers
78 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
59 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
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2answers
241 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
89 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
107 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
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
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2answers
48 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
38 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
180 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
224 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
64 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
127 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
127 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
757 views
8
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4answers
732 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
165 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
104 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
84 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
384 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
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1answer
50 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 ...
2
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1answer
86 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
votes
1answer
65 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
164 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
34 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, ...
0
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0answers
43 views

Is there a way to use CoefficientRules in a parallel way?

Probably this question is too general. I have an extremely large polynomial expressions exp0 and CoefficientRules[exp0,var] takes too much time. Is it possible to find a way to get the ...
2
votes
2answers
223 views

Extract Coefficient from Root Formula

I have a solution in the form Root[a + b #1 + c #1^2 &, 1] with {a,b,c} very long symbolic expressions How can I extract the coefficient {a,b,c}? I'd like to ...
2
votes
1answer
77 views

Specifying variable in CoefficientRules

I am trying to determine the number of terms in an expression, but I have created a matrix to represent variables: xMat = Table[sGain[[i, 1]] + 4, {i, 1, 3}] ...
0
votes
1answer
33 views

Coefficient on expression in InputForm

I am having trouble understanding what is going wrong when trying to use the Coefficient function on expressions in InputForm. A very simple example serves to illustrate. ...
0
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0answers
35 views

How to produce list of variables when ExpandAll is used beforehand?

I am having an issue with Variables[] and Coefficient[] functions. I have a very long expression obtained where I utilize ...
1
vote
3answers
159 views

How to extract variables with time subscript and their coefficients

I have a expression of the following form: $$x_{t}=a_{0}+a_{1}x_{t-1}+a_{2}y_{t-2}$$ where $a$'s are just coefficients and anything with time subscript is a variable. I would like to have list of ...
2
votes
2answers
150 views

Extracting coefficients from exponential function

I would like to extract the coefficients A,b0,b1,b2 from the following form: A0 * Exp [b0 + b1*x + b2*x^2] I am aware that the command Coefficient or CoefficientList would be able to do so for ...
0
votes
2answers
109 views

Extracting order n coefficients from a non-closed form summation

I am trying to evaluate the following expression when $c=0$: $$\sum _{k=1}^{\infty} \dfrac{(k+1) c^{k-1} g(k)}{(k-1)!}+\left(\sum_{k=0}^{\infty} \dfrac{(k+1) c^k g(k)}{k!}\right)^2$$ (copyable ...
0
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0answers
35 views

Error in storing the output of a module (subroutine) into an array

For a physics application, I have to compute components of a rank-4 tensor, the Riemann tensor. I do this using a module (subroutine) which looks like this ...
2
votes
4answers
425 views

collect a multivariate polynomial, and simplify all coefficients

I have a polynomial like this: (a x + b c y + d z) (d x + e c y + g z) I would like to rewrite it as something like this: a d x^2 + b c^2 e y^2 + d g z^2 + (c (b d + a e)) x y + (d^2 + a g) x z ...
1
vote
1answer
109 views

Extract coefficients from polynomial with specific form [closed]

I have following polynomial: $$ f(x,t)=a_0(x)(x-t)^0+a_1(x)(x-t)+a_2(x) (x-t)^2+...+\frac{a_{n-1}(x)}{(n-1)!}(x-t)^{n-1}$$ Can I extract that $\frac{a_{n-1}(x)}{(n-1)!}$ coefficients? ...