Questions on the functionality operating on polynomials

learn more… | top users | synonyms (1)

0
votes
1answer
72 views

Why are CoefficientRules and MonomialList so slow?

Why is CoefficientRules so slow in this example (v10.2 on OS X 10.11.4)? ...
-3
votes
0answers
36 views

Polynomial Equation/Function With Even Degree Order [on hold]

I have the following data for $x$ and $y$ axis, which I am reading from an Excel file by using the Import command and plotting by using the ...
4
votes
3answers
117 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
315 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
55 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
233 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 ...
1
vote
1answer
48 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 ...
0
votes
1answer
35 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
84 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
100 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
29 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
84 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
74 views
27
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
180 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
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 ...
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
483 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
37 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
65 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 ...
5
votes
2answers
308 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: ...
8
votes
1answer
209 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
31 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
39 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), ...
8
votes
2answers
222 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} ...
0
votes
2answers
102 views

Finding all complex polynomial roots in a specified range efficiently

I need to find the roots of a rational polynomial that are near i. In the following code, I try that two different ways. First, I use a constraint to only find roots in the right region. Second, I ...
6
votes
5answers
204 views

Create a list of all possible multivariate monomials of a certain order

Given variables x[i] for i=1,2,...,n I would like to create a list of all possible multivariate monomials of order ...
1
vote
0answers
43 views

How can I use x->Root outputs from Solve? [duplicate]

Do not understand the meaning of the output given by Mathematica to this equation: ...
8
votes
2answers
286 views

On the definition of the associated Legendre polynomials

Mathematica computes for n = 1,2,...: (-1)^n (LegendreP[n, -1, -3]/Sqrt[2]) -I, -3 I, -11 I, -45 I, -197 I, ... Maple ...
3
votes
1answer
55 views

How to gather terms into Elementary Symmetric Polynomials?

I would like to gather the terms of this polynomial (and much higher order ones): $$q = 1-3 c+c^2+p[1]-2 c p[1]+p[2]-2 c p[2]+p[1] p[2]-c p[1] p[2]+p[3]-2 c p[3]+p[1] p[3]-c p[1] p[3]+p[2] p[3]-c ...
2
votes
2answers
64 views

How do I find a polynomial in a field?

If I have a polynomial: $$f(x) = c_0 x^0 + c_1 x^1 + c_2 x^2 + \dots + c_n x^n$$ How can I find the polynomial, modulo a prime number $p$? In other words, I want to take all of the coefficients ...
4
votes
1answer
88 views

How to equate coefficient of two polynomials? [closed]

Given two polynomials, How can I equate coefficients of them in Mathematica? For instance a + b x + (c+d) x^2 + (e+f)x^3 == 0
3
votes
3answers
129 views

General function for the expansion of a polynomial of operators

This question is motivated by a Quantum mechanical problem - but in explaining the problem - I assume no knowledge of quantum mechanics. I want to define a function that can expand and simplify the ...
1
vote
2answers
79 views

What's the easiest way to remove overall factors from polynomials?

I have code that outputs polynomials (in #1) such as the ones below (note that the trailing Function character ...
2
votes
1answer
99 views

How do I find the analytical roots of this polynomial? [closed]

I want to find the analytical roots of this polynomial - x - a^3*x*(a^2*x*(a*x*(x - 1) + 1)*(x - 1) + 1)*(a*x*(x - 1) + 1)*(x - 1) ...
0
votes
1answer
98 views
2
votes
3answers
81 views

How to set/adjust Precision for an iterative calculation?

How should I restructure this code? I generate a high-order polynomial poly with integer coefficients, then find roots and divide them out of poly one at a time. ...
10
votes
3answers
383 views

Bug: Wrong results from NSolve on coupled polynomials. WorkingPrecision->Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
3
votes
1answer
80 views

How to prevent fractions in polynomial quotients?

(This was a hard question to give a succinct title to, so feel free to edit it.) When I divide polynomials, I would like Mathematica to NOT create negative powers of variables. For example: ...
7
votes
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 ...
1
vote
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 ...
3
votes
6answers
298 views

Avoiding a For-loop when finding the solution to a set of polynomial equations

There are several examples and questions regarding Map, but I couldn't find what I need. This is a minimal working example. I have two functions $\qquad ...
3
votes
2answers
76 views

Workaround for issues with Coefficient in 10.0.2

Coefficient is Mathematica 10.0.x seems to be affected by a bug. While in 10.3.1 the following ...
3
votes
4answers
510 views

NSolve didn't get the answer for my equations within 24 hours

I have two polynomials as function of $wa$ and $wb$ , I am going to show those polynomials. This is the expression for $GS65$: ...
1
vote
2answers
66 views

Complex polynomial variable transformation

I have two real polynomials that depend in variables (xi1, xi2) and parameters (eps, e2). I apply the following ...
3
votes
0answers
296 views

Negative power instead of fraction [duplicate]

Solve returns a solution in the form {{ x -> y / a^2 + y^2 / a^7 }}. Since I want to process the input (with another program) in terms of Laurent polynomials, I ...