Questions on the functionality operating on polynomials

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Ideals in Mathematica

I am having trouble finding the commands for ideals and basic manipulation of them, such as: (1) how to designate my field, (2) how to create a polynomial ring over this field in several variables, ...
0
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1answer
119 views

Conditions for real roots of a cubic polynomial with complicated, yet constant, parameter values

Can anyone find conditions on the following parameters $\sigma_{\ell}$, $\mu_{\ell}$, $d_{\ell}$ and $\sigma_M$ such that the cubic: $$ (d_{\ell}-d_{\ell}\sigma_M)\ell^3 + ...
5
votes
0answers
95 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
1
vote
0answers
57 views

FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
7
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3answers
223 views

Interval calculations in wolfram mathematica

If x = Interval[-100,100], then obviously x^2 + x = Interval[-0.25,10100], because as we know, ...
8
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2answers
223 views

How can I get the solutions of $x^n-x-t=0$ in hypergeometric form?

$x^3-x-t=0$ has three roots that can be expressed in hypergeometric form, for example $$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} ...
1
vote
1answer
114 views

Polynomial decomposition algorithm with a hint

If $p,f,g$ are polynomials of degree 2 or higher and $p(x)=f(g(x))$ we have a polynomial decomposition of $p$. When Mathematica (as noted below this was actually on Wolfram Alpha) says ``decomposition ...
1
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2answers
129 views

Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
7
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3answers
248 views

Write a function that returns the coefficient of x^n

Write a function C[p_, x_, n_] that returns the coefficient of $x^n$ in the polynomial equation. C[p_, x_, n_] := ... If we ...
6
votes
6answers
388 views

Rewrite a real polynomial in real (but only linear and quadratic) factors

According to my calculus book: "Every real polynomial can be factored into a product of real (possibly repeated) linear factors and real (also possibly repeated) quadratic factors having no real ...
3
votes
3answers
180 views

FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
1
vote
2answers
87 views

Creating a random complex univariate polynomial

I am a newbie in Mathematica, but I need to create a random univariate polynomial of degree d with complex coefficients whose entries are random complex variables with real and imaginary parts being ...
0
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2answers
73 views

Fit a polynomial/curve to an NIntegrate result

I want to NIntegrate a function which also contains some parameter. In the end, I would like to plot the result as a function of one of these parameters. The thing ...
1
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2answers
55 views

How to reorder and combine terms in a polynomial with multi-variables?

I have a polynomial with the coefficients of {a1, b1, b2} ...
1
vote
1answer
73 views

Graph of second order polynomials [closed]

As I mentioned before, I want to write a notebook for teaching graphs of second order polynomials that shows discriminant and the conditions when a>0, a<0, having real roots, having no real roots. ...
4
votes
1answer
415 views
0
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2answers
136 views

Don't understand results from solving easy polynomial equations

I am alarmed by the behavior of Mathematica (9.0) when given the following simple set of equations to solve: ...
2
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1answer
113 views

Cannot get plot of polynomial (x^2 + y^2 + z^2 - 4)^2 == 0 from ContourPlot3D [closed]

I'm trying to make a 3D contour plot the polynomial equation $$(x^2 + y^2 + z^2 - 4)^2 == 0, \quad \quad (1)$$ Without power 2 $$ (x^2 + y^2 + z^2 - 4) == 0, \quad \quad (2)$$ it plots a ...
1
vote
1answer
95 views

Is Factor reliable to find factorization? [closed]

I have two polynomials given by: ...
4
votes
1answer
98 views

Points on discriminant variety?

I am trying to find a way in Mathematica to compute points on discriminant variety for modest size systems, but I couldn't find one. The system is something like: ...
2
votes
1answer
64 views

RootReduce-Part of Solve

I have given the following expression in $M$ and $z$: \begin{equation} a = \frac{-4 M^2+M (-3 z-5)+\frac{1.1875 z}{\sqrt{\frac{0.015625 z}{M+1}-1.5625} \sqrt{\frac{0.765625 ...
3
votes
4answers
100 views

CoefficientList with multivariable [closed]

Consider: t = (1 + x)^3 (1 - y - x)^2 Expand[t] Now: CoefficientList[t, {x, y}] The output is: {{1, -2, 1}, {1, -4, 3}, ...
4
votes
1answer
276 views

Counting the number of terms in a polynomial using Length command

I have the following polynomial which depends on $n$: poly = (Sum[(i - 1) y[i], {i, 1, n, 1}])^2 - Sum[(i - 1)^2 y[i]^2, {i, 2, n, 1}] // Expand; The ...
3
votes
1answer
137 views

Factor fraction, where variable occurring in both, numerator and denominator, only appears once

I have an expression like $$\frac{1+a^2+2 a \cos\left(p\right)}{\left(1+b^2\right)z-1-a^2-2 \left(a+b z\right)\cos\left(p\right)}\text{.}\tag{1}$$ Is there a combination of Mathematica functions to ...
2
votes
1answer
63 views

Efficient way to apply linear function to multivariate polynomial [closed]

Suppose I start with an expression that is a multivariate polynomial in $x_k$'s, $$W = a + b \cdot x_1^{n_1} x_2^{n_2} x_3^{n_3} x_4^{n_4} + c \cdot x_1^{m_1} x_2^{m_2} x_3^{m_3} x_4^{m_4}$$ where ...
0
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1answer
63 views

Primitive polynomials of a field [closed]

I would like to know how I can get the primitive polynomials to generate the points of the fields GF(7) and GF(9) using Mathematica. Any help is appreciated.
0
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0answers
43 views

Timing of associated Legendre polynomials

I encountered a strange issue with the associated Legendre polynomials implemented with LegendreP[l,m,z]. Quite simply, the time used for the numerical computation of those quantities depends on ...
4
votes
1answer
123 views

Solving for the roots of a trilinear system of polynomials

I have been trying to solve for the roots of the following system of trilinear polynomials: ...
6
votes
2answers
183 views

How does Mathematica calculate LaguerreL

About the function LaguerreL[n,a,x], the helping documents in Mathematica only say that this function satisfies equation $xy^{\prime\prime}+(a+1-x)y^\prime+ny=0$. ...
1
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0answers
55 views

How can I find the formal derivative of a polynomial w.r.t. to its coefficients [duplicate]

I want to define a function $f(x)$ as in $\quad \quad f(x) = \sum^{n}_{i=0} c_i x^i$ as a symbolic expression. Then I'd like to do operations on it. For example, take derivatives of it with respect ...
2
votes
1answer
96 views

Funny behavior when computing dot product of coefficients with high-order polynomials

I have a similar problem to Funny behaviour when plotting a polynomial of high degree and large coefficients. However, the thing being evaluated is not just a polynomial but a dot product of some ...
4
votes
1answer
78 views

Fishing for monomials in a nested or partially factored polynomial stream

I have a problem where I'd like to be able to take a multivariate polynomial whose variables are nonscalar and is not written explicitly as a sum of it's nonzero monomial terms and determine which ...
4
votes
1answer
40 views

Relative factorisation with scalar quantities

I'd like to find a natural way to tell mathematica that a given unknown in a polynomial should be treated as a number, unlike the other variables. Typically I'd like to sum two polynomials in several ...
3
votes
0answers
83 views

Memory Management for Large Datasets [closed]

I've written some Mathematica code to generate polynomial roots. The code take an argument n as the highest degree of polynomial to solve for and then exports a file containing a list of the roots: ...
2
votes
1answer
81 views

Polynomials with integer coefficients vs. polynomials with rational coefficients

My problem is very simple. From two different functions $f_1$ and $f_2$, I create two multivariate polynomials. Because of theoretical reasons those two functions (evaluated with the same input $x$) ...
16
votes
1answer
199 views

Undocumented fourth parameter of Collect; how long has it been there?

While tinkering with How to get a list of monomials of a polynomial without coefficients? on a whim I tried a fourth argument in Collect and found: ...
4
votes
3answers
344 views

How to get a list of monomials of a polynomial without coefficients?

Giving a polynomial, say a x^2 + b x y + c y^2 MonomialList[a x^2 + b x y + c y^2, {x, y}] just gives ...
-2
votes
1answer
52 views

Generic approaches for multivariable polynomials across different domains [closed]

Mathematica newbie here. So I don't have a lot of time to read through the whole library of functions and language rules. So I'm trying to settle in on generic ways of doing the math that I'm going to ...
6
votes
2answers
209 views

NSolve erroneously gives no solution to a polynomial system

I have a polynomial system with three equations in three unknowns, the maximum degree is 26. Two equations are symmetric, i.e. eq1(x,y,z)=eq2(y,x,z). If I search ...
2
votes
3answers
157 views

Question on alternate forms of polynomial output

EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
2
votes
4answers
168 views

Symbolic cut-off of high-order terms

I know that I can cut-off high-order terms of a $1$-variable polynomial P = a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4 + a5*x^5; simply by doing for example ...
2
votes
1answer
66 views

Recurrence relation for multivariate polynomials

I am trying to define a function which recursively computes a polynomial associated to every binary string: ComputePoly[s_]:=(** Recurse on the string s**) For ...
0
votes
2answers
87 views

Generating polynomials with conditions on coefficients

I want to define polynomials with coefficients given in some range. Namely, let $p$ be a prime number and $n$ be a positive integer. For all positive integer $k\leq n$ I want to generate all ...
1
vote
1answer
129 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: ...
0
votes
0answers
56 views

Extracting coefficients of very large polynomials (perhaps by improving Expand or ExpandAll)

Is there a way to improve or bypass Expand (or ExpandAll) for extremely large polynomials? I have a polynomial system of the form $$ 0 = \sum_n a_n d_{i_1,i_2} \cdots d_{i_{p-1},i_p},$$ in which ...
8
votes
1answer
209 views

Trouble with polynomial multiplication

Bug introduced in 10.1.0 and fixed in 10.4.0 ...
0
votes
1answer
95 views

How to order a polynomial in descending powers of x? [duplicate]

This should be very simple, even silly If I ask this mathematica Expand [(x + 1) (x + 2) (x + 3)] Mathematica delivers me well ...
0
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1answer
71 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 ...
2
votes
1answer
114 views

Precision of LinearModelFit with Polynomials

I have a Problem regarding the fit of given points with a polynomial up to the fifth degree. tableofvalues=Import["tableofvalues.csv"] My polynomial is: ...
2
votes
2answers
55 views

Format polynomial output for cutting and pasting into a text file

Suppose I have the polynomial given by the determinant of this matrix: matry = {{1 - R, 3, -3}, {1, 0 - R, 0}, {0, 1, 0 - R}} I am feeding the Mathematica output ...