# Tagged Questions

Questions on the functionality operating on polynomials

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### Expectation of Largest Roots of Bernoulli distributed coefficient Monomials

I am interested in determining the most probable maximum values of the real roots of polynomials of form $P(x)=\sum_{k=0}^n a_{k} x^k$ where the degree $n$ will have a defined value (say 3,4,5...) and ...
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### expand[] without multiplying binomial coefficients

I'd like to expand an expression of the form (ax+b)^5 without the binomial coefficents being multiplied out. I would like to see Binomial[5,0], Binomial[5,1] , etc... that intermediate step for ...
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### Create a polynomial of a given degree

In Mathematica, how can I create a polynomial function in given variables of a given degree with unknown coefficents? That is, I am looking for a function ...
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### How to extract all the coefficients of a homogeneous polynomial [duplicate]

Suppose p is a homogeneous polynomial in four variables, say p = x^10 y^10 z^5 w^5 + 3 a x^10 w^20; ...
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### Finding an analytic solution of a cubic equation

I have been trying to solve a cubic equation $$y=zy^3 + z$$ in $y$ – that is, my desired result is a function $y(z)$ satisfying the equation. Now, there are three solutions of this equation and ...
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### Transforming Determinant to Polynomial Expression

I have determinant which equals zero. In determinant, i have x expressions. i want to transform the determinant to polynomial expression so i can solve that with mathematica. Note : Apologize for ...
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### Finding Real Roots and Determining Range

I am interested in determining the minimum and maximum values of the real roots of polynomials of form $P(x)=\sum_{k=0}^n a_{k} x^k$ where $n$ will have a defined value (say 3,4,5...) and $a_k$ are ...
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### Finding and plotting a parametric solution to a complicated equation (transcendental, log-polynomial)

I am trying (desperately) to find a way to solve a transcendental equation whose solution $x$ depends on non-numerical parameters $a$ and $b$. And then to produce a ...
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### Issue finding roots in a polynomial [closed]

I am trying to find the roots of the polynomial (-2 + x)^3 (-2 + x^2) (-4 + x^3) (4 + 2 x^2 + x^4) (-8 - 8 x - 2 x^2 + x^3 + x^4) . I am using the command ...
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### Error In polynomial Root Finding

I have a polynomial in y like so: 2.00855*10^20 + 6.89796*10^20 x y + (5.17347*10^20 + 5.92241*10^20 x^2) y^2 - 1.4806*10^21 x y^3 + 7.77316*10^20 y^4 == 0 I ...
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### Finding a maximum of a Bézier function

Suppose I have a Bézier function $f:\mathbb{R}^2\to\mathbb{R}$ with random coefficients: ...
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### Check Zagier theorem about Mahler's measure

I want to check the following theorem by using Mathematica: (from Heights of Polynomials and Entropy in Algebraic Dynamics, page 22) $\textbf{Theorem}.$ Let $\omega$ denote a primitive $6th$ ...
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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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### 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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### Expanding rational functions with minimal denominator

I'm working with rational functions and I want to be able to put them in a specific form and then get a list of terms in which the numerators are monomials. Take for example ...
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### Using Mathematica to find an alternative continued fraction for $\zeta(5)$

Given the Riemann zeta function $\zeta(n)$. I. $x=\zeta(3)$ Using Euler's continued fraction formula, we can form $\zeta(3)$'s cfrac as, Ax+B = \cfrac{1}{v_1 - \cfrac{1^6}{v_2 - \cfrac{2^6}{...
Suppose I have a favourite basis for polynomials in $x_1,\dotsc,x_n$, say non-symmetric Macdonald polynomials to be specific. I can easily compute these, and thus the change-of-basis matrix that takes ...