# Tagged Questions

Questions on the functionality operating on polynomials

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### Factoring an arbitary variable in mathematica

Imagine we have a equation like this gf= 1 + (a3 - a1 x)^2 w1 + (b3 - b2 x)^2 w2 how can I reach the following equation ...
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### Does Solve[] find ALL the exact roots of rational polynomials?

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. But is the ...
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### PolynomialExtendedGCD in 2 variables

Consider a field $R$ and the ring $A=R[y]$. Consider two polynomials $g,h\in A[x]$. I want to obtain $d=\gcd(g,h)\in A[x]$ and two polynomials $s,t\in A[x]$ satisfying the Bézout relation: $sg+th=d$. ...
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### Why are CoefficientRules and MonomialList so slow?

Why is CoefficientRules so slow in this example (v10.2 on OS X 10.11.4)? ...
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### Polynomial Equation/Function With Even Degree Order [closed]

I have the following data for $x$ and $y$ axis, which I am reading from an Excel file by using the Import command and plotting by using the ...
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### Alternative forms to Table for iterating over replacement rules

I have a multivariate polynomial x. I get coefficients of various monomials using CoefficientRules, which returns a list of ...
319 views

### Convert polynomial to Chebyshev

I want to convert a polynomial in "standard form" to Chebyshev form. Here's one way to do it: ...
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### Maximize simple Polynom: Wrong answer

I want to maximize $poly$ under the constraints $g1,g2,g3=0$ ...
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### Can Mathematica factor a polynomial over an algebraic number field?

If I input: Factor[x^2 + x + 1, Extension -> Sqrt[-3]] Mathematica returns: ...
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### How many solutions do you get from simultaneous polynomial equations?

I have the following four simultaneous polynomial equations ...
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### Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree $29$ on the domain $[0,1]$, with fairly large coefficients: ...
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### the exact real solutions of cubic polynomial?

Such as the equation:$x^3-5 x+1=0$, according to the cubic discriminant we know it has three real solutions. We can also find the exact expressions of them from Mathematical handbook. However, by MMA ...
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### 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 ...
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 ?
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### Small Issue with Chebyshev Derivative Approximation

I am trying to approximate the derivative of a function from its Chebyshev expansion. I start out with the following random function: ...
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### Finding all complex polynomial roots in a specified range efficiently

I need to find the roots of a rational polynomial that are near i. In the following code, I try that two different ways. First, I use a constraint to only find roots in the right region. Second, I ...
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### Create a list of all possible multivariate monomials of a certain order

Given variables x[i] for i=1,2,...,n I would like to create a list of all possible multivariate monomials of order ...
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### How can I use x->Root outputs from Solve? [duplicate]

Do not understand the meaning of the output given by Mathematica to this equation: ...
289 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 ...
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### How to equate coefficient of two polynomials? [closed]

Given two polynomials, How can I equate coefficients of them in Mathematica? For instance a + b x + (c+d) x^2 + (e+f)x^3 == 0
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### 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 ...
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### 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 ...
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### 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) ...
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### How to calculate the pseudo-remainder and pseudo-quotient of two multivariate polynomials

I have fixed some code, but it always gives me errors. Can anybody tell me its right code? ...
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### 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. ...
383 views

### Bug: Wrong results from NSolve on coupled polynomials. WorkingPrecision->Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
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### How to prevent fractions in polynomial quotients?

(This was a hard question to give a succinct title to, so feel free to edit it.) When I divide polynomials, I would like Mathematica to NOT create negative powers of variables. For example: ...
248 views

### Write a function that returns the coefficient of x^n

Write a function C[p_, x_, n_] that returns the coefficient of $x^n$ in the polynomial equation. C[p_, x_, n_] := ... If we ...
129 views

### Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
298 views

### Avoiding a For-loop when finding the solution to a set of polynomial equations

There are several examples and questions regarding Map, but I couldn't find what I need. This is a minimal working example. I have two functions \$\qquad ...