Questions on the functionality operating on polynomials

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3
votes
0answers
55 views

Memory Management for Large Datasets [on hold]

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: ...
5
votes
5answers
2k views

Series expansion in terms of Hermite polynomials

I am trying to expand a polynomial in terms of orthogonal polynomials (in my case, Hermite). Maple has a nice built-in function for this, ChangeBasis. Is there a ...
2
votes
1answer
44 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 $x$) ...
1
vote
2answers
300 views

How to know form of plotted Bézier function

Simple scenario is to see the Bézier function, but how to know which polynomial approximate it? ...
0
votes
0answers
4 views

How should this power series be solved [on hold]

-c+3 a^2 b +3 a^2 d -3 a^2 f + O(3)/-a^2 c + a^3 b + 1/2 a^3 d -2 a^3 f + O(4) then its answer is required up to O(a) here in both equations a is a variable and b,c,d,f are constants. solving a ...
13
votes
1answer
312 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
15
votes
4answers
851 views

How to keep Collect[] result in order?

For example, Collect[(1 + x + Cos[s] x^2)^3, x] gives the result ...
14
votes
4answers
1k views

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

Oftentimes you find yourself looking for polynomials in multiple variables. Consider the following expression: a(x - y)^3 + b(x - y) + c(x - y) + d as you can ...
5
votes
1answer
56 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 ...
13
votes
0answers
100 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
258 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 ...
7
votes
2answers
203 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 ...
-2
votes
1answer
41 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 ...
2
votes
3answers
113 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 ...
6
votes
2answers
128 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 ...
4
votes
2answers
138 views

Number of complex roots for the system of polynomials

I have a system of algebraic equations. For example: $$ \left\{ \begin{aligned} x^2 y + 2 x y + 2 &= 0,\\ y^3 + 2 x + 1 &= 0. \end{aligned} \right. $$ (In my problem the system contains 16 ...
4
votes
3answers
251 views

What is the best way to write a polynomial in the Bernstein basis?

The Bernstein basis of polynomials of degree $n$ is the set of polynomials of the form $$\binom{n}{k} t^{n-k}(1-t)^k$$ where $0 \leq k \leq n$. What is the best way to transform a given polynomial ...
3
votes
1answer
207 views

How to enforce mathematica to analytically evaluate roots?

I am interested in simplifying expressions involving HeavisideTheta. A simple example could be: HeavisideTheta[1 + x - x^2 + x^3] The best I can achieve is with ...
6
votes
0answers
204 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
0
votes
2answers
61 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 ...
2
votes
4answers
140 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
41 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 ...
1
vote
1answer
108 views
0
votes
0answers
29 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 ...
0
votes
1answer
53 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
56 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
97 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
40 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
54 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
2answers
120 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 : ...
0
votes
0answers
85 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 ...
2
votes
1answer
104 views

Numerical evaluation of ChebyshevT

When I evaluate the following Chebyshev series of the first kind in two different ways, I get two very different results: ...
11
votes
3answers
545 views

How can we plot the complex roots of an equation?

If we'd like to display the $n$ roots of a polynomial on the complex plane as points, how can we do this? For example, if we have the equation $x^3 + x^2 + x + 1$, how can we plot the 3 roots as ...
1
vote
1answer
80 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
92 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 ...
10
votes
9answers
1k views

Defining a function that completes the square given a quadratic polynomial expression

How can I write a function that would complete the square in a quadratic polynomial expression such that, for example, CompleteTheSquare[5 x^2 + 27 x - 5, x] ...
0
votes
0answers
56 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: ...
2
votes
2answers
174 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
0
votes
1answer
95 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
1answer
126 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 ...
2
votes
2answers
290 views

Generating complete lists of polynomials

I would like to generate a list of all $3$-variable Laurent polynomials with non-negative integer coefficients using a looping construct so that I can, one-by-one, check them for specific ...
4
votes
6answers
202 views

What is the inverse of CoefficientList?

I have numbers in vector notation. I need to get polynomial notation from them. My numbers are {0, 1, 23, 5, 15, 0, 0, 0}. I want to get $x + 23x^2 + 5x^3 + ...
7
votes
4answers
117 views

Unexpected behavior using FromDigits to reconstruct polynomial

I have an issue with the reconstruction of a polynomial using FromDigits. The documentation of the function CoefficientList says: Fold the operation for multivariate polynomials: ...
2
votes
0answers
47 views

Puiseux series for algebraic curves

Has anyone implemented a function in Mathematica that computes Puiseux expansions of algebraic curves? Using something like ...
2
votes
1answer
88 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, ...
3
votes
2answers
72 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
0answers
38 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 ...