Questions on the functionality operating on polynomials

learn more… | top users | synonyms (1)

0
votes
0answers
35 views

Numerically finding a single root of a polynomial system

I may be off base, but from the documentation, it sounds like NSolve is specifically tailored to finding (all) roots of a polynomial system. On the other hand, ...
4
votes
1answer
76 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
54 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
58 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
109 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 ...
2
votes
1answer
58 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
votes
1answer
43 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.
-1
votes
0answers
28 views

Coefficients to Polynomial expression [duplicate]

How could I create a polynomial function from a list of coefficients. ...
0
votes
0answers
33 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 ...
3
votes
0answers
71 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
157 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
vote
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
0answers
63 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 ...
3
votes
1answer
53 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
33 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
62 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
47 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 $x$) ...
14
votes
0answers
149 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
276 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
45 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
132 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
117 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
142 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 ...
1
vote
1answer
59 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
68 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
110 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
30 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 ...
7
votes
1answer
152 views

Trouble with polynomial multiplication

Bug introduced in 10.1.0 and persisting through 10.2.0 or later ...
0
votes
1answer
60 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
60 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
100 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
43 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
55 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
81 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
97 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
97 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
727 views
2
votes
0answers
57 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
123 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
44 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
90 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
43 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
55 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
100 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 ...
5
votes
1answer
61 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
90 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
46 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
79 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
57 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
71 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 ...