Questions on the functionality operating on polynomials

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2
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0answers
28 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 ...
2
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0answers
189 views

Negative power instead of fraction

Solve returns a solution in the form {{x->y/a^2 + y^2/a^7}}. Since I want to process the input (with another program) in terms of Laurent polynomials, I would ...
1
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2answers
105 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 ...
1
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2answers
306 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
1
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3answers
627 views

The plot of roots of polynomials

I have polynomial equation like Tribonacci Polynomials for example: $T_3(x)=x^4+x$. After finding the roots of this polynomial, I want to show these roots in the complex plane. I have tried lots of ...
1
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3answers
248 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. ...
1
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2answers
176 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: ...
1
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1answer
183 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 ...
1
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2answers
199 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: ...
1
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1answer
52 views

Compose two special power series expansions

I have two functions $A(x), B(x)$, given in a special power series form: $A(x)=1-x^{2}\left(\frac{a}{10}-\sum_{k=1}^{9}b_{k}\left(\frac{(x^{2}-1)}{r}\right)^{k}\right)$ ...
1
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2answers
89 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 ...
1
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2answers
82 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 $x$ ...
1
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3answers
346 views

Convert coefficients of polynomials into a matrix

I have several sets of 5 polynomials of the form: ...
1
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1answer
129 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 ...
1
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1answer
49 views

sum polynomial H(x,y) [closed]

I want to write and evaluate an expression something like $$H_1=\sum_{i+j=0}^3 e_{ij}x^iy^j$$ or $$H=\frac{\sum_{i+j=0}^3 e_{ij}x^iy^j}{\sum_{i+j=0}^3 a_{ij}x^iy^j}$$ with correct syntax.
1
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1answer
65 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. ...
1
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1answer
56 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 ...
1
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1answer
87 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 ...
1
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2answers
797 views

Solving cubic equation for real roots

I'm looking to solve the following cubic equation for x: $\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this ...
1
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0answers
125 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 ...
1
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0answers
108 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 ...
1
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0answers
171 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: ...
1
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0answers
98 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 ...
0
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3answers
357 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 ...
0
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3answers
217 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 ...
0
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1answer
215 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 ...
0
votes
1answer
98 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 ...
0
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1answer
214 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 ...
0
votes
1answer
117 views

Determinant of a square matrix with univariate polynomial entries is not a polynom? [closed]

I have a 15x15 Matrix with all polynomial entries. I want to calculate the determinant of the matrix. To my understanding the determinant should be a (albeit high order) polynom, too. And the paper, I ...
0
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1answer
70 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 ...
0
votes
1answer
70 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 ...
0
votes
1answer
305 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 ...
0
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1answer
50 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 ...
0
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1answer
74 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
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2answers
64 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 ...
0
votes
1answer
50 views

Why the tensor product of list of variable change the subscript position in products

{Subscript[g, 1],Subscript[e, 1]}\[TensorProduct]{Subscript[g, 2],Subscript[e, 2]}\[TensorProduct]{Subscript[g, 3],Subscript[e, 3]} I am expecting answer like ... ...
0
votes
1answer
219 views

How to represent complex expression as f(x)/g(x) in which f(x) and g(x) are both polynomial expression [closed]

I have some complex expression like this F[x] = x*x/(1-x^2)*x/(1-x/(1-x)), I want to represent F[x] in the form of f(x)/g(x) in which both f(x), g(x) are normal ...
0
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1answer
340 views

Generating lots of Examples in Polynomials Rings

I'm studying polynomial rings and i would like to know some tricks for generating lots of examples. For instance, suppose i'm interested in polynomials over the integers mod (2,x^3 + 1). To get a ...
0
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2answers
161 views

Dynamically change the variables plotted against in Plot3D

This question posed by @Cam is the closest I can find to my question but I feel that the answers don't really guide me in the way in which I'd like to proceed.... How do I dynamically change ...
0
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1answer
89 views

How to transform the polynomial in this way?

I have two functions f and g and a polynomial ...
0
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1answer
194 views

Solve[polynomial, x, Reals] doesn't get all real roots or correct ones?

My main confusion is about the difference between the two code blocks at the end of this long spiel, but the spiel contains the code to create the polynomial if its coefficients are helpful for ...
0
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1answer
176 views

Transforming Sin into Abs[Sin] dynamically

Is it possible to interpolate a polynomial that approximates Sin, and then be able to manipulate the polynomial or a sample of its points to make sections of the ...
0
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2answers
92 views

Rearranging a simple algebraic equation

Suppose I have a simple algebraic equation like: ChebyshevT[4, p] == 0 1 - 8 p^2 + 8 p^4 == 0 and I want to solve for the ...
0
votes
1answer
418 views

Factoring a quintic

I am trying to prove that a quintic polynomial, $p(x) = A5 x^5 + A4 x^4 + A3 x^3 + A2 x^2 + A1 x + A0$, which admits at most three real roots. Unfortunately Descartes' rule of signs does not help, ...
0
votes
1answer
85 views

Solving one equation, then inputting the values into another for NonlinearModelFit

Considering the equation a*x^3 + a*x^2 + x + b == 0 I'm looking to find the best value for a and ...
0
votes
1answer
200 views

Table of Polynomials [closed]

I made a function makePolynomial that creates a random Polynomial of a certain degree, e.g. 2+T+3T^2+8T^3-5T^4... now I ...
0
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0answers
40 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, ...
0
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0answers
32 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. ...
0
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1answer
35 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: ...