# All Questions

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28 views

### Solving a polynomial equation involving gamma function

I am trying to solve an equation having degenerate limit of Fermi-Dirac integral. My code basically is ...
70 views

### expression containing radicals of imaginary numbers

I can't bear an expression containing radicals of imaginary numbers, in case it can be expressed as in terms of radicals of real numbers only. For example, I can't bear the expression Sqrt[2 + i] ...
171 views

### NSolve gives weird result for $n=101$ with NSolve[$\frac{d}{dx}\prod \limits_{k=1}^n (x-k)$==0,x]

Coming from this post: What would be the roots of the derivate of this polynom I did a quick check with Mathematica and arrived at a wrong result. I was initially confused but chose to trust ...
79 views

### Zeros of high degree polynomials

I am working with Hermite polynomials in Mathematica with the built-in function HermiteH. I want to compute the zeros of the polynomial ...
68 views

### How to find the largest degree of a polynomial?

I have a huge polynomial, and I am having the following issues 1. I wanted to find the largest and smallest degree of that polynomial. 2. How to truncate the lower order terms, sometimes higher order ...
65 views

### Have I found bugs in Solve and Reduce? [closed]

f[x_] := x^3 - 2 x + 1; Solve[f[x] == 0, x] {{x -> 1}, {x -> 1/2 (-1 - Sqrt[5])}, {x -> 1/2 (-1 + Sqrt[5])}} But ...
81 views

### How to make GroebnerBasis Work or to speed NSolve up [closed]

I consider a set of three polynomials of two variables ...
96 views

78 views

### problem in finding roots of a large polynomial

I have a problem with finding the roots of a huge polynomial with mathematica: it finds the roots but they are wrong! I tried to use both "NSolve" as well as "Roots", but I always get the same wrong ...
33 views

### What algorithm does NSolve use for real solutions of underdetermined systems of polynomial equations?

I am trying to write up a paper with some results form Mathematica (11.2) among other things. I need to know what algorithm does it use when I solve a system of polynomial equations which is ...
210 views

### Solve quintic equation using differential equation

Background DiffResolvent.nb, here gives a method that solve quintic equations using differential equations. There's a progress to transform polynomial equation into differential equation. Then he ...
268 views

### Using a Grobner basis to calculate common roots of a system of polynomial equations

We are trying to solve the inverse kinematics of a robot with $3$ revolute joints and one prismatic arm, link $4$, able to take lengths between $1$ and $2$. We assume all other lengths are $1$. Image ...
162 views

### Solve polynomial with a condition

I need to get algebraic expression for r by solving the polynomial mention below with a condition, the condition is that [Lambda]<=0. I used solve command and set the polynomial equal to 0 and ...
146 views

### Third degree equation resolution

On page 17 of the Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables by Abramowitz and Stegun, it is written that given the third degree equation: z^3 + a_2\,z^2 + ...
30 views

### Groebner bases with symbolic exponents [duplicate]

I'm trying to eliminate variables using Groebner bases or polynomial resultants with symbolic exponents. I'm wondering if it is possible to do it in general case for non-negative integers $C_{ij}$. ...
220 views

### Fastest way to find roots

I'm working with generative polynomials, and would like to know if there is a faster way to calculate roots. Using the technique below I've managed to cut the time down significantly. However at n=35, ...
139 views

### Root and ToRadical[Root] do not preserve order of roots

When I look for roots to a quartic polynomial of the form $A - B x^3 + Cx^4$ for positive $A$, $B$, and $C$, it seems that ToRadicals does not preserve the root ...
207 views

### solutions to complex polynomial systems

I can not find anywhere whether Mathematica finds ALL the complex solutions to complex polynomial systems or just some of them. For example, I typed ...
128 views

### Transformation Rules [closed]

I've managed to obtain general solutions to a cubic polynomial with arbituary constants (x1, x2, x3 are solutions). By using transformation rules, how would I get x1x2x3,x1x2+x2x3+x3x1 and x1+x2+x3. ...
58 views

### NSolve not working unless I use Expand before in Mathematica 11 [duplicate]

I am using Mathematica 11, and I noticed this weird thing when using NSolve. Given the same equation in one variable, there are cases in which NSolve only finds the zeroes of the function if I first ...
202 views

### Eliminating variables from system of equation using Eliminate or Solve

I have a system of equations for algebraic curve given by the zero locus of some polynomial encoded in the system of equations (I want to eliminate variable z and get algebraic curve in terms of x and ...
59 views

### Solving this system of two algebraic equations

I'd like to find symbolically the common roots of two polynomial of second order in X and Y. Though this is not possible in general, with the present coefficients, MMA manages to output a result. <...
147 views

### Find Root condition for polynomial

I have the following 12-th order polynomial in $\lambda$ with a parameter dependency in $u$: ...
243 views

### Rationalizing expression with Roots v2

I want to generalize the answer from my previous question: Rationalizing expressions with Roots, so I want to rationalize a very ugly expression that I can't paste here since it's way too long so I ...
151 views

### Rationalizing expressions with Roots

I'm looking for a way to rationalize a very ugly expression given by the code I pasted in. What do I mean by this? The expression is a solution to the zero locus of some polynomial. In my previous ...
126 views

### Coefficients of Knuth's “Convolution Polynomials”

Donald E. Knuth gives in his paper Convolution Polynomials the code ...
333 views

### Homotopy Continuation solution of system of polynomials

I have very large systems (>20) of polynomial (max degree 3) equations that I would like to find a solution to. I'm not interested in all solutions as presumably there are too many (a huge number ...
88 views

### When does Root have a third argument

In Mathematica "11.0.1 for Microsoft Windows (64-bit) (September 20, 2016)", Root[#^4 + 1 &, 2]; actually has three arguments, as can be seen from ...
1k views

I need to find an explicit expression in radicals for the real root of the quintic equation ...
381 views

### Solve polynomial for coefficients in a range

I want to create a list of all roots of quadratics with coefficients in a range of $-5$ to $5$ I tried this : NSolve[Range[-5,5]*z^2+Range[-5,5]*z+Range[-5,5] == 0]...
### How can I find the roots for $x^4-18x^2-8x+21$ in a nice form?
I'm trying to find the roots for $x^4-18x^2-8x+21$. Theoretically, one can show that it has four real roots. But the following line returns four complicated forms including complex numbers. Is there ...