Questions on the functionality operating on polynomials

learn more… | top users | synonyms (1)

0
votes
1answer
37 views

Splitting a polynomial into sum of factors, not necessarily linear

How can I split a given polynomial as sum of factors in Mathematica? For example, let's say I have this polynomial: $2\cdot x^2+7\cdot x+2$. I would like the output to be $(x+1)(x+2)+x(x+4)$. Is ...
2
votes
1answer
26 views

General function for the expansion of a polynomial of operators

This question is motivated by a Quantum mechanical problem - but in explaining the problem - I assume no knowledge of quantum mechanics. I want to define a function that can expand and simplify the ...
0
votes
1answer
40 views

NSolve taking too long to solve system of polynomial equations

I am trying to solve a system of polynomial equations (10 variables and 10 equations) using NSolve in an attempt to find all solutions. ...
1
vote
1answer
29 views

Factor bivariate polynomial over the complex numbers

This is very much like Factoring polynomials to factors involving complex coefficients except that I'm concerned about bivariate polynomials, not univariate polynomials. Take for example the ...
0
votes
0answers
22 views

PolynomialMod: Unexpected results

Executing PolynomialMod[(X - 1) (X^3 + 2) (X^2 + 1), 2 - 2 X] 0 But ...
2
votes
3answers
170 views

Alternative representations of a polynomial

Suppose we have the polynomial $z^4-2 z^3-12 z^2+13 z+11$. $\;$Is there a way to manipulate it into $(z^2-z)^2-13 (z^2-z)+11$ ? How should I tackle this problem ?
1
vote
1answer
63 views

Fitting Legendre polynomial - Integer constraints in Fitting functions

I have some data in the form of {theta,y} and I am trying to fit a Legendre polynomial to it, however I don't know how I can get it to vary the m and l parameters in integer increments as I don't know ...
1
vote
2answers
89 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 ...
10
votes
1answer
256 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: ...
0
votes
0answers
33 views

Does Mathematica support Laguerre Polynomials of Matrix Argument?

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: ...
0
votes
0answers
51 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 ...
2
votes
2answers
137 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
76 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
72 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 ...
0
votes
1answer
128 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 ...
3
votes
1answer
116 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 ...
0
votes
0answers
49 views

Finding an instance of parameters, for which a polynomial has no zeros

I have a polynomial in $p(x,y) \in\mathbb{R}[x,y]_{\leq 4}$, of degree 4. The coefficients are simple functions of 12 real parameters. In particular, the coefficients are in ...
3
votes
0answers
80 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
321 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
114 views

Coefficients of a polynomial in powers of 10

Can I express a polynomial function in Mathematica in power (ScientificForm) ? I was trying: ...
2
votes
0answers
55 views

Drop all powers from multinomial [closed]

How to automatically replace an expression like x^3 y + x y z^2 by x y + xyz in Mathematica, i.e. replace all ...
2
votes
0answers
38 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
1answer
128 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
26 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
4
votes
2answers
66 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
184 views

Maximize simple Polynom: Wrong answer

I want to maximize $poly$ under the constraints $g1,g2,g3=0$ ...
0
votes
0answers
38 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
44 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
200 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
78 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
42 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 ...
7
votes
3answers
382 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
93 views

CoefficientRules for negative powers

CoefficientRules acts like the following. ...
2
votes
2answers
134 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
49 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
116 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 ...
2
votes
2answers
96 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
146 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
98 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 + ...
6
votes
2answers
377 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
215 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 ...
0
votes
0answers
105 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
315 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
61 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
117 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 ...
5
votes
3answers
437 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
116 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
167 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 ...
6
votes
2answers
249 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
449 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) = ...