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votes
1answer
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 ...
0
votes
3answers
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] ...
2
votes
2answers
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 ...
1
vote
2answers
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 ...
0
votes
1answer
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 ...
1
vote
1answer
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 ...
3
votes
0answers
81 views

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

I consider a set of three polynomials of two variables ...
0
votes
2answers
96 views

Find $k= constant$ so that $disc= 0$ [closed]

Find $k= constant$ so that $\lceil$ https://www.wolframalpha.com/input/?i=discriminant%5By%5E6%2By%5E2z%5E6%2Bz%5E2-y%5E2z%5E2(1%2By%5E2%2Bz%5E2)-k(1%2Bz%5E2)z%5E2(y%2Bz)(y-z)(z-1)(z%2B1)%5D,z%5D $\...
0
votes
1answer
85 views

Finding the inverse of a function

I am to solve for $r(\rho)$ given the function, \[Rho]Asymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)] This can be ...
1
vote
2answers
41 views

How to reduce the residue in NSolve for a system of 3 non-linear equations

I have written the following snippet in Mathematica to solve a system of 3 non-linear equations? ...
0
votes
1answer
43 views

Coercing FullSimplify to groups results

Is there a way to coerce FullSimplify to group the second result (below) to be similar to the first result? ...
0
votes
0answers
62 views

Solving a real polynomial system takes forever, am I asking the impossible?

I want to find all stationary points of a particular 3 dimensional polynomial function. Sounds easy enough, right? Just get the gradient with Grad[], and solve the ...
0
votes
3answers
104 views

How to solve this 4th degree polynomial equation with complex coefficients numerically in Mathematica?

I have a polynomial equation: $-(a-ib)e^{(4\pi i/3)}(\sqrt{2}i+x^3/\sqrt{3})x- (a+ib) e^{(2\pi i/3)}(\sqrt{2}ix^3+1/\sqrt{3})=0$ (which in code is): ...
2
votes
1answer
80 views

Range of contour plot for polynomial

...
0
votes
1answer
52 views

Choice of variables name affects the behavior of expression evaluation

I tried to expand this polynomials. With x, it is increasing with the right order, however with b it is in a random order. The only difference is that I change b to x and it works. ...
1
vote
0answers
55 views

Solve polynomial system

I am trying to solve ...
0
votes
0answers
220 views

PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD.Error

Not exactly sure whats wrong with my code but it keeps giving me a PolynomialGCD: Exponent is out of bounds for function PolynomialGCD error. The equation that I do NSolve for is very big and it takes ...
0
votes
2answers
184 views

Why does my Solve output contain this symbol? [duplicate]

I have a pair of coupled polynomial equations that I need to solve, so I tried using Mathematica's solve tool. This is the code that I wrote: ...
0
votes
1answer
68 views

Recurrences with some relation to Dedekind eta functions

Dedekind eta functions are know to satisfy certain difference equations/recurrence relations. The same is true for ratios of eta functions. Suppose some ratio of eta functions, say $A(q)$ satisfies ...
-1
votes
1answer
70 views
1
vote
2answers
102 views

Solving a 4th order polynomial [closed]

I have a fourth order polynomial of the form: $$y = a_{0} + a_1 x + a_{2}x^{2} + a_{3}x^{3} + a_{4}x^{4}$$ Where the coefficients $a_{0}$, $a_{1}$, $a_{2}$, $a_{3}$ and $a_{4}$ are determined from the ...
2
votes
1answer
200 views

Solving for coefficients in a polynominal

I've the following problem: how can I solve for the coefficients in a polynominal? So, I mean the following: I've the following expression: $$\left(56-85689\cdot x\right)^2-3136\tag1$$ And I ...
9
votes
2answers
293 views

Finding the condition for root of a third degree polynomial

I've a third degree polynomial (in $s$): $$as^3+bs^2+cs+d\tag1$$ I need to find the roots of the polynomial, so I can use the code: ...
0
votes
2answers
119 views

Finding the roots of a polynomial that meet specified conditions

Find the largest real root and the largest real part of a root of the polynomial below. Clearly indicate which is which. $f(x) = 5 -\sum\limits_{k=1}^{100}k^2x^k$. To get all roots, solve ...
1
vote
1answer
107 views

Plot the critical points of degree $d$ polynomials with zeros randomly chosen in given region

I wish to be able to scatter slightly (by at most some fixed $\varepsilon>0$) the zeros of a given complex polynomial $p(z)$ in a random way, and then see the effect on the critical points. For ...
0
votes
0answers
30 views

Solving in terms of polynomials for F,G such that Ff+Gg=c

I'm pretty new to mathematica and am trying to solve the following: I have two explicit polynomials $f(x), g(x)$ with integer coefficients and a constant $c$ and I'm looking for two polynomials $F(x),...
2
votes
1answer
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 ...
0
votes
0answers
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 ...
6
votes
1answer
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 ...
7
votes
1answer
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 ...
-1
votes
2answers
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 ...
2
votes
3answers
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 + ...
0
votes
0answers
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 $C_{ij}$. ...
1
vote
3answers
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, ...
4
votes
2answers
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 ...
1
vote
2answers
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 ...
1
vote
2answers
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. ...
3
votes
0answers
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 ...
0
votes
0answers
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 ...
1
vote
0answers
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. <...
0
votes
2answers
147 views

Find Root condition for polynomial

I have the following 12-th order polynomial in $\lambda$ with a parameter dependency in $u$: ...
3
votes
1answer
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 ...
3
votes
1answer
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 ...
3
votes
1answer
126 views

Coefficients of Knuth's “Convolution Polynomials”

Donald E. Knuth gives in his paper Convolution Polynomials the code ...
4
votes
0answers
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 ...
6
votes
0answers
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 ...
11
votes
1answer
1k views

Solving quintic in radicals

I need to find an explicit expression in radicals for the real root of the quintic equation ...
3
votes
4answers
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]...
1
vote
1answer
108 views

solving of a polynomial equation with large coefficients

m trying to solve a polynomial equation with degree 4.. i have given the code below.. but it's taking too long and at the end shows a message that it has exceeded the time limit.. please help ...
9
votes
5answers
2k views

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 ...