Questions on the functionality operating on polynomials

learn more… | top users | synonyms (1)

2
votes
2answers
1k views

Calculating Taylor polynomial of an implicit function given by an equation

I'd like to write a procedure that will take an equation: F(x,y,z) = 0 chosen variable: x a point: ...
2
votes
3answers
721 views

Convert coefficients of polynomials into a matrix

I have several sets of 5 polynomials of the form: ...
2
votes
1answer
71 views

Improving working precision of LegendreP[n,x]? [duplicate]

I was trying to evaluate N[LegendreP[5,0.1]] The cell gives me: N[LegendreP[5,0.1]]=0.178829 However I wanted more ...
2
votes
3answers
322 views

Symbolic manipulation of functional form

I have a functional polynomial expression of the form: ...
2
votes
1answer
159 views

Implementation of Decompose

I'm curious as to how Decompose works so I decided to use Trace with the option ...
2
votes
1answer
85 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) ...
2
votes
1answer
71 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 $x$) ...
2
votes
1answer
110 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
47 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 ...
2
votes
3answers
207 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 ?
2
votes
2answers
167 views

Rounding only coefficients

does Mathematica have built in functionality to round the coefficients of a polynomial to a certain accuracy. Say, we do Print[0.2134320980x^2+0.0023432x] Can ...
2
votes
1answer
296 views

Is there any way to force Mathematica to collect a symbol in a polynomial?

Let's say that I have a polynomial like this: a + b + c Is there any way that I can get Mathematica to transform it to: ...
2
votes
2answers
327 views

How to find solutions that yield of root of unity?

I have a polynomial with coefficients that are integer polynomials in another (complex) variable. For example: 1 + (1 - v^2) #1 + (-3 - v^2) #1^2 + #1^3 & I ...
2
votes
3answers
75 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. ...
2
votes
1answer
98 views

Cannot get plot of polynomial (x^2 + y^2 + z^2 - 4)^2 == 0 from ContourPlot3D [closed]

I'm trying to make a 3D contour plot the polynomial equation $$(x^2 + y^2 + z^2 - 4)^2 == 0, \quad \quad (1)$$ Without power 2 $$ (x^2 + y^2 + z^2 - 4) == 0, \quad \quad (2)$$ it plots a ...
2
votes
1answer
62 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 ...
2
votes
1answer
144 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
2answers
572 views
2
votes
1answer
115 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: ...
2
votes
1answer
97 views

How can I sort the polynomial by the degree of $x$

f1 = a x^2 + b x + c + x^3 (* a x^2+b x+c+x^3 *) f1 /. x -> (x - a/3) // Expand (* (2 ...
2
votes
1answer
532 views

Formatting results of a polynomial long division

I am teaching polynomial long division to my high school students. Not a pleasant topic to have to cover. I went to use Wolfram|Alpha and obviously, internally, they have a really elegant way to ...
2
votes
1answer
151 views

How to transform an expression using algebraical instead of pattern rules [duplicate]

I would like to transform rules algebraically. A very simple example would be: - k^2 - 2 k x + x^2 /. {2*k -> 1} This transforms to: - $$k^2-2 k x+x^2$$ ...
2
votes
1answer
66 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 ...
2
votes
1answer
96 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, ...
2
votes
1answer
139 views

NSolve for system of polynomial equations

I would like to find all the solutions to the following system of 8 polynomial equations for the variables w1, w2, w3, w4, w5, w6, w7, w8 ...
2
votes
1answer
203 views

Issue with Coefficient command [closed]

I'm trying to used the Coefficient command to extract the numerical values in front of a Chebyshev polynomial. I know that there is a numerical way to do this, presented in numerical recipes, which I ...
2
votes
1answer
505 views

Expanding a polynomial with fractional powers

Given an expression like a + b*y + c*y^2 + d*Sqrt[f + g*y + h*y^2] How can I programatically, expand this to a quartic without any fractional powers? Right ...
2
votes
2answers
2k views

Solving cubic equation for real roots

I'm looking to solve the following cubic equation for x: $\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this ...
2
votes
0answers
76 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
0answers
107 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
0answers
58 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 ...
2
votes
0answers
39 views

How to simplify a polynomial and get the results in the order that I want? [duplicate]

How to simplify a polynomial in a order that I want? Assume that I have a polynomial here, for example, $a^3 b^4 c^2$, the order of symbels is the dictionary order, $a>b>c$. But what if I want ...
1
vote
2answers
211 views

Stopping Mathematica from reordering expressions [duplicate]

I want Mathemtica to stop manipulating my polynomials! I mean, I want the output of Print[3 x + 5 + x^2] to be just $3x+5+x^2$, not $5+3x+x^2$ as Mathematica ...
1
vote
3answers
2k views

The plot of roots of polynomials

I have polynomial equation like Tribonacci Polynomials for example: $T_3(x)=x^4+x$. After finding the roots of this polynomial, I want to show these roots in the complex plane. I have tried lots of ...
1
vote
2answers
427 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
1
vote
1answer
67 views

Graph of second order polynomials [closed]

As I mentioned before, I want to write a notebook for teaching graphs of second order polynomials that shows discriminant and the conditions when a>0, a<0, having real roots, having no real roots. ...
1
vote
1answer
111 views

Polynomial decomposition algorithm with a hint

If $p,f,g$ are polynomials of degree 2 or higher and $p(x)=f(g(x))$ we have a polynomial decomposition of $p$. When Mathematica (as noted below this was actually on Wolfram Alpha) says ``decomposition ...
1
vote
4answers
109 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 ...
1
vote
3answers
376 views

List of Tribonacci Polynomials with Mathematica? [duplicate]

I want to list top ten of Tribonacci polynomials. I have following algorithm, but it doesnt work. ...
1
vote
2answers
190 views

Strange integration result

In Mathematica 8, the Integrate command sometimes strangely integrates polynomials yielding unsimplified (and unexpected) fractional results. As an example, the line: ...
1
vote
1answer
403 views

Plotting solutions of a 4th order polynomial equation

I have a polynomial equation of the fourth order, which has $4$ roots depending on a variable parameter s1. For each s1 I have ...
1
vote
2answers
358 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? ...
1
vote
2answers
39 views

Inserting numbers or polynomials into a polynomial

Essentially my issue is that, in the algorithm im working on, I construct a polynomial by taking factors out of a list and multiplying them. For example, i have ...
1
vote
2answers
76 views

Creating a random complex univariate polynomial

I am a newbie in Mathematica, but I need to create a random univariate polynomial of degree d with complex coefficients whose entries are random complex variables with real and imaginary parts being ...
1
vote
1answer
117 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 ...
1
vote
2answers
406 views

Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: ...
1
vote
2answers
72 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 ...
1
vote
1answer
92 views

Is Factor reliable to find factorization? [closed]

I have two polynomials given by: ...
1
vote
1answer
71 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 ...