Questions on the functionality operating on polynomials

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0
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2answers
67 views

Wrong numerical results from LegendreP

{Cos[Pi/180] // N, LegendreP[46, 0.9998476951563913`], LegendreP[46, Cos[Pi/180]] // N} give ...
3
votes
1answer
219 views

Is there a package to find ALL exact roots of a polynomial, if they exist?

There are polynomials with roots not expressible with radicals but expressible as trigonometric or other functions, for which Solve[] only returns ...
5
votes
3answers
325 views

Implementation of a complex recurrence relation for polynomials

I would like to implement the recurrence relation for the polynomials $U_n(x)$ appearing in the large order asymptotics of the Bessel functions. The recurrence in question is: ...
0
votes
1answer
52 views

Solving for Polynomial roots

This simple Solve gives the roots of a quadratic: Solve[a x^2 + b x + c == 0, x] However, if I factor the polynomial in terms ...
4
votes
1answer
119 views

Expand power of a polynomial

I'm very new to Mathematica, so excuse my innocence. I have the following expression: $$ \left( \sum_{n=0}^r \frac{(-1)^n}{n!} y^n \right)^f $$ I would like Mathematica to expand out the expression ...
1
vote
5answers
132 views

How find constant term of quadratic with square already completed?

Suppose I have a quadratic polynomial in two variables x and y in which the squares with respect to ...
0
votes
0answers
22 views

Factorising polynomials in Z[i] over Z[i] [closed]

I know that you can use the 'factor' command to factorise polynomials with real coefficients over the Gaussian Integers doing something like this: ...
0
votes
0answers
30 views

Find the variables in a set of linear equations [closed]

Suppose I have a set of linear polynomials with integer coefficients, how could I extract the list of variables? Say given the following ...
2
votes
1answer
55 views

Crash after long GroebnerBasis calculation

I am running a long computation of a GröbnerBasis and after some hours the kernel crashes. The memory usage increases enormous, and it crashes, when it reaches somewhat 4 GB RES, however it is ...
0
votes
0answers
39 views

Extract Hermite Polynomial from Interpolation of Data

I have a set of data points which I interpolate like s = Import["data.dat"] sinterp = Interpolation[s] LogLogPlot[sinterp[x], {x, 100, 10000}] which gives me ...
4
votes
6answers
424 views

Easiest way to extract the coefficient of a polynomial

For a term in a polynomial, say 387 a1^4 a2^3 x^3 y^7 z^100 w^364 What is the most efficient way to extract the coefficient of this term, i.e. 387?
0
votes
1answer
36 views

Selecting terms on only one variable from a multiple-variable expression

Say I have a polynomial like $x y^2+15x^2 y+x+3y+10$ and I want to obtain, say, only the coefficient in $x$ alone, namely a 1. Using ...
7
votes
1answer
246 views

GroebnerBasis without specifying variables

All the examples in the Mathematica documentation specify that the syntax for the GroebnerBasis command is ...
0
votes
0answers
33 views
0
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0answers
32 views

ApartSquareFree function

I have a doubt concerning the ApartSquareFree function in Mathematica. Roughly speaking, it is supposed to compute the partial fraction decomposition of a rational function $h/g$ with the denominators ...
2
votes
1answer
57 views

Expanding rational functions with minimal denominator

I'm working with rational functions and I want to be able to put them in a specific form and then get a list of terms in which the numerators are monomials. Take for example ...
1
vote
4answers
91 views

Symbolic calculation on roots of polynomial

Given a polynomial like $x^3 + a_2 x^2 + a_1 x + a_0$ with roots $r_i$, I would like to symbolically compute the coefficients of a polynomial whose roots are $r_i^3 + r_i + 1$. How can I do this in ...
2
votes
3answers
80 views

expressing a rising factorial as a polynomial

I have an equation in $x$ as follows: $f(x)=\prod\limits_{j=0}^{k}(j+x)=x(1+x)(2+x)\cdots(k+x)$ I want to express this as a polynomial in $x$, i.e., as $a_0x^0+a_1x^1+\cdots+a_kx^k$ I tried doing ...
4
votes
3answers
233 views

Get the coefficient matrix from a quadratic form

Suppose I have a quadratic form of qf = a x^2 + b y^2 + c z^2 + 2 d x y + 2 e x z + 2 f y z How can I easily to get the symmetric matrix A, such that ...
0
votes
1answer
26 views

How do you collect trigonometric functions in a polynomial?

I have an expression that has various forms of Sin and Cos and I want to collect them specifically so that I can make substitutions. As you can see I cannot figure out how to separate i Cos[theta] ...
2
votes
3answers
153 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 ...
3
votes
1answer
84 views

How to efficiently find only the rational roots of a rational complex polynomial?

I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this? My best effort on an example polynomial: ...
4
votes
1answer
99 views

Does Solve[] find ALL the exact roots of rational polynomials?

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. But is the ...
1
vote
1answer
111 views

Factoring an arbitary variable in mathematica

Imagine we have a equation like this gf= 1 + (a3 - a1 x)^2 w1 + (b3 - b2 x)^2 w2 how can I reach the following equation ...
0
votes
0answers
27 views

PolynomialExtendedGCD in 2 variables

Consider a field $R$ and the ring $A=R[y]$. Consider two polynomials $g,h\in A[x]$. I want to obtain $d=\gcd(g,h)\in A[x]$ and two polynomials $s,t\in A[x]$ satisfying the Bézout relation: $sg+th=d$. ...
0
votes
1answer
75 views

Why are CoefficientRules and MonomialList so slow?

Why is CoefficientRules so slow in this example (v10.2 on OS X 10.11.4)? ...
4
votes
3answers
125 views

Alternative forms to Table for iterating over replacement rules

I have a multivariate polynomial x. I get coefficients of various monomials using CoefficientRules, which returns a list of ...
6
votes
5answers
345 views

Convert polynomial to Chebyshev

I want to convert a polynomial in "standard form" to Chebyshev form. Here's one way to do it: ...
2
votes
0answers
61 views

Crash on use of CoefficientList

The Kernel of my Mathematica 10.4 seems to crash on certain use of the CoefficientList command. The line CoefficientList[x + y^2, {x, y}] Produces the matrix $$ ...
5
votes
2answers
236 views

Orthogonalize polynomials with respect to Gagliardo seminorm?

For a function $f\colon [-1,1]\to\mathbb{R}$, the Gagliardo seminorm of $f$ is defined to be $$ |f| = \int_{-1}^1\int_{-1}^1 \frac{(f(x)-f(y))^2}{(x-y)^2}\, \mathrm{d}x\, \mathrm{d} y. $$ Given ...
0
votes
1answer
37 views

How to find the lowest power in multi-variable expression?

I am sorry for asking similar question again, I asked How to find the lowest power of variable in expression? and I got wonderful answer, but I have a more question for multi-variable expression. One ...
2
votes
2answers
90 views

How to find the lowest power of variable in expression?

If I have expression like a1/x +a2/x^2 + a3/x^3 I want to return 1/x^3. In general case, ...
4
votes
2answers
106 views

Efficiently strip off coefficients in front of variables?

I am working with multivariate polynomials and need a very efficient way to decompose monomials into coefficients and pure monomials. for instance consider variables ...
2
votes
0answers
31 views

Solving for coefficients of a polynomial? [closed]

I'm sure I'm doing something wrong here, but I'm damned if I can figure out what. I'm trying to find a cubic function that passes through (0, 270), (1, 312), (2,230), (3,0), but the first way I tried ...
1
vote
0answers
33 views

Rearrange generic expression into a quartic polynomial

I'm rather new to mathematica. I'm attempting to express: $$\sqrt{x} = \frac{\gamma \sqrt{y}}{-i(\Delta - g \sqrt{1 - (\frac{\tau}{4lhx})^2})+\frac{\gamma}{2}}$$ as $$0 = Ax^4 + Bx^3 + Cx^2 + Dx + ...
2
votes
2answers
220 views

Maximize simple Polynom: Wrong answer

I want to maximize $poly$ under the constraints $g1,g2,g3=0$ ...
3
votes
1answer
91 views

Can Mathematica factor a polynomial over an algebraic number field?

If I input: Factor[x^2 + x + 1, Extension -> Sqrt[-3]] Mathematica returns: ...
4
votes
1answer
77 views
28
votes
3answers
1k views

Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree $29$ on the domain $[0,1]$, with fairly large coefficients: ...
3
votes
2answers
184 views

the exact real solutions of cubic polynomial?

Such as the equation:$x^3-5 x+1=0$, according to the cubic discriminant we know it has three real solutions. We can also find the exact expressions of them from Mathematical handbook. However, by MMA ...
2
votes
1answer
98 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 ...
2
votes
4answers
217 views

Alternative representations of a polynomial

Suppose we have the polynomial $z^4-2 z^3-12 z^2+13 z+11$. $\;$Is there a way to manipulate it into $(z^2-z)^2-13 (z^2-z)+11$ ? How should I tackle this problem ?
4
votes
1answer
499 views

Small Issue with Chebyshev Derivative Approximation

I am trying to approximate the derivative of a function from its Chebyshev expansion. I start out with the following random function: ...
4
votes
0answers
44 views

Using Mathematica to find an alternative continued fraction for $\zeta(5)$

Given the Riemann zeta function $\zeta(n)$. I. $x=\zeta(3)$ Using Euler's continued fraction formula, we can form $\zeta(3)$'s cfrac as, $$Ax+B = \cfrac{1}{v_1 - \cfrac{1^6}{v_2 - ...
3
votes
0answers
69 views

Change of basis of polynomials

Suppose I have a favourite basis for polynomials in $x_1,\dotsc,x_n$, say non-symmetric Macdonald polynomials to be specific. I can easily compute these, and thus the change-of-basis matrix that takes ...
8
votes
1answer
213 views

Trouble with polynomial multiplication

Bug introduced in 10.1.0 and fixed in 10.4.0 ...
0
votes
0answers
28 views

Obtain a SymmetricReduction of a bivariate (symmetric) function given in Piecewise form

I would like to re-express the following bivariate (symmetric) function (defined over the unit square) ...
2
votes
0answers
32 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
5
votes
1answer
40 views

How to order terms in a polynomial in two variables negative lexicographically

I have several polynomials in variables p and q, each term in which has total degree n, a constant. I would like to output the polynomial in increasing powers of p (and hence decreasing powers of q), ...