# Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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### Tropical Operation Conversions: Multiple Operations

I apologize if my syntax is bad. I looked around, but didn't see anything on this in the stack exchange. I would like to be able to transform a classical real-valued polynomial to a tropical ...
• 143
1 vote
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### While inside a function body does not work as expected [closed]

I'm trying to write a function that return a randomly created rational polynomial function that has a discontinuities points. I already have a function that generates random rational polynomial (...
• 69
1 vote
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### How to perform the first and second derivatives of Nth polynomials?

Suppose  $P(x,y)=\displaystyle\sum^{N}_{i+j=0}\alpha_{ij}x^{i}y^{i} \equiv \alpha_{00}+\alpha_{10}x+\alpha_{01}y+a_{11}xy+\ldots+a_{0N}y^{N}$ is a multivariable polynomial of $N$th degree. I want to ...
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### Finding the roots of a quartic [closed]

I try to find the roots of $f(x)=x^4+(4a-2)x^3+(6a^2-6a)x^2+(4a^3-7a^2)x+ a^4-2a^3 =0$ with $0<a<1$. How do i get with Mathematica all solutions (general expressions, real and complex)? With <...
86 views

### How to solve this equation analytically?

Why can't Mathematica 13 solve this equation in radicals? Solve[x^5 - 5*x^4 - 10*x^3 - 10*x^2 - 5*x - 1 == 0, x] // ToRadicals I also tried to use ...
• 71
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### Three equation solving analytically in Mathematica

Im doing coding in iterative schemes but I do not know to solve three equations analytically in Mathematica step by step. For example I given thre equations in the attached figure. I want to solve ...
• 169
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• 101
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### Algorithms or Mathematica definition for functions ideals of polynomial Rings

This question was well posed four years ago without answer at Operations on ideals of polynomial rings. I asked again in Nov 2021 and posted possible function defininitions. Lichtblau commented ...
• 41
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### How can I find the only real and then the smallest root of a 4th-order polynomial?

I just want to solve the below polynomial for real roots only, where I have mentioned the conditions on all variables, a,d,m,L. ...
• 155
1 vote
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### Replace coefficients in a polynomial

I want to replace the coefficients of a polynomial by new coefficients. For example, my polynomial of variable 'r' is in the picture I want to replace the coefficients with 'a subscripts' similar to ...
• 11
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### Reduce returning redundant solutions

When I call reduce on the following system: ...
• 55
216 views

### Solving quadratic equations bug in Mathematica 12.3

There seems to be some sort of bug in mathematica, where sometimes it will treat a quadratic equation as a quartic equation. For example: ...
66 views

### Why is PolynomialQ[y^2,x] True? [closed]

Why is PolynomialQ[y^2,x] True? The documentation says PolynomialQ[] returns ...
• 41
1 vote