Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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2
votes
1answer
64 views

odd output from DifferenceDelta

I would appreciate an explanation of why DifferenceDelta produces a complicated expression for a simple quadratic. I see that this is caused by the Real value <...
1
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1answer
145 views

Help with solving an equation [closed]

Could anyone please help me find the real solution(s) to a system of equations, or could anyone please help me find an effective solver to solve it? The function ...
0
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3answers
109 views

How to check if an arbitrary equation is a polynomial?

I am has some equation, how to check if it is a polynomial(or can be converted to polynomial)? Example equation: $a+\frac{1}{a}=k$ I know about PolynomialQ, but ...
4
votes
1answer
98 views

Finding a Rational univariate representation (RUR) for a Polynomial System

According to Wikipedia, a RUR of a zero-dimensional system consists in a linear combination of the variables, $x_0$ called ''separating variable'', and a system of equations : \begin{cases} h(x_0)=0\\...
0
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1answer
104 views

why is the plot like this?

Does anybody know the problem? why is the plot hatched ? I just want a simple plot. g[z_, t_] := 1 + t*z + z^3 ...
1
vote
1answer
257 views

Search for squares

Could anyone please help me find $a\left(x,y,z\right)$, $b_{i}\left(x,y,x\right),$$c_{i}\left(x,y,z\right)$ and $d\left(x,y,z\right)$ that are sums of squares of polynomials or rational functions such ...
0
votes
1answer
83 views

How to plot residue of a complex polynomial which coefficients are function? [closed]

It is easy to find residue when we know roots of polynomials, such as : g[z_, t_] := 1 + t*z Residue[1/(1 + t*z), {z, -1/t}] <...
3
votes
1answer
152 views

How to determine irreducibility over the algebraic numbers in Mathematica? [closed]

How can the irreducibility over the algebraic numbers be determined in Mathematica for a given univariate or multivariate polynomial with algebraic coefficients? In particular: How should the field ...
1
vote
1answer
68 views

Plotting the roots of polynomials which coefficients are functions [closed]

I am working on Mathematica just for few days and I am confused to plot the roots of a polynomial which coefficients are functions. In Mathematica examples, I found some simple examples such as : <...
0
votes
2answers
367 views

How to automatically generate polynomial with roots known

For example I give wolfram alpha the equations $a^2=b, b^2 = c, c^2 = a$ to solve, and I get the following as answers. However, I want $a,b,c$ to be the three roots of a degree $3$ polynomial, is ...
1
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1answer
46 views

How to discard the polynomials with small coefficients? [closed]

I have a list like this ...
2
votes
1answer
86 views

Enumeration of the roots of a polynomial

In Root[f,k], how exactly are the roots of a polynomial f enumerated? The Mathematica manual seems to only say that The ...
1
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1answer
111 views

Mathematica code to Math symbols and equations

Can anyone please help me determine what the following Mathematica code is doing in terms of Math equations: (I'm having trouble putting the code here, so I attached in a picture) Is the code doing ...
2
votes
1answer
67 views

How can I find all polynomials that fit an equation?

How can I ask Mathematica to find all polynomial $ f \! $s such that, for a constant $ k $: $$ f(x) \ f(y) = f(x) + f(y) + f(xy) + k $$ I've solved it on paper and want to check my results. I've ...
3
votes
2answers
197 views

For a multivariable polynomial of degree t, how can you find the coefficients of monomials of degree t?

Hello Mathematica StackExchange community, I'm hoping that someone can be of help! Let p be a fixed prime. I have a multivariable polynomial g (of degree t). I need a list of all the monomial terms ...
2
votes
1answer
71 views

Dealing with zero at high precision

I am using mathematica to deal with rational functions, $p(x)/q(x)$, where the polynomials, $p,q$ have a high degree and coefficients with high order of precision, e.g: ...
2
votes
2answers
72 views

How to find parameters under which a six-order polynomial in four variables is globally nonnegative?

Let $$f(\xi_1,\xi_2,\xi_3,\xi_4)=\frac{1}{120} \xi _3 \xi _1^5\left(15 (\alpha -6) (\alpha-5) (\alpha -4) (\alpha-2)+120 c_3 (\alpha +\beta-5)\right)+c_1 \xi _2^2 \xi_1^4 (\alpha +\beta-5)+\frac{1}{...
2
votes
1answer
73 views

How to chop complex number from solution solve using a model

Hi I have a set of 4 solution that was solved using a 4th order polynomial equation. I have noticed that some of the real number solution occurred through the list of 4 set of solutions. I have ...
1
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2answers
61 views

The ordering problem of multivariate polynomials

This is the result of Taylor expansion of a binary function ...
5
votes
4answers
399 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
53 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
133 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 ...
1
vote
0answers
110 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
707 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
vote
1answer
124 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 ...
0
votes
2answers
180 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 ...
9
votes
2answers
373 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
161 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
140 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
69 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
120 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
121 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 ...
1
vote
1answer
86 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 =...
2
votes
0answers
180 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
175 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
94 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
91 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
63 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 ...
9
votes
1answer
892 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
70 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
39 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
137 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
64 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 ...
1
vote
4answers
172 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
138 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
54 views

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

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

Finding a coefficient that satisfies and intersecting condition

Suppose I have the following polynomial: ...
0
votes
1answer
148 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
93 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 ...
1
vote
2answers
63 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. ...

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