Questions on the functionality operating on polynomials

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2
votes
4answers
136 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 ...
0
votes
0answers
39 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
58 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
104 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
25 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 ...
1
vote
1answer
111 views
0
votes
1answer
49 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
votes
1answer
51 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
95 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
39 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 ...
1
vote
2answers
46 views

Coefficients in multidimensional polynomials

I have a multidimensional polynomial depending on {x[1],x[2],x[3],x[4]}. If I want to selectively collect the coefficient corresponding to e.g. ...
1
vote
1answer
79 views

How do I find the constant term of a multivariate polynomial, when (x^0)(y^0)?

So let's say f[x_,y_]:=(2x+2y+1)^2, when I type Coefficient[f[x,y],x y] I recieve 8. But what can I input to recieve 1, when ...
1
vote
4answers
89 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
1answer
90 views

Solving and plotting a non-linear and polynomial equations of degree 3 and higher

I'm doing the following and cannot plot the function, could anyone spot a problem please ...
8
votes
5answers
712 views
2
votes
0answers
39 views

Puiseux series for algebraic curves

Has anyone implemented a function in Mathematica that computes Puiseux expansions of algebraic curves? Using something like ...
1
vote
2answers
119 views

Slow program- Mathematica shuts down

I've been trying to draw dynamic pictures of level sets of certain polynomials. The code right now looks like that : ...
1
vote
0answers
36 views

Working with rational polynomials

I work a lot with transfer functions (Laplace transform) and I often need to convert them into different forms: rational transfer functions pole/zero representation pole/zero/gain representation ...
2
votes
1answer
86 views

Interactive level sets of polynomials

I'm new to Mathematica and I need some help with the following problem. I would like given some positive integer n, to have mathematica plot the level sets of a (say monic) polynomial of degree n, ...
0
votes
0answers
42 views

How to invert the default order of polynomial? [duplicate]

By default, Mathematica outputs polynomials starting with smallest degree. How can I invert this?
1
vote
1answer
47 views

Get Coefficient of polynomial excluding variables

I'd like to write a function that returns the coefficient of a polynomial, but excludes some 'cross-term' coefficients. The function could be called CoefficientExclude, and the first argument would ...
1
vote
1answer
88 views

Improving Performance - Finding Polynomial Roots [duplicate]

I'm fairly new to Mathematica. In the past, my usage has mostly been limited to solving the occasional equation, making some plots, and working with small scaled statistics. None of these have been ...
2
votes
1answer
38 views

Is there a way to Collect[] for more than one symbol in Mathematica 10.0?

This question has already been asked three years ago (Is there a way to Collect[] for more than one symbol?) but I'm not allowed to comment since I'm new at Mathematica StackExchange. The first ...
1
vote
1answer
69 views

Plot roots of polynomial system of equations in 3 variables

I have the two equations $x^2 + 2y^2 + z^2 = 1$ and $xz -y^2 = 0$ I want to plot the roots in 3D. i.e the coordinates $x,y$ znd $z$
1
vote
1answer
42 views

Symmetric group action on polynomials

I am working with polynomials in several variables with the obvious action of $S_n$. That is, given a polynomial $f$ in the variables $x_1, \dots, x_n$, a permutation $\sigma \in S_n$ acts on $f$ by ...
0
votes
0answers
65 views

NIntegrate Polynomial of high degree

I want to integrate a polynomial of degree 100 and higher over a domain that is the intersection of two balls like ...
0
votes
0answers
56 views

Inconsistent Outputs Produced By Eliminate

I have tried the solver "Eliminate" in Mathematica to find the elimination ideal of a polynomial system, and compared the results to examine effectiveness, by simply switching the order of "set the ...
0
votes
1answer
63 views

Splitting a polynomial into sum of factors, not necessarily linear

How can I split a given polynomial as sum of factors in Mathematica? For example, let's say I have this polynomial: $2\cdot x^2+7\cdot x+2$. I would like the output to be $(x+1)(x+2)+x(x+4)$. Is ...
3
votes
2answers
71 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 ...
0
votes
1answer
53 views

NSolve taking too long to solve system of polynomial equations

I am trying to solve a system of polynomial equations (10 variables and 10 equations) using NSolve in an attempt to find all solutions. ...
1
vote
1answer
59 views

Factor bivariate polynomial over the complex numbers

This is very much like Factoring polynomials to factors involving complex coefficients except that I'm concerned about bivariate polynomials, not univariate polynomials. Take for example the ...
0
votes
0answers
27 views

PolynomialMod: Unexpected results

Executing PolynomialMod[(X - 1) (X^3 + 2) (X^2 + 1), 2 - 2 X] 0 But ...
2
votes
3answers
188 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 ?
1
vote
1answer
86 views

Fitting Legendre polynomial - Integer constraints in Fitting functions

I have some data in the form of {theta,y} and I am trying to fit a Legendre polynomial to it, however I don't know how I can get it to vary the m and l parameters in integer increments as I don't know ...
1
vote
2answers
135 views

Getting the polynomial from a polinomial root equation

After doing some preceding work I end up with a polynomial equation that should look something like this: Eq = c + b x + a x^2 - d x^2 == k I would like to ...
11
votes
1answer
299 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...
0
votes
0answers
83 views

Computing Poincaré symbolic solution for an arbitrary integer order polynomial

In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be "natural" generalizations of the elliptic ...
0
votes
0answers
55 views

Does Mathematica support Laguerre Polynomials of Matrix Argument?

I am wondering whether Mathematica can also compute the Laguerre polynomials of matrix argument as the appear in multivariate statistics? For example, they appear in this paper here: ...
0
votes
0answers
67 views

Applying the square root of operator on polynomial functions

I am trying to apply an "operation" on polynomial functions: apply the operator $(\frac{\partial f}{\partial x}-y\frac{\partial f}{\partial z})^2+(\frac{\partial f}{\partial y}+x\frac{\partial ...
2
votes
2answers
171 views

Polynomial expansion of operator

I am new to Mathematica, I am trying to generate the polynomial function of a operator. So for example, the operator $L $ is $\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} $, and I want ...
3
votes
1answer
91 views

Bug in associated Legendre Polynomials?

Mathematica's definition of the connection of associated Legendre polynomials with $m$ and $-m$ is: $P_l^{-m}=(-1)^m \frac{(l-m)!}{(l+m)!} P_l^m$. We also now that $|m|>l \Rightarrow P_l^m=0$. ...
0
votes
2answers
74 views

How to exract the roots from “Roots”? [duplicate]

Given how the output looks like, as in a set of "==" assignments, is it possible to extract specific roots from the output of, http://reference.wolfram.com/language/ref/Roots.html ? And then do a ...
0
votes
1answer
230 views

How do I write nested for-loops?

Looking through the reference.wolfram, I couldn't see an example of how to write a multiple line "for" loop in Mathematica. I need to nest many for-loops in such a way I can do many things in the ...
3
votes
1answer
128 views

How to reduce a quartic form to a quadratic form with equal roots

Preface: To clear the theoretical background this question is cross-posted on math.stackexchange here. I have a polynomial in $n$ variables of the form ...
0
votes
0answers
52 views

Finding an instance of parameters, for which a polynomial has no zeros

I have a polynomial in $p(x,y) \in\mathbb{R}[x,y]_{\leq 4}$, of degree 4. The coefficients are simple functions of 12 real parameters. In particular, the coefficients are in ...
3
votes
0answers
101 views

Extracting an equation from an interpolated function

Im trying to use LibraryLink to do some calculations in C but part of the expression i want to calculate is an Interpolating Function. C cant use that obviously so I'm trying to shift it to a data ...
4
votes
3answers
345 views

Specific factoring of fourth degree polynomial

I have a pretty unspecific question about a really specific thing -- How would one use Mathematica to find values for an integer, m, such that this polynomial ...
4
votes
1answer
128 views

Coefficients of a polynomial in powers of 10

Can I express a polynomial function in Mathematica in power (ScientificForm) ? I was trying: ...
2
votes
0answers
57 views

Drop all powers from multinomial [closed]

How to automatically replace an expression like x^3 y + x y z^2 by x y + xyz in Mathematica, i.e. replace all ...
8
votes
1answer
118 views

Decomposition of a semialgebraic set into connected components

Is there any built-in function for doing decomposition of a semialgebraic set into connected components? The only way I now can think of is to use ...