Questions on the functionality operating on polynomials

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3
votes
1answer
203 views

How to enforce mathematica to analytically evaluate roots?

I am interested in simplifying expressions involving HeavisideTheta. A simple example could be: HeavisideTheta[1 + x - x^2 + x^3] The best I can achieve is with ...
1
vote
0answers
32 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
6
votes
4answers
108 views

Unexpected behavior using FromDigits to reconstruct polynomial

I have an issue with the reconstruction of a polynomial using FromDigits. The documentation of the function CoefficientList says: Fold the operation for multivariate polynomials: ...
2
votes
2answers
199 views

Maximize simple Polynom: Wrong answer

I want to maximize $poly$ under the constraints $g1,g2,g3=0$ ...
0
votes
0answers
52 views

Change of basis from monomial basis to Chebyshev basis of polynomials

I have a certain multivariate polynomial (in 4 variables) written in terms of monomials, and I would like to change the basis into Chebyshev orthogonal basis. Is there any function to do that?
1
vote
1answer
48 views

Filtering out 'no solutions' after solving a high order polynomial

I am dealing with a fourth order polynomial. I get all of the desired out put however above a certain range I also get these - {}. From my understanding this means that there is no solution. I am ...
4
votes
3answers
220 views

Polynomial with alternating sign coefficients from the odd degree terms of a Truncated Power Series

I'm trying to make a function that will take any truncated power series I give it, strip away all the even degree terms, then change the sign of the coefficients of every other term. So that we have a ...
1
vote
1answer
93 views

Collect powers of variables and integers separately?

Let expr contain a sum of powers of x with some coefficients ci. The exponents of ...
0
votes
1answer
51 views

How to rearrange CharacteristicPolynomial[ ] terms?

I have a symbolic matrix A, which I need to find the characteristic polynomial, then order the polynomial in greatest-to-least form. (Ultimately to find the matrix inversion via Cayley-Hamilton ...
11
votes
3answers
518 views

How can we plot the complex roots of an equation?

If we'd like to display the $n$ roots of a polynomial on the complex plane as points, how can we do this? For example, if we have the equation $x^3 + x^2 + x + 1$, how can we plot the 3 roots as ...
4
votes
4answers
99 views

CoefficientRules for negative powers

CoefficientRules acts like the following. ...
4
votes
3answers
238 views

What is the best way to write a polynomial in the Bernstein basis?

The Bernstein basis of polynomials of degree $n$ is the set of polynomials of the form $$\binom{n}{k} t^{n-k}(1-t)^k$$ where $0 \leq k \leq n$. What is the best way to transform a given polynomial ...
1
vote
0answers
52 views

Finding related roots to a polynomial

I posted this in math.stackexchange, but this might be a better place. Assume that $f(X,Y,Z,V,W)\in \mathbb{Z}[X,Y,Z,V,W]$ is some polynomial and assume that $f(x,y,z,v,w)=0$. I would like to know if ...
2
votes
2answers
168 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
2
votes
2answers
113 views

Convert polynomial to Chebyshev

I want to convert a polynomial in "standard form" to Chebyshev form. Here's one way to do it: ...
4
votes
1answer
171 views

On the definition of the associated Legendre polynomials

Mathematica computes for n = 1,2,...: (-1)^n (LegendreP[n, -1, -3]/Sqrt[2]) -I, -3 I, -11 I, -45 I, -197 I, ... Maple ...
3
votes
1answer
108 views

Rewrite an expression as a sum of $SU(2)$ characters?

I have an expression of the form $$q^{-3/2} t^{-7/2}[4qt^2(t + q t^2) + t^2 (q + t) (1 + q t (1 + q t))],$$ I can factor it and write it as $4((qt)^{1/2} + (qt)^{-1/2}) + (qt+1 + ...
7
votes
2answers
460 views

Finding the coefficient of a certain power in a generating function

I want to compute $(t^1+\dots +t^5)(t^2+\dots+ t^6)(t^3+\dots +t^9)$ and find the coefficient of $t^{15}$ for example. $t$ is an indeterminate Now in Maple this is simply as ...
0
votes
2answers
265 views

Find Root Iteration

I have an iterative sum from $k=0$ to $k=n$ where the resulting sum is a polynomial of degree $n$. I want to find the numerical root of this polynomial using FindRoot, starting from $x_0$ where the ...
1
vote
0answers
126 views

Best way to determine polynomial coefficients in series expansion

I would like to solve the equation $$h'(\boldsymbol{x}_1)\left[B_1\boldsymbol{x}_1+g_1(\boldsymbol{x_1},h(\boldsymbol{x}_1))\right]=B_2h(\boldsymbol{x}_1)+g_2(\boldsymbol{x}_1,h(\boldsymbol{x}_1))$$ ...
7
votes
3answers
334 views

Generating a polynomial that's accurate to within an error of no more than 1/10^5

I'm currently stuck on a question for class that asks... "Find a polynomial p[x] that you can use to calculate 6 ArcTan[x] to ...
0
votes
1answer
71 views

PolynomialReduce inconsistent results

I was playing around with gröbner basis and s-polynomials and I fell upon the PolynomialReduce, and I was wondering why it gives different results when I move around the polynomials in its second ...
0
votes
1answer
129 views

Is it possible to plot a second-order curve by its non-canonical equation?

I have this second-order polynom: $$ 6xy+8y^2-12x-26y+11=0 $$ And I need to reduce it to a canonical form of a second-order curve. I solved this, but is it possible to draw a plot of the original ...
6
votes
3answers
584 views

Piecewise Polynomial Interpolation

Given some data pairs $(x_i,y_i)$, with $i=0,...,m$, and a degree $r$, I wish to build a piecewise polynomial function to interpolate these data. That interpolation should be continuous, and, on every ...
0
votes
0answers
125 views

Finding Roots of Non-linear Systems: Rescaling polynomials

I'm trying to get all isolated finite equilibria of a moderate multi-dimensional non-linear system of equations. Particularly I have 9 independent variables and third order at most. It turns out that, ...
3
votes
3answers
174 views

Multivariate Polynomial Manipulation

I have a large homogenous multivariate polynomial in, say, 5 variables $a,b,c,d,e$. As an example take the polynomial $$a^4+2abcd+a^2 b^2+e^4+cde^2.$$ Now I would like to replace $k$-th power of any ...
2
votes
1answer
103 views

Numerical evaluation of ChebyshevT

When I evaluate the following Chebyshev series of the first kind in two different ways, I get two very different results: ...
6
votes
2answers
267 views

NSolve missing solutions in Mathematica 10

Running Mathematica 8.0.4 and 10.0.0 on a Windows 8.1 machine. Processed the same code with both kernels: ...
7
votes
1answer
490 views

How can I plot a Chebyshev spiral?

The Chebyshev polynomials T_n of the first kind are a certain set of orthogonal polynomials. They can be defined by T_n(cos(x))=cos(nx), the first of them are T_0(x) = 1 T_1(x) = x T_2(x) = ...
0
votes
0answers
71 views

How to solve equations over polynomial rings

sorry if my question is very basic but I don't know what to even search to look it up and the only "obvious" places I thought of had nothing. Some background, for whatever context it might provide. ...
-1
votes
2answers
140 views

3D Plot from 3 Polynomial Equations

Here is my code: ...
0
votes
1answer
122 views

Truncating out higher order polynomials in series of fractions

I have taken sequential partial derivatives of a two variable polynomial fraction, resulting in a very long series of polynomials of form: ...
2
votes
1answer
125 views

NSolve for system of polynomial equations

I would like to find all the solutions to the following system of 8 polynomial equations for the variables w1, w2, w3, w4, w5, w6, w7, w8 ...
1
vote
2answers
177 views

Stopping Mathematica from reordering expressions [duplicate]

I want Mathemtica to stop manipulating my polynomials! I mean, I want the output of Print[3 x + 5 + x^2] to be just $3x+5+x^2$, not $5+3x+x^2$ as Mathematica ...
4
votes
2answers
124 views

Number of complex roots for the system of polynomials

I have a system of algebraic equations. For example: $$ \left\{ \begin{aligned} x^2 y + 2 x y + 2 &= 0,\\ y^3 + 2 x + 1 &= 0. \end{aligned} \right. $$ (In my problem the system contains 16 ...
4
votes
2answers
304 views

Why doesn't Roots work on a certain quartic polynomial equation?

In everything that follows I am using Roots to get the solutions to the equations. I start off with this equation: $$ \frac{A}{3}x^4 - x^2 + 2ax - b^2 = 0$$ Now ...
2
votes
2answers
122 views

Rounding only coefficients

does Mathematica have built in functionality to round the coefficients of a polynomial to a certain accuracy. Say, we do Print[0.2134320980x^2+0.0023432x] Can ...
1
vote
1answer
350 views

Finding solutions of polynomials system

Let $f_1,...,f_n$ be a set of polynomials in $x_1,...,x_n$ with rational coefficients. I need to check whether a system $$f_1=a_1,...,f_n=a_n$$ has a real solution for large enough count of points. ...
1
vote
1answer
299 views

Find polynomial equation for set of 3D data

data was given in columns in the order {y, x, z}, with y dependent on x, z ...
0
votes
2answers
222 views

Symmetric function of the roots of a polynomial

First, I'm a beginner. I can compute the sum of roots with the follwing: Roots[x^7 + 5 x^6 + x^5 + x + 1 == 0, x] Plus @@ (x /. {ToRules[%]}) // Simplify Of ...
1
vote
1answer
78 views

Compose two special power series expansions

I have two functions $A(x), B(x)$, given in a special power series form: $A(x)=1-x^{2}\left(\frac{a}{10}-\sum_{k=1}^{9}b_{k}\left(\frac{(x^{2}-1)}{r}\right)^{k}\right)$ ...
2
votes
2answers
280 views

Generating complete lists of polynomials

I would like to generate a list of all $3$-variable Laurent polynomials with non-negative integer coefficients using a looping construct so that I can, one-by-one, check them for specific ...
4
votes
3answers
370 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
2
votes
0answers
36 views

How to simplify a polynomial and get the results in the order that I want? [duplicate]

How to simplify a polynomial in a order that I want? Assume that I have a polynomial here, for example, $a^3 b^4 c^2$, the order of symbels is the dictionary order, $a>b>c$. But what if I want ...
1
vote
1answer
305 views

Plotting solutions of a 4th order polynomial equation

I have a polynomial equation of the fourth order, which has $4$ roots depending on a variable parameter s1. For each s1 I have ...
6
votes
0answers
204 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
0
votes
1answer
109 views

Solutions of cubic equation D>0 or D<0

I have problem to obtain three roots of cubic equation N[Solve[a x^3 + b*x^2 + c*x + d == 0, x], 15] using analytical procedure ...
4
votes
1answer
406 views

Polynomial GCD over a ring (with composite characteristic)

I'd like to implement the "Franklin-Reiter Related Message Attack" (see section 4.3 of Boneh's paper). As part of the implementation, I require to compute the GCD of two polynomials over ...
0
votes
1answer
129 views

Numerical method for solving a polynomial equation

I am looking for a numerical solution of a equation which contains, in general, one polynomial equation with unknown variable x. I have tried Reduce, ...
2
votes
4answers
252 views

Working with symmetric polynomials

I have a question related to working with symmetric polynomials in some variables. Let us say, I have an expression ...