Questions on the functionality operating on polynomials

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0
votes
2answers
143 views

3D Plot from 3 Polynomial Equations

Here is my code: ...
0
votes
1answer
133 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
128 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
182 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
141 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
320 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
131 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
360 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
330 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
257 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
79 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
307 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
390 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
37 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
325 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 ...
8
votes
1answer
232 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
113 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
417 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
132 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
257 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 ...
0
votes
0answers
59 views

PolynomialReduce not working

I have a polynomial $f(x_1, x_2, \ldots , x_n)$ with coefficients in $Z[q,t]$, and I have a list of polynomials $g = g_1, g_2, \ldots , g_k$ where they are also polynomials in $(x_1, x_2, \ldots, ...
7
votes
1answer
402 views

How to substitute the following conditions into an expression?

I have an expression: $p=a\;b\; x + b^2\; y + a\;c\; z$. I want to substitute $a\;b=1$, $b^2 = 2$ and $a\;c = 4$ to obtain $p = x + 2y + 4z$. How can I tell Mathematica to do that? I dont know how to ...
1
vote
1answer
77 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. ...
4
votes
3answers
306 views

Creating a function with integral zeroes of the 0th, 1st, and 2nd derivatives

I would like to be able to randomly generate functions, each of which satisfies $f : [-10, 10] \rightarrow [-10, 10]$ All the zeroes, critical points, and inflection points have an integral ...
0
votes
1answer
150 views

Finding the InverseFunction of a polynomial function restricted to an interval [duplicate]

I want to calculate the inverse of f[x_] := 1/2 - (x (4 x^2 - 9))/12 /; -1/2 <= x <= 1/2 f[x] is monotonic inside ...
4
votes
0answers
202 views

Discriminant of Characteristic Polynomial

I'm doing a calculation which finds the characteristic polynomial of a matrix with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 ...
0
votes
1answer
62 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
2answers
211 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 ...
2
votes
4answers
929 views

Solving a polynomial equation with a condition of equality on roots

Let the following equation have two equal roots: f[x_] := x^3 - p x^2 + q x - r And I want to find out what the three roots are. Not knowing how to put this ...
1
vote
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 ...
3
votes
1answer
89 views

How to order lexicographically the monomers of a parametrized polynomial?

I want to order lexicographically the monomials in a "parametrized polynomial", i.e. polynomials whose "symbolic bits" may be either "variables" or "parameters". For example: ...
3
votes
2answers
337 views

Tweaking Solve for systems of polynomial equations

I am trying to solve the following system of $6$ quadratic equations in $6$ variables: ...
0
votes
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 ...
1
vote
1answer
96 views

How to transform the polynomial in this way?

I have two functions f and g and a polynomial ...
6
votes
2answers
263 views

Why does PolynomialQ[x^n, x] return False?

From what I can see PolynomialQ will return False whenever some exponent is another variable such as here: ...
4
votes
1answer
283 views

Factoring a two variable polynomial in a special way

Let $$f=x^9-x^6+4x^5y+2x^3y^2-y^4$$ I would like to factorize $f$ into form: $$(y-F_1(x))\cdots(y-F_k(x))$$ over complex numbers. How can I do it with Mathematica?
6
votes
2answers
229 views

Finding common roots of a specific system of polynomials

Some of my colleges are interested in finding common zeros of the following four polynomials: ...
1
vote
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 ...
4
votes
2answers
240 views

Dimension of an algebraic variety

I would like to compute, using Groebner bases, the dimension of the variety defined by a set of polynomials in several variables. In the wikipedia page the method is described, and an implementation ...
2
votes
4answers
159 views

Get the first positive coefficient in polynomial?

I have Polynomial $F(x) = \sum_{i \leq n}{a_ix^i}$. How to get the first $a_i > 0$? Thanks,
1
vote
1answer
152 views

How can I calculate all irreducible polynomials of 31 degree in $\mathbb Z_2[x]$?

How can I calculate all binary irreducible polynomials of degree 31? or how i calculate all irreducible $f$ in $\mathbb Z_2[x]$? (The irreducible polynomial in $\mathbb Z_2[x]$ and $\mathbb R$ are ...
0
votes
1answer
239 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 ...
2
votes
1answer
447 views

Formatting results of a polynomial long division

I am teaching polynomial long division to my high school students. Not a pleasant topic to have to cover. I went to use Wolfram|Alpha and obviously, internally, they have a really elegant way to ...
3
votes
6answers
360 views

Collecting terms of even exponents

Say I've got a polynomial of $4$ or $5$ variables (we'll say $d_1$, $d_2$, $d_3$, and $d_4$). How would you collect the terms where each $d$ is raised to an even power? It collects the terms of the ...
6
votes
1answer
174 views

The third argument of the Root function

Consider the roots of an arbitrary indecomposable polynomial: sol = Solve[x^5 + 2 x + 1 == 0, x] The returned expression is ...
0
votes
1answer
261 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 ...
4
votes
4answers
267 views

How to compute MIN$(A(x), B(x))$

I have two polynomials: $\;A(x) = \sum a_i\;x^i$, $\quad B(x) = \sum b_i\;x^i$. Given $A(x)$, $B(x)$, I want to compute $\;C(x) = $MIN$(A(x), B(x)) = c_i\;x^i$ where $c_i = $MIN$(a_i, b_i)$. How can ...
4
votes
2answers
174 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
12
votes
4answers
356 views

How to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively?

I would like to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively. How to do it with the simplest code in Mathematica? For example, ...