Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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2
votes
2answers
43 views

The ordering problem of multivariate polynomials

This is the result of Taylor expansion of a binary function ...
5
votes
2answers
65 views

A problem with `Eliminate`.`

Consider this expression: Eliminate[a x + b y == 0 && c x + d y == 0, {x, y}] Mathematica returns ...
1
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0answers
44 views

Why is the result of MMA polynomial mod factor different from that of this article? [closed]

Why the polynomial mod factor of MMA is not the same as the result of this SE answer: ...
0
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2answers
99 views

How can I decompose polynomials in a certain way?

I' ve learned that the following examples can be used to decompose a factor in this way ...
0
votes
0answers
26 views

Finding a Laurent polynomial that behaves at a pole like a given function [migrated]

I need to find a polynomial $P$ such that $P(1/x)$ behaves like given function $f(x)$ at zero (their difference vanishes), even if $f(x)$ has a pole at $0$ or unknown order. P.S. I need to find a ...
1
vote
0answers
59 views

How to write Horner's Algorithm in Mathematica? [closed]

The pseudocode we were given is: Right now I have: ...
1
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3answers
640 views

How would I solve this math problem on Mathematica?

$(3t^2 + 5t + a ) (4t^2 + bt - 2) = 12t^4 +26t^3 - 8t^2 - 16t + 6$ What is a + b? The answer would be: $6=-2a$ $a=-3$ $-16t=(5t\cdot-2)+a\cdot bt\Longrightarrow-16t=-10t+(-3)bt\Longrightarrow b=...
1
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0answers
53 views

How does MMA calculate the Galois group of a polynomial over the rational number field? [closed]

How MMA calculates the Galois group of the following polynomials over the rational number field ...
1
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0answers
47 views

Taking real number from polynomial equation [closed]

Hi I have a set of 4 different solution that was solved using a 4th order polynomial equation. We can see that the set of real number solution occurred in set 2 and 4 from the solutions. See code : ...
2
votes
1answer
80 views

MMA has an error in calculating the minimum polynomial of a rational number

The minimum polynomial of Power[2, (3)^-1] (-(1/2) + (I Sqrt[3])/2) Python minimal_polynomial function can get the result as ...
-1
votes
2answers
125 views

Testing whether polynomial is in algebra of bunch of given polynomials

I know that mathematica can check whether one polynomial is in the ideal of a given collection of polynomials, but I was wondering whether it can check if a polynomial is in the algebra of a given ...
1
vote
0answers
56 views

Solutions given by WolframAlpha [closed]

When I try to solve, the following equation over the integers using WolframAlpha: $$x^2(1+x)=y(3y-1)\tag1$$ WolframAlpha gives me the following solutions $(x,y)$: $$(-1,0),(0,0),(1,1),(4,-5),(6,-9)\...
9
votes
2answers
321 views

Partial monomial pattern matching

Is there an elegant way to "partially" match monomials in a polynomial expression? Let me explain what I mean by "partially" with an example. Suppose I have ...
3
votes
2answers
119 views

Using the solve function for big numbers, getting a failure now

When I try to solve: Solve[y^2==441+48*x*(1+x)(-13+16*x)&&1100*10^9<=y<=1200*10^9&&x>=2,{y,x},Integers] My code runs for 169 seconds and ...
3
votes
1answer
95 views

Taking Real, Im, and Abs of polynomial fractions

I want to find out real imaginary and Abs of polynomial fractions composed of real-valued variables. For example, consider we have a polynomial fraction $f=\dfrac{a_1 +b_1 i }{a_2 +b_2 i }$ where $...
0
votes
0answers
56 views

Smooth approximation near a non differentiable point

Let $f:\mathbb{R}_+\rightarrow \mathbb{R}$ be a function differentiable for $x>0$ but non differentiable at $x=0$ (for instance $f=\sqrt{\cdot}$) and $g$ be a polynomial function. I know how to ...
3
votes
0answers
87 views

How to invert Expand

How do I invert Expand? I have lis={1 + x^2, 2 + 2 x^2 + x^4, 5 + 8 x^2 + 8 x^4 + 4 x^6 + x^8} and want to get ...
0
votes
1answer
36 views

Solving a fifth order polynomial with changing values of coefficients [closed]

I have a fifth order polynomial in x whose coefficients depend on a certain variable k. Now, I want to find the real roots of that polynomial for each value of k, say from 0.1 to 2 in steps of 0.05 ...
0
votes
0answers
41 views

How to solve the equation of polynomial with uncertain degrees?

Consider the following equation \begin{equation} \frac{g^{a_{1}}+g^{a_{2}}}{\left(1-g^{a_{1}}\right)\left(1-g^{a_{2}}\right)}+\frac{g^{c_{1}}+g^{c_{2}}}{\left(1-g^{c_{1}}\right)\left(1-g^{c_{2}}\right)...
1
vote
1answer
39 views

Polynomial transformation coefficients

Given a 3D polynomial of degree $m$ and coefficients $a_{ijk}^0$, $$p(x_0, y_0, x_0) = \sum_{i,j,k}^{m} a_{ijk}^0 x_0^i y_0^j z_0^k, \quad i + j + k \le m,$$ I want to make the transformation: $$x_0 =...
1
vote
0answers
63 views

Root finding over finite field extension

I'd like to know if there exists any method on Mathematica, third-party coded resource or library that can compute roots of a polynomial over an extension $\mathbb{E}$ where $E=F_p[x]/f(x)$ and $f(x)$ ...
1
vote
1answer
67 views

Factoring after polynomial long division [closed]

I have gotten the code to do polynomial long division, but I want my students to also factor the solution if possible.
2
votes
1answer
76 views

How can Cases detect x as Times[1,x]

I'm trying to use Cases to extract the coefficients of a polynomial $$x^5+6x^4+2x^3-8x^2+x+10$$ I was hoping I can first find the coefficients of the $x,\,x^2,\,...,...
0
votes
2answers
60 views

Simplifying polynomial in one variable by substitution

I want to simplify a polynomial in variable $x$ with integer coefficients by substitution $x\to{x}/d$ so that the coefficients become smallest possible integers. Input: ...
1
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0answers
49 views

Editing the Horner's method demonstration

The following code is from the Mathematica demonstration of Horner's method, I am wondering if anyone can help me remove the 2nd row in the table of the demonstration ...
8
votes
1answer
470 views

How can I find a parametric equation for an implicit surface?

I need a parametric equation for the Taubin heart surface, which is defined in implicit form. I asked a similar question in math branch, but didn't get an answer. This is the implicit form: $$\\\...
1
vote
2answers
51 views

IrreduciblePolynomialQ[] = True; Factor[] doesn't do anything [closed]

b[x_] := (((x^3) (y^2)) - ((3 x^2) (y)) - ((2 x) (y^3)) + (6 y^2)) fg = Factor[b[x]] IrreduciblePolynomialQ[fg] fg gives me (x^2-2y)y(-3+xy) ...
0
votes
0answers
35 views

Arrange a polynominal

I have a complex polynomial in more than ten line. I want to rearrange it by the power of another polynomial. For example, I have a powers of (1-A(x)/x^2) as a factor in it, and I want to sort the ...
4
votes
1answer
93 views

n-th derivative of an arbitrary polynomial / power series

How can I tell mathematica to give me the symbolic derivative of the following sum $$ \frac{\partial^n}{\partial x^n}\sum_{j=0}^N\gamma_jx^j=\sum_{j=n}^N\frac{j!}{(j-n)!} \gamma_jx^{j-n} $$ I only get ...
0
votes
0answers
46 views

What is the algorithm used by SolveAlways function?

The syntax of SolveAlways function is SolveAlways[eqns, vars] For example, SolveAlways[ax + b == 1, {x}] Mathematica ...
0
votes
4answers
78 views

Solve for coefficients to express polynomial in terms of another polynomial

If I have a polynomial, say $p(x) = 6x^3 - x^2 + x$, and I want to express that in terms of a sum of other polynomials, how may I do that in Mathematica? Specifically I would like to say that $$p(x) = ...
0
votes
3answers
62 views

Solving the issues related to the Coefficient command?

I am trying to extract coefficients of a complex expression which is a polynomial in two variables $x,y$ and has max order up to $x^{18},y^{18}$. I am trying to get the coefficient of say $x$ , $x^2$, ...
1
vote
1answer
40 views

How to check if 0 polynomial lies in span of some polynomials?

I have lot of polynomials like this ...
0
votes
1answer
30 views

Finding a coefficient that satisfies and intersecting condition

Suppose I have the following polynomial: ...
0
votes
1answer
59 views

Transform rational equations to polynomial equations

I have a list of rational equations and I would like to convert it to a list of polynomial equations. I know that none of the variables and none of the denominators could ever be 0. So far I have ...
4
votes
1answer
85 views

Is it possible to make Decompose work with coefficients containing radicals?

It appears that Decompose works reliably only on polynomials with integer coefficients, although it seems to be not mentioned in the docs. Can I make it work (or ...
0
votes
2answers
55 views

Better fit for points with exaggerated deviations

I used the InterpolatingPolynomial function to get a polynomial that meets my points. But I noticed that there is a deviation in the final intervals. ...
0
votes
1answer
32 views

Solving a polynomial equation involving gamma function

I am trying to solve an equation having degenerate limit of Fermi-Dirac integral. My code basically is ...
0
votes
1answer
61 views

Factor to measure polynomial fit

I am trying to use InterpolatingPolynomial to fit a polynomial to a given set of points representing a relationship between two variables. I would like to find a ...
0
votes
1answer
85 views

Formatting results of a polynomial long division (Extension for finite fields)

I've just read Formatting results of a polynomial long division with great interest. For my teaching purposes it would be great to enable the code given in that post to treat polynomial division with ...
0
votes
0answers
27 views

How to transform polynomial to differential operator?

How to transform the multiariate polynomial to corresponding differential operator? For instance, for a polynomial $ \frac{1}{2} z_1^2 z_3^6 $ is the goal operator $ \frac{\partial ^8}{\partial ^2x_1\...
0
votes
3answers
81 views

expression containing radicals of imaginary numbers

I can't bear an expression containing radicals of imaginary numbers, in case it can be expressed as in terms of radicals of real numbers only. For example, I can't bear the expression ...
5
votes
3answers
117 views

Optimal way to extract “positive part” of a multivariate polynomial

I've got multivariate polynomials with numerical coefficients, like e. g. p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3 and ...
0
votes
2answers
80 views

Array of polynomials

So I have a big list of 75 polynomials which I need to apply a sequence of operations to. My original program (an extract of which is below) worked fine: ...
5
votes
2answers
352 views

Plotting Chebyshev polynomials using PolarPlot and FilledCurve

This question is related to this answer. What should I change in the following code to replace black color with blue color in the second image? ...
0
votes
1answer
48 views

Generalize polynomial coefficients from multiple equations

I have following equations: $$\frac{1}{((a_1 - 1) f + 1)} + \frac{1}{((a_2 - 1) f + 1)} -k = 0$$ $$\frac{1}{((a_1 - 1) f + 1)} + \frac{1}{((a_1 - 1) f + 1)} + ... + \frac{1}{((a_n - 1) f + 1)} -k = 0$...
1
vote
1answer
81 views

How to extract only real part of 2nd root solution to C code?

I have this cubic polynomial: ...
2
votes
2answers
185 views

NSolve gives weird result for $n=101$ with NSolve[$\frac{d}{dx}\prod \limits_{k=1}^n (x-k)$==0,x]

Coming from this post: What would be the roots of the derivate of this polynom I did a quick check with Mathematica and arrived at a wrong result. I was initially confused but chose to trust ...
10
votes
4answers
502 views

Mathematica function equivalent to MATLAB's residue function (partial fraction expansion)

I am looking for a Mathematica function equivalent to MATLAB's residue function. If there is no Mathematica equivalent, I would like to write a function that given ...
5
votes
2answers
375 views

Turning arguments into exponents

I'd like to replace every instance of L[stuff], e.g., L[-1,-2,-2] in an expression with ...