# Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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### 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 ...
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 ...
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 ...
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: ...
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: ...
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 ...
117 views

### How to factor a polynomial expression in MATHEMATICA?

I want to factorize the following polynomial in MATHEMATICA: $1 - 2 r + r^2 - 2 s + 2 r s + s^2 - 2 t + 2 r t + 2 s t - 4 r s t + t^2$. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: $f(x)=\frac{\pi ^2}{\left(\frac{\pi }{2}-\tan ^{-1}(k (x-1))\right)^2}$ ...
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: ...
39 views

### Approximation of roots using Series

I am solving a fifth degree polynomial using Series. My equation looks like ...
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 ...
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 ...
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 ...
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 ...
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) /(...
48 views

### How to rearrange polynomials to be more readable?

Why is Mathematica not able to identify that this polynomial: ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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.
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 ...
180 views

### Fast way to pick up certain terms in Polynomial multiplication?

I have one case (Nn=1) for 7 Polynomials as following: ...
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 ...
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 ...
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 ...
35 views

### How to find the regular chain?

How do we find the regular chain from the Gröbner basis ...
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?
189 views

### Taking some terms from a polynomial

I have a polynomial like this: ...
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 ...
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 ...
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 <...
143 views

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### 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 ...
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\\...
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### 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 ...
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 ...