Questions on the functionality operating on polynomials

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1
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2answers
432 views

Getting the polynomial from a polinomial root equation

After doing some preceding work I end up with a polynomial equation that should look something like this: Eq = c + b x + a x^2 - d x^2 == k I would like to ...
11
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1answer
353 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...
2
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1answer
157 views

Computing Poincaré symbolic solution for an arbitrary integer order polynomial

In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be "natural" generalizations of the elliptic ...
0
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0answers
72 views

Does Mathematica support Laguerre Polynomials of Matrix Argument? [duplicate]

I am wondering whether Mathematica can also compute the Laguerre polynomials of matrix argument as the appear in multivariate statistics? For example, they appear in this paper here: http://www.jstor....
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0answers
100 views

Applying the square root of operator on polynomial functions

I am trying to apply an "operation" on polynomial functions: apply the operator $(\frac{\partial f}{\partial x}-y\frac{\partial f}{\partial z})^2+(\frac{\partial f}{\partial y}+x\frac{\partial f}{\...
2
votes
2answers
278 views

Polynomial expansion of operator

I am new to Mathematica, I am trying to generate the polynomial function of a operator. So for example, the operator $L $ is $\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} $, and I want ...
3
votes
1answer
146 views

Bug in associated Legendre Polynomials?

Mathematica's definition of the connection of associated Legendre polynomials with $m$ and $-m$ is: $P_l^{-m}=(-1)^m \frac{(l-m)!}{(l+m)!} P_l^m$. We also now that $|m|>l \Rightarrow P_l^m=0$. ...
0
votes
2answers
105 views

How to exract the roots from “Roots”? [duplicate]

Given how the output looks like, as in a set of "==" assignments, is it possible to extract specific roots from the output of, http://reference.wolfram.com/language/ref/Roots.html ? And then do a ...
1
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1answer
1k views

How do I write nested for-loops?

Looking through the reference.wolfram, I couldn't see an example of how to write a multiple line "for" loop in Mathematica. I need to nest many for-loops in such a way I can do many things in the ...
4
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1answer
155 views

How to reduce a quartic form to a quadratic form with equal roots

Preface: To clear the theoretical background this question is cross-posted on math.stackexchange here. I have a polynomial in $n$ variables of the form $$P(x_1,x_2,\dots,x_n)=\left(\sum_{i,j}a_{ij}...
3
votes
0answers
175 views

Extracting an equation from an interpolated function

Im trying to use LibraryLink to do some calculations in C but part of the expression i want to calculate is an Interpolating Function. C cant use that obviously so I'm trying to shift it to a data ...
4
votes
3answers
460 views

Specific factoring of fourth degree polynomial

I have a pretty unspecific question about a really specific thing -- How would one use Mathematica to find values for an integer, m, such that this polynomial ...
4
votes
1answer
181 views

Coefficients of a polynomial in powers of 10

Can I express a polynomial function in Mathematica in power (ScientificForm) ? I was trying: ...
8
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1answer
239 views

Decomposition of a semialgebraic set into connected components

Is there any built-in function for doing decomposition of a semialgebraic set into connected components? The only way I now can think of is to use ...
3
votes
2answers
383 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
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0answers
41 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
8
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4answers
151 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
223 views

Maximize simple Polynom: Wrong answer

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

Change of basis from monomial basis to Chebyshev basis of polynomials [duplicate]

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
63 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
288 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
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1answer
137 views

Collect powers of variables and integers separately?

Let expr contain a sum of powers of x with some coefficients ci. The exponents of ...
3
votes
1answer
137 views

Solving a system of generated equations?

I would like to generate a function in the following form, where the number of terms can be specified arbitrarily: ...
1
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1answer
84 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 method)...
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3answers
1k 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
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4answers
122 views

CoefficientRules for negative powers

CoefficientRules acts like the following. ...
5
votes
3answers
541 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
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0answers
67 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
1answer
76 views

Improving working precision of LegendreP[n,x]? [duplicate]

I was trying to evaluate N[LegendreP[5,0.1]] The cell gives me: N[LegendreP[5,0.1]]=0.178829 However I wanted more ...
3
votes
2answers
265 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 ...
6
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5answers
384 views

Convert polynomial to Chebyshev

I want to convert a polynomial in "standard form" to Chebyshev form. Here's one way to do it: ...
8
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2answers
314 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
130 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 + (qt)^{-1})((\frac{...
8
votes
2answers
669 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
415 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
225 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
412 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
99 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
171 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
969 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 ...
3
votes
3answers
217 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
122 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
394 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: ...
8
votes
1answer
650 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
2answers
161 views

3D Plot from 3 Polynomial Equations

Here is my code: ...
0
votes
1answer
238 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
144 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
248 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
158 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 ...
5
votes
2answers
382 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 ...