Questions tagged [polynomials]
Questions on the functionality operating on polynomials
1
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1answer
63 views
Have I found bugs in Solve and Reduce? [closed]
f[x_] := x^3 - 2 x + 1;
Solve[f[x] == 0, x]
{{x -> 1}, {x -> 1/2 (-1 - Sqrt[5])}, {x -> 1/2 (-1 + Sqrt[5])}}
But ...
0
votes
0answers
28 views
Optimisation in the solution of Newton Interpolation
I have an exercise in which I have to solve the following Problem:
Given Newton formula for the representation of a polynomial $q(x)$ given the values $y_j$ of $q(x)$ for $j$ between 0 and 5
$q(x)= \...
1
vote
1answer
44 views
Parametric solution of a system of polynomial equations
I have the following system of equations,
1+x+y+z==0, 1+x*y+y*z+x*z==0
which I want to solve in the extension field of GF(2), the algebraic closure of GF(2) for ...
0
votes
1answer
66 views
Fastest way to simplify rational functions
I am using Series to approximate function of two variables:
Series[f[x,y],{x,0,m}]
the function is a complicated sum of ...
2
votes
1answer
359 views
How to write the shifted Chebyshev polynomials (the first kind) in mathematica?
Is it possible to write the shifted Chebyshev polynomials (the first kind) in Mathematica? The formula is:
$$P_n(x)=\sum_{k=0}^{\left\lfloor\tfrac{n}{2}\right\rfloor}(-1)^k 2^{n-2k-1}\frac{n}{n-k}\...
1
vote
1answer
72 views
How to expand a composite function into series?
I need to expand such a function
$$g[y,z(x,y)]=\frac{-y (z+1)^4-z^4-4 z^3+8 z+8}{z+1},\tag{1}$$ into powers of $x$ and $y$. Among $x,y,z$ there is a constraint equation, for example
$$(3 y+3) z^4+z^...
0
votes
0answers
36 views
Discrete convolution power
In my previous question we have discussed the posibility of various definition of convolution of power function within Mathematica. Now the question is "How to define convolution power in Mathematica ?...
0
votes
2answers
48 views
Factor not factoring quadratic polynomial [closed]
I'm using version 11.3
Expand[(Sqrt[2] - t)^2]
2 - 2 Sqrt[2] t + t^2,
but
...
1
vote
1answer
28 views
(Ir)reducible polynomials over some field
When I want to factor a polynomial, say $p(x)$ over $\mathbb{Q}[\sqrt{2}]$,
I can do
Factor[p(x), Extension -> {Sqrt[2]}]
what if I want to factor a ...
0
votes
0answers
29 views
Solving Polynomial Functions [duplicate]
How would I code the solution to this problem?
Let P be a polynomial satisfying P(x + 1) + P(x − 1) = x^3
for all real numbers x.
I am trying to find P(x)
5
votes
5answers
151 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
0answers
64 views
Monitoring PolynomialReduce/Alternatives for other CAS packages
I have a large generic polynomial That looks like
$N = \sum_{i_1,i_2\cdots}c_{i_1,i_2,i_3,\cdots} {x_{1}}^{i_1}{x_{2}}^{i_2}\cdots $
This could have anywhere between 3000-9000 terms with a maximum ...
1
vote
1answer
46 views
Splitting a general rational polynomial ansatz into powers
EDIT
This question is completely wrong and useless. It is mathematically incorrect. I think something like Series is sufficient if you're trying to do something ...
0
votes
1answer
27 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
0answers
76 views
How to make GroebnerBasis Work or to speed NSolve up [closed]
I consider a set of three polynomials of two variables
...
2
votes
1answer
146 views
Rewrite the power sum in terms of convolution
Let be an identity
$$n^{2m+1}=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1}k^r(n-k)^r,$$ where $A_{m,r}$ are real coefficients, see A302971 for numerators and formula of $A_{m,r}$. Here we can notice that $\...
0
votes
2answers
67 views
How to write a function of a polynomial
I will illustrate my problem with this example:
I want to make a function which, given a polynomial, gives me the value of the integral $\int_0^1(ax+bx^2)dx=a/2+b/3$.
Therefore, in this example, I ...
1
vote
1answer
56 views
Polynomial PowerMod
Is there equivalent of PowerMod for polynomials in Mathematica?
We have Mod[a^e,m]==PowerMod[a,e,m], $a$, $e$ and $m$ all ...
0
votes
2answers
80 views
Find $\text{k}$ such that $:$ $\text{discriminant}= 0$ [closed]
I tried to find $\text{k}$ such that $:$
$$\text{discriminant}\left [ \text{discriminant}\left [ z^{\,2}\left ( z^{\,2}- 1 \right )^{\,2}\left ( z^{\,2}+ 1 \right )+ \left ( y^{\,2}- z^{\,2} \...
1
vote
2answers
41 views
Collect term in a distributive way
Consider
P = x (a2 b2 v^a2-1+a3 b3 v^a3-1+d1+d2-2 y)-(y-d1)(y-d2)-x
I would like to collect terms in (x,y,z) in a distributive way, that is
to get an expression ...
1
vote
2answers
87 views
Polynomial fit and Fourier transform plot
I'm pretty new to Mathematica so excuse me for obvious questions.
I have a dataset, second column contains invoice amount and the first column contains days passed between each invoice date starting ...
0
votes
1answer
66 views
Algebraic substitution for polynomial simplification
Consider a polynomial $p(x,y)$ and we want to simplify $p(x,y_0)$ where $y_0$ is a root of some other polynomial $q(y)$.
In Maple I would use something like:
...
1
vote
2answers
74 views
Simplifying polynomials [closed]
I have noticed a strange behaviour in Mathematica regarding simplifying polynomial expressions.
Take the following polynomials
pol1=3-8s+4s^2
pol2=(2s-1)(2s-3)
...
3
votes
2answers
175 views
6
votes
2answers
74 views
How to make Orthogonalize simplify each new vector before using it to orthogonalize the next one?
I'm trying to construct a set of orthogonal polynomials, starting from a specially-prepared initial polynomials:
...
4
votes
2answers
75 views
The set of polynomials under the action by a symmetric group
Let
$$f(x_1,x_2,x_3)=\frac{x_1^r x_2^r \left(1-x_1 x_3\right) \left(1-x_2 x_3\right)}{\left(1-\frac{x_2}{x_1}\right) \left(1-\frac{x_3}{x_1}\right)\left(1-\frac{x_3}{x_2}\right)},$$
where $r$ is a ...
3
votes
1answer
41 views
Ranking polynomials based on global maxima
Suppose I have the following polynomials in an association i.e. <|...|>, they are:
...
0
votes
1answer
58 views
Finding the inverse of a function
I am to solve for $r(\rho)$ given the function,
\[Rho]Asymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)]
This can be ...
0
votes
3answers
54 views
Simplifying polynomial Roots with assumptions
I have acquired the following root from a minimization problem:
...
0
votes
0answers
43 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:
...
1
vote
2answers
41 views
How to reduce the residue in NSolve for a system of 3 non-linear equations
I have written the following snippet in Mathematica to solve a system of 3 non-linear equations?
...
0
votes
1answer
46 views
Computing subresultants
Let $f=f(x), g=g(x) \in \mathbb{C}[x]$
Write $f=(x-a_1)\cdots(x-a_n)$ and $g=(x-b_1)\cdots(x-b_m)$,
where $n,m$ are natural numbers (distinct or not).
Let $\lambda,\mu \in \mathbb{C}$.
How do we ...
0
votes
1answer
42 views
How to avoid polynomial roots solution to be in a “power m/n” form?
How to find complex polynomial roots not in a weird "power m/n" form but in an "a+ib" form (e.g. for x^2+x+1==0)?
3
votes
4answers
196 views
Continuous non-piecewise equivalent of smoothstep function?
I have a smooth step function given by the piecewise function
...
0
votes
1answer
72 views
Convert a piecewise definition of a single impulse into an impulse train
NOTE: See update at end of question
I have a function smoothstep (based on the derivative of a smoothstep function) that gives a single impulse as follows:
...
5
votes
2answers
82 views
Basic 3D Interpolation Failing
I've seen a few other posts asking about the "unstructured grid" error in Interpolation. Here's a minimal (non)working example of the issue:
...
6
votes
1answer
89 views
Loss of accuracy in orthogonalisation of polynomials using Orthogonalize
Context
As a mean to understand the growth of structure in the universe,
I am interested in characterising the curvature of random fields such as this one:
For this purpose I start with a PDF of the ...
0
votes
2answers
93 views
Roots of a polynomial
In Mathematica I have represented the following polynomial $a x^4 + b x^2 + c x+2$ using the Plot command and, through the ...
4
votes
2answers
202 views
How to check whether Laguerre polynomials are orthogonal?
I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal.
I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. ...
1
vote
1answer
38 views
Finding constraints on polynomials from their plot
Suppose I have the following list of rational functions (fraction of polynomials):
...
-2
votes
1answer
62 views
Plot a polynomial of two variables without giving the variables' limits [closed]
How to do make Plot automatically figure out a domain interval?
what I mean to say is "I have a cubic polynomial with two variables "lambda" and "k".where as lambda is a function of "k". i.e lamda(k)
...
0
votes
3answers
97 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 ...
0
votes
1answer
51 views
Finding the best representation of a numerically-inverted function via InterpolatingPolynomial and/or variations
Below is the routine I am using to sort of represent the numerically-inverted function $TP$. Basically I am finding a necessary interpolating polynomial $TPint$ that fits with the data points given by ...
0
votes
1answer
38 views
Coercing FullSimplify to groups results
Is there a way to coerce FullSimplify to group the second result (below) to be similar to the first result?
...
3
votes
2answers
103 views
Programming with Mathematica Syntax - Dunford decomposition
I am always amazed while I am reading some solutions of problems in mathematical problems of this site with Mathematica.
For instance, look at the problem 48.
Whereas I am writing 100 lines of code ...
2
votes
1answer
72 views
Simplifying elliptic functions
I am working with (long) elliptic functions, which are rational functions in WeierstrassP and WeierstrassPPrime. As expressed in ...
4
votes
1answer
95 views
rational parameterization of a plane curve
Say one has a plane curve defined by a polynomial equation
$$P(x,y)=0$$
and one knows that the curve has genus 0. Is there an implementation in Mathematica of a (proper) rational parameterization, i.e....
0
votes
0answers
60 views
Solving a real polynomial system takes forever, am I asking the impossible?
I want to find all stationary points of a particular 3 dimensional polynomial function. Sounds easy enough, right? Just get the gradient with Grad[], and solve the ...
4
votes
1answer
42 views
Default weight matrix for EliminationOrder
For the computation of elimination ideals via Mathematica's GroebnerBasis method, e.g.
grob = GroebnerBasis[eqs, {a, b, c, d, e}, {x, y}, MonomialOrder -> EliminationOrder];
what is the default ...
0
votes
1answer
58 views
how to color edges of a convex polygon,say a square, using interpolation with respect to the color in Mathematica
How do I color edges of a convex polygon, say a square, using interpolation with respect to the color (to form parametric polynomials) in Mathematica, so that the colors displayed on the 4 edges would ...
