Questions on the functionality operating on polynomials

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3
votes
0answers
159 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 ...
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 ...
2
votes
3answers
300 views

Is it possible to use Composition for polynomial composition?

I want to do this: $P = (x^3+x)$ $Q = (x^2+1)$ $P \circ Q = P \circ (x^2+1) = (x^2+1)^3+(x^2+1) = x^6+3x^4+4x^2+2$ I used Composition for testing if that could ...
2
votes
2answers
245 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 ...
2
votes
4answers
275 views

Working with symmetric polynomials

I have a question related to working with symmetric polynomials in some variables. Let us say, I have an expression ...
2
votes
2answers
85 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, ...
2
votes
2answers
367 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 ...
2
votes
4answers
168 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 ...
2
votes
2answers
220 views

Maximize simple Polynom: Wrong answer

I want to maximize $poly$ under the constraints $g1,g2,g3=0$ ...
2
votes
4answers
160 views

Get the first positive coefficient in polynomial?

I have Polynomial $F(x) = \sum_{i \leq n}{a_ix^i}$. How to get the first $a_i > 0$? Thanks,
2
votes
1answer
433 views

How to get the coefficient list

polynomial=-x^4+2 b x^3+(b^2-c^2+2 c) x^2+(2 b c-2 c d) x+c^2-d^2 This is good CoefficientList[polynomial, x] But how to ...
2
votes
2answers
65 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 ...
2
votes
1answer
64 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 ...
2
votes
3answers
157 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
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 ?
2
votes
2answers
345 views

Evaluating Polynomials at Grid Points

I am continuing my quest on B-splines. The code below builds a 5x5 matrix out of B-splines, using the BSplineBasis[] routine. I now want to evaluate the polynomials that are stored in each matrix ...
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
770 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
1answer
216 views

How can I calculate all irreducible polynomials of 31 degree in $\mathbb Z_2[x]$?

How can I calculate all binary irreducible polynomials of degree 31? or how i calculate all irreducible $f$ in $\mathbb Z_2[x]$? (The irreducible polynomial in $\mathbb Z_2[x]$ and $\mathbb R$ are ...
2
votes
3answers
329 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
100 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
81 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
114 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
55 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
2answers
182 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
306 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
345 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
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. ...
2
votes
1answer
113 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
63 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
151 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
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
2answers
589 views
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
1answer
118 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
107 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
594 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
108 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
142 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
218 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
542 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
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 $$ ...
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 ...
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 ...
2
votes
0answers
122 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 ...