Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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5
votes
1answer
91 views

Removing terms with odd degrees in polynomial

I have a polynomial in four variables and I would like to eliminate all terms that are odd in at least one of these variables. For example, if $p(x,y,z,t)=3x^2y+y^4z^2+x^2yt + x^2t^2$, then the only ...
3
votes
1answer
65 views

Sorting out polynomials with roots of an undesireable magnitude

I have a list of polynomials polys. I want a set of $f(x) \in$ polys which have roots strictly in $\{S^1,0\}$, with $S^1$ being ...
1
vote
0answers
28 views

Generating a list of the degree-$n$ Kronecker polynomials

A Kronecker polynomial is a polynomial such that Its coefficients are integers, Its roots are on the unit circle or $0$, Its leading coefficient is $1$. From here, there are finitely many Kronecker ...
0
votes
1answer
61 views

How to remove global constants in front of polynomial expressions?

I have a list of polynomials, many of them are equals up to some constants. For instance I have: ...
0
votes
1answer
114 views

How can I obtain the matrices of coefficients of quadratic form?

I'm trying to find the matrices of coefficients of a quadratic form: ...
1
vote
0answers
42 views

Solving a cubic equation in mathematica

I am trying to solve a cubic equation using Mathematica of a rather complicated expression say $f(r,\beta,\theta)$ , and in terms of $r$ the maximum degree term that appears is of degree $3$ so I ...
0
votes
2answers
117 views

How to factor a polynomial expression in MATHEMATICA?

I want to factorize the following polynomial in MATHEMATICA: $1 - 2 r + r^2 - 2 s + 2 r s + s^2 - 2 t + 2 r t + 2 s t - 4 r s t + t^2$. ...
2
votes
1answer
43 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 ...
0
votes
0answers
18 views

Identifying which polynomials from a list are factors of other polynomials

I have a list of integer polynomials $c_i(x)$ given by s = Table[c[i,x],{i,1,N}] for some large $N$. These polynomials are increasing in degree. I am trying to ...
2
votes
1answer
73 views

How to generate a set of orthogonal polynomials with a special weight function

Regarding to $e^{-ax-bx^2}$ as the weight function , how can I generate a set of orthogonal polynomials? I just know the Orthogonalize command in Mathematica which ...
1
vote
1answer
42 views

Force factor extraction from a polynomial [closed]

I have the following polynomial $$27 m^7 + 117 m^6 s^{\frac{1}{2}} - 114 m^5 s - 273 m^4 s^{\frac{3}{2}} + 15 m^3 s^2 + 91 m^2 s^{\frac{5}{2}} - 7 s^{\frac{7}{2}}$$ and I want to force Mathematica to ...
2
votes
1answer
91 views

Solving a system of polynomial equations - can I be sure that the number of solutions, and the solutions are correct?

I need to solve a system of two polynomials with integer coefficients in two variables, $\{Q_1(w,z)=0,\,Q_2(w,z)=0\}$, and want to compute all real solutions. I'm able to run ...
0
votes
1answer
60 views

Counting real roots of bivariate polynomial

For a proof, I'm working with a polynomial $p(x,m)$ and I need to show that: For any $m\in (0,6)$, $p_m(x)\equiv p(x,m)$ has a unique real root in $(0,1/2)$. I find that this is true by using Reduce ...
5
votes
2answers
98 views

What exactly does FactorTermsList do?

What exactly does FactorTermsList do? The documentation is not complete in that it only gives examples, not a precise definition: What exactly is the "overall ...
2
votes
1answer
67 views

FindFit low speed when fitting polynomial coefficients: is it possible to significantly increase the speed?

I work in Mathematica with a Butterworth filter, the transfer function of which depends on the selected order and cutoff frequency. I want to evaluate the change in the location of the roots on the ...
1
vote
0answers
75 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: $f(x)=\frac{\pi ^2}{\left(\frac{\pi }{2}-\tan ^{-1}(k (x-1))\right)^2}$ ...
0
votes
1answer
29 views

Reducing large polynomial expression to product of simplar polynominals

A beginner to Mathematica. I am trying to express a large symbolic polynomial expression as a product of factors of simpler polynomials: For example I was able to factor this expression: ...
2
votes
0answers
39 views

Approximation of roots using Series

I am solving a fifth degree polynomial using Series. My equation looks like ...
1
vote
0answers
35 views

How does Mathematica determine if a multivariate polynomial is absolutely irreducibile?

I am working with a collection of multivariate polynomials over Q in 5 or more indeterminates, all of which are irreducible over Q. However, after testing their absolute irreducibility via ...
1
vote
0answers
52 views

Optimal code generation for evaluation of a fixed set of multivariate rational polynomials

Given a set of multivariate rational polynomials, is it possible to find the optimal (shortest or least expensive in some other sense) sequence of arithmetical operations, such that it results in ...
0
votes
0answers
35 views

ComplexExpand in Module doesn't work as it should, when there is function at the left

I'm new with mathematica and I'm having a problem. I hope you can help me. I made a module to built a system that I can use to find some condition for given polynomial is a Shur polynomial. (Actually ...
0
votes
0answers
79 views

How to have a 3d plot of a complex polynomial?

I'm trying to have a 3d plot for a complex polynomial using the ContourPlot3D It shows me a plot which does not vary when the input values of different variables are varied. So, I guess it is just a ...
1
vote
2answers
71 views

Finding a third degree polynomial that passes through given points

If I have three points xi-1,xi, xi+1 where y(xi) =1 and y(xi-1)=0, y(xi+1)=0 (basis function) and I need to define a line that passes through these points I will use the line equation y-y1=(y2-y1) /(...
1
vote
1answer
48 views

How to rearrange polynomials to be more readable?

Why is Mathematica not able to identify that this polynomial: ...
5
votes
1answer
120 views

(Eisenbud) Factorization of a polynomial into factors with matrix coefficients (“matrix factorisation”)

According to the work of David Eisenbud cited below, it is possible to factorize almost any polynomial with matrices (exclusions ~ no linear terms), and this has apparently been of great use to string ...
3
votes
0answers
68 views

Right or wrong answer obtained when using two ways to represent the same number [closed]

Using Mathematica 10.1 Depending on whether I write a numerical constant as 0.6 * 10^-15, or 6 * 10^-16, I get very different ...
-1
votes
2answers
51 views

Releasing multiple nested Hold in a single expression simultaneously

Trivia: I need to take a coefficient list of a long list of complicated expressions of the form $\prod c_{ij} \left( p_{i,j}(x_1,x_2) \right)^n$ where $n$ is positive integer, and $i,j$ label ...
1
vote
0answers
49 views

How to apply PolynomialMod to a SparseArray?

I have a list bdrs of SparseArrays, whose entries are polynomials in the variable t with ...
1
vote
1answer
51 views

Is it possible to expand a polynomial written as a product with symbolic range?

I have an expression of a polynomial here $$\prod_{k=1}^n{x+2(-1)^k\cos{\frac{k\pi}{2n+1}}}.$$ I'd like to expand the product, but the function Expand just give me the same expression. I wonder if ...
2
votes
1answer
45 views

How can I find whether a given algebraic expresion T can be obtained as linear combination from a set S (with number coeficients)

We might take: s = {(x-y)^2, x*y+z}; e = (x+y)^2 + 4*z; and linearDecompose[e,s] could give ...
0
votes
1answer
33 views

Factor polynomial with specific common variables (terms)

I want to factor the following polynomial: b*p - b*q + c*q - c*r - a*(p - r) When I use the function FactorTerms. I get the ...
1
vote
1answer
53 views

How to do a long division over a multivariate polynomial in Mathematica

Does anyone know how to do a long division of a multivariate polynomial over another multivariate polynomial to effectively find the remainder, hopefully with fewest terms and/or lowest degree, in ...
1
vote
2answers
26 views

How do I get the maximum the maximum degree of a polynomial? [duplicate]

For example applied to y^2*x^3 + z^2+1 it should give 5 due to the y^2*x^3component.
1
vote
0answers
49 views

Fast way to apply permutations in large list?

I have one Polynomial in the form of FF[x1,x2,x3,x4,x5,x6,x7,x8], where xi pick numbers from ...
4
votes
3answers
180 views

Fast way to pick up certain terms in Polynomial multiplication?

I have one case (Nn=1) for 7 Polynomials as following: ...
-1
votes
1answer
36 views

Finding the roots of quintic equation

I want to solve my quintic equation with methods Newton and Bisection , and compare them. And I want to know, how to call Nsolve or Roots and told them that they use only for example Bisection ...
0
votes
2answers
55 views

Pattern matching for products of variables [closed]

What I am trying to do is very simple: In an expression that is polynomial in x,y, I want to check if there are products of the form ...
0
votes
0answers
32 views

Why PlotLegends does not work in Plot3D? [duplicate]

I'm trying to plot a complex polynomial function in 3D using the Plot3D function. The PlotLegends seems not working as it does not show the legends. A similar issue I've while plotting a 2D plot using ...
0
votes
0answers
35 views

How to find the regular chain?

How do we find the regular chain from the Gröbner basis ...
3
votes
2answers
118 views

Move variables of a certain degree to one side of an equation

I have an equation x^2 + 2x + 1 + y^2 + 4y + 4 == 20 and I want it so that only the linear terms are on the left and the constants and squared terms are on the right. Is there an easy way to do this?
6
votes
5answers
189 views

Taking some terms from a polynomial

I have a polynomial like this: ...
0
votes
1answer
32 views

Grouping complicated polynomial with respect to vectors/matrix

i recently wrote a code which computes the trace of a general 2-qubit density matrix to the fourth power (i´m studying physics :D), in terms of two bloch vectors and a matrix of the correlations. Here ...
0
votes
1answer
50 views

Understanding Root and Solving higher degree polynomials [duplicate]

I have trouble understanding Root in Mathematica. For instance: Solve[x^5 + 2 x + 1 == 0, x] gives me a strange solution ...
2
votes
1answer
46 views

odd output from DifferenceDelta

I would appreciate an explanation of why DifferenceDelta produces a complicated expression for a simple quadratic. I see that this is caused by the Real value <...
1
vote
1answer
143 views

Help with solving an equation [closed]

Could anyone please help me find the real solution(s) to a system of equations, or could anyone please help me find an effective solver to solve it? The function ...
0
votes
3answers
89 views

How to check if an arbitrary equation is a polynomial?

I am has some equation, how to check if it is a polynomial(or can be converted to polynomial)? Example equation: $a+\frac{1}{a}=k$ I know about PolynomialQ, but ...
4
votes
1answer
57 views

Finding a Rational univariate representation (RUR) for a Polynomial System

According to Wikipedia, a RUR of a zero-dimensional system consists in a linear combination of the variables, $x_0$ called ''separating variable'', and a system of equations : \begin{cases} h(x_0)=0\\...
0
votes
1answer
99 views

why is the plot like this?

Does anybody know the problem? why is the plot hatched ? I just want a simple plot. g[z_, t_] := 1 + t*z + z^3 ...
1
vote
1answer
221 views

Search for squares

Could anyone please help me find $a\left(x,y,z\right)$, $b_{i}\left(x,y,x\right),$$c_{i}\left(x,y,z\right)$ and $d\left(x,y,z\right)$ that are sums of squares of polynomials or rational functions such ...
0
votes
1answer
65 views

How to plot residue of a complex polynomial which coefficients are function? [closed]

It is easy to find residue when we know roots of polynomials, such as : g[z_, t_] := 1 + t*z Residue[1/(1 + t*z), {z, -1/t}] <...

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