Questions tagged [coefficients]
The coefficients tag has no usage guidance.
171
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Simplifing equation with complex coefficients
I'm trying to simplify an expression with complex coefficients. It should be very straightforward, but for some reason, I cannot get the correct answer. Please, see the code below:
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Continuous Wavelet Transform Coefficients
I am trying to reconstruct the continuous wavelet transform coefficients from Mathematica without using the ContinuousWaveletTransform function. I need to create this reconstruction for my data in a ...
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Simplifying fractional powers and collecting coefficient list from it
Problem
I want to generalize a solution I already have for a simpler situation. In my case I need to collect coefficients from a variable assuming fractional powers and on. First I'll present some ...
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Getting coefficients list of a series expansion at a point different from 0
I would like to get the coefficients of a series expansion at a point different from 0. Example:
Series[Cos[Pi*x], {x,1,6}]
which gives
$-1+\frac{1}{2} \pi ^2 (x-...
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3
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How can I extract the constant coefficient in polynomial?
I have an equation with this form: eq1 = 0.38*u1[t] + 0.285*u1[t]*v1[t] + 0.85*u1[t]^2.
I want to extract the coefficient of ...
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102
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Differential behaviour of FreeQ function depending on the number of terms in a sum
I have an expression consisting of a sum of terms. It looks like this in simplified form:
$-\frac{e^{-t/t_1} \,a \, b \, c}{d} \, U_1 - \frac{e^{-t/t_2} \,a \, e \, c}{d} \, U_2 -\frac{e^{-t/t_2} \,a \...
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Extracting matrix coefficients from multivariate matrices
Suppose we have a multivariate polynomial matrix $P(\mathbf x) = \sum_\alpha A_\alpha\mathbf x^\alpha$ (in multi-index notation) where the $A_\alpha$ are constant coefficient matrices.
I am looking ...
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How can I extract a matrix and vectors of coefficients from this quadratic expression?
Consider the following expression
(x-y+a)^2 + (x-z+b)^2 // Expand
The result is
...
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47
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58
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Numeric coefficients of a series/polynomial
In my work, i usually come across expressions of the form: $$\text{L3}=\frac{625 f_5^{30} q^4}{f_1^{31}}+\frac{24458 f_5^{24} q^3}{f_1^{25}}+\frac{25436 f_5^{18} q^2}{f_1^{19}}+\frac{25415 f_5^{12} q}{...
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Problem with using RuleDelayed (:>) [closed]
I have defined a rule using rule delayed function as follows:
innerWithDxU = (f1_ D[f2_[x,y],x]f3_[x,y] :>-f2 [x,y]D[f1 f3[x,y],x] );
...
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Cannot add a constant coefficient to LineIntegrate
I'm quite confused on how you're supposed to use constant coefficients in Mathematica integrals. The upvoted and accepted answer on Mathematics stackexchange (https://math.stackexchange.com/a/48021/...
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Creating function with array input with desired coefficient and evaluate it
I had asked the same question before here Creating a list of functions with desired coefficients
but did not get the desired answer, may be I was not clear in my question.
I have defined this function ...
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Neglecting coefficients of a given list
Suppose I have some complicated expressions, I want to extract some terms with $\{a_1, \cdots, a_n\}$ out of the complicated expressions without considering coefficients.
For example, here is my trial....
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Creating a list of functions with desired coefficients
I have defined this function to results some list of functions, however its not returning what I want
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How to extract coefficients and powers from expressions with non integer powers?
I want to extract coefficients and powers of the expression
$$3-2x+7x^{2.1}+x^{2.4}-5x^3$$
Code:
expr = 3 - 2 x + 7 x^2.1 + x^2.4 - 5 x^3;
To get a result such as:...
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How can I find the coefficient of some function of varying inputs in a list? [duplicate]
I have a list
klist={4 K[{1}, {1}], K[{2}, {2}], (2 K[{2}, {1, 1}])/("Ndim")}
where K[{list_1}, {list_2}] is some ...
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Finding the coefficients of a decomposition of complicated expression into products of special functions
I have the following expression which arises while studying minimal models in CFT. The 4-point amplitude of scalars is given by
$$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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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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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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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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115
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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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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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Can't use Coefficient properly
I could successfully solve an ODE (Ordinary Differential Equation) with this:
...
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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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147
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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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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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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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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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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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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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