Questions on the functionality operating on polynomials

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2answers
389 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
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4answers
92 views

How find constant term of quadratic with square already completed?

Suppose I have a quadratic polynomial in two variables x and y in which the squares with respect to ...
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3answers
336 views

List of Tribonacci Polynomials with Mathematica? [duplicate]

I want to list top ten of Tribonacci polynomials. I have following algorithm, but it doesnt work. ...
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2answers
189 views

Strange integration result

In Mathematica 8, the Integrate command sometimes strangely integrates polynomials yielding unsimplified (and unexpected) fractional results. As an example, the line: ...
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1answer
315 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 ...
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2answers
301 views

How to know form of plotted Bézier function

Simple scenario is to see the Bézier function, but how to know which polynomial approximate it? ...
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1answer
99 views

Improving Performance - Finding Polynomial Roots [duplicate]

I'm fairly new to Mathematica. In the past, my usage has mostly been limited to solving the occasional equation, making some plots, and working with small scaled statistics. None of these have been ...
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2answers
333 views

Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: ...
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1answer
62 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 ...
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2answers
179 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 ...
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2answers
55 views

Coefficients in multidimensional polynomials

I have a multidimensional polynomial depending on {x[1],x[2],x[3],x[4]}. If I want to selectively collect the coefficient corresponding to e.g. ...
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1answer
80 views

How do I find the constant term of a multivariate polynomial, when (x^0)(y^0)?

So let's say f[x_,y_]:=(2x+2y+1)^2, when I type Coefficient[f[x,y],x y] I recieve 8. But what can I input to recieve 1, when ...
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1answer
78 views

Plot roots of polynomial system of equations in 3 variables

I have the two equations $x^2 + 2y^2 + z^2 = 1$ and $xz -y^2 = 0$ I want to plot the roots in 3D. i.e the coordinates $x,y$ znd $z$
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1answer
78 views

Compose two special power series expansions

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

How to get a rule for, e.g., (x + y) to apply to (-x - y), etc.?

For example, the substitution (x + y) -> s fails here: In[1]:= (-x - y) /. (x + y) -> s Out[1]= -x - y Of course, I ...
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2answers
89 views

The order of the result $x^2 \left(b-\frac{a}{2}\right)+(a-2) x^3+\left(2-\frac{b}{2}\right) x+4 x^4-1$ [duplicate]

Can you explain me a little how Mathematica sort this result, and how to sort in descending powers of $x$ ...
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1answer
44 views

Symmetric group action on polynomials

I am working with polynomials in several variables with the obvious action of $S_n$. That is, given a polynomial $f$ in the variables $x_1, \dots, x_n$, a permutation $\sigma \in S_n$ acts on $f$ by ...
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1answer
101 views

Collect powers of variables and integers separately?

Let expr contain a sum of powers of x with some coefficients ci. The exponents of ...
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1answer
59 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 ...
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1answer
315 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 ...
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1answer
96 views

How to transform the polynomial in this way?

I have two functions f and g and a polynomial ...
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1answer
143 views

Factorize Parametric Polynomials

Is there a possibility to factorize a parametric polynomial expression - meaning that the coefficients are defined as parameters, and not as specific numbers? My example - a polynomial in ...
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1answer
108 views

How to find zeros of 16th degree polynomial with coefficients which contain one symbolic parameter?

I'm trying to find eigenvalues of matrix which is 16x16. Here is a part of matrix: ...
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2answers
120 views

Slow program- Mathematica shuts down

I've been trying to draw dynamic pictures of level sets of certain polynomials. The code right now looks like that : ...
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1answer
50 views

Get Coefficient of polynomial excluding variables

I'd like to write a function that returns the coefficient of a polynomial, but excludes some 'cross-term' coefficients. The function could be called CoefficientExclude, and the first argument would ...
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1answer
90 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 ...
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1answer
49 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 ...
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1answer
357 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. ...
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1answer
76 views

Reducing a multi-variate polynomial to have terms upto certain degree

I have a polynomial in x and y. I want to keep all the terms with (combined) degree 4. Any pointers will be appreciated. Simple tricks for doing the same with univariate polynomial don't seem to work. ...
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1answer
64 views

How can I sort the polynomial by the degree of $x$

f1 = a x^2 + b x + c + x^3 (* a x^2+b x+c+x^3 *) f1 /. x -> (x - a/3) // Expand (* (2 ...
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1answer
109 views

Factorize and find the null space of a polynomial in several variables [duplicate]

I've been asked to factor the following polynomial: poly = 6 x^3 + x^2 y - 11 xy^2 - 6 y^3 - 5 x^2 z + 11 xyz + 11 y^2 z - 2 xz^2 - 6 yz^2 + z^3 And to solve for z so that poly = 0 Can anyone help ...
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0answers
39 views

Working with rational polynomials

I work a lot with transfer functions (Laplace transform) and I often need to convert them into different forms: rational transfer functions pole/zero representation pole/zero/gain representation ...
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0answers
34 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
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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 ...
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0answers
128 views

Best way to determine polynomial coefficients in series expansion

I would like to solve the equation $$h'(\boldsymbol{x}_1)\left[B_1\boldsymbol{x}_1+g_1(\boldsymbol{x_1},h(\boldsymbol{x}_1))\right]=B_2h(\boldsymbol{x}_1)+g_2(\boldsymbol{x}_1,h(\boldsymbol{x}_1))$$ ...
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0answers
173 views

Issue with Coefficient command

I'm trying to used the Coefficient command to extract the numerical values in front of a Chebyshev polynomial. I know that there is a numerical way to do this, presented in numerical recipes, which I ...
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0answers
193 views

Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
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0answers
326 views

Polynomial factorization over finite fields with non-prime order

One can easily factor a polynomial over finite fields of prime order, using Factor command: ...
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0answers
109 views

Know the degree of the equation with the radicals expanded

I have an equation with radicals. I would like to know what would be the degree of the polynomials if I'd move the terms and square the equation a number of times sufficient to remove all the ...
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3answers
413 views

Creating simple procedure for The Least-Square $m^\text{th}$ Degree Polynomials

I am CS major, taking Computational Numerical Analysis course. Instructor gave us freedom of choice, we were allowed to use anything or any computer language we picked, I picked Mathematica.This is my ...
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3answers
269 views

How to evaluate all the essentially distinct polynomials in 4 variables over $F_2$ on points of $F_2 ^ 4$

I am a beginner with Mathematica. For my research purpose I would like to get a list of all the polynomials in $F_2[x,y,z,w]$ and for each polynomial I would like to know the result that it gives then ...
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2answers
323 views

Integrating polynomial functions over polytopes with an add-on package

There is a Mathematica package to evaluate integrals over polytopes: http://library.wolfram.com/infocenter/Books/3652/ In the documentation (Functions.nb file) I ...
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1answer
244 views

Is the formula $\sum _{m=1}^{n-1} \prod _{k=m+1}^n x_k x_m$ wrong in the wiki's page

SymmetricPolynomial[2, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4]}] $$\begin{align*}x_1 x_2+x_3 x_2+x_4 x_2+x_1 x_3+x_1 x_4+x_3 ...
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2answers
75 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 ...
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1answer
235 views

Partial factorization of multivariate polynomials in terms of given polynomials

I have calculated several homogeneous polynomials in 4,5 or 6 variables $t_1,\dots,t_6$. I would like to rewrite them as a sum of products of specific lower degree polynomials, which have a meaning in ...
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1answer
112 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 ...
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1answer
76 views

Solving polynomial equations takes infinit time

I need to solve an polynimial equation, but when i try to use Solve or NSolve in mathematica, its cant find the solution in appropriate time (i interrupted calculation after 5 hour left). The ...
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1answer
869 views

How to neglect higher power terms in a polynomial expression

I have a polynomial expression of order n (say n=20). F(x)=1+x+x^2+x^3++...x^20. I want to approximate the polynomial for order 3 only. So I need to make the ...
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1answer
56 views

Complex Polynomial roots [closed]

I have the polynomial $p(z)=1-z^3$, I am using mathematica to get all three roots of $p$, say $a, b$ and $c$, obviously $$ 1-z^3=(z-a)(z-b)(z-c) $$ However, mathematica gives a wrong answer by saying ...
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1answer
95 views

Solving and plotting a non-linear and polynomial equations of degree 3 and higher

I'm doing the following and cannot plot the function, could anyone spot a problem please ...