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6
votes
0answers
91 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 ...
5
votes
0answers
159 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
4
votes
0answers
354 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 ...
2
votes
0answers
80 views

Finding related roots to a polynomial

I posted this in math.stackexchange, but this might be a better place. Assume that $f(X,Y,Z,V,W)\in \mathbb{Z}[X,Y,Z,V,W]$ is some polynomial and assume that $f(x,y,z,v,w)=0$. I would like to know if ...
1
vote
0answers
63 views

Root finding over finite field extension

I'd like to know if there exists any method on Mathematica, third-party coded resource or library that can compute roots of a polynomial over an extension $\mathbb{E}$ where $E=F_p[x]/f(x)$ and $f(x)$ ...
1
vote
0answers
56 views

Solve polynomial system

I am trying to solve ...
1
vote
0answers
61 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. <...
1
vote
0answers
408 views

Best way to determine polynomial coefficients in series expansion

I would like to solve the equation $$h'(\boldsymbol{x}_1)\left[B_1\boldsymbol{x}_1+g_1(\boldsymbol{x_1},h(\boldsymbol{x}_1))\right]=B_2h(\boldsymbol{x}_1)+g_2(\boldsymbol{x}_1,h(\boldsymbol{x}_1))$$ ...
1
vote
1answer
63 views

Parametric solution of a system of polynomial equations

I have the following system of equations, 1+x+y+z==0, 1+x*y+y*z+x*z==0 which I want to solve in the extension field of GF(2), the algebraic closure of GF(2) for ...
0
votes
0answers
41 views

How to solve the equation of polynomial with uncertain degrees?

Consider the following equation \begin{equation} \frac{g^{a_{1}}+g^{a_{2}}}{\left(1-g^{a_{1}}\right)\left(1-g^{a_{2}}\right)}+\frac{g^{c_{1}}+g^{c_{2}}}{\left(1-g^{c_{1}}\right)\left(1-g^{c_{2}}\right)...
0
votes
0answers
44 views

What is the algorithm used by SolveAlways function?

The syntax of SolveAlways function is SolveAlways[eqns, vars] For example, SolveAlways[ax + b == 1, {x}] Mathematica ...
0
votes
1answer
115 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 ...
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
0answers
268 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
0answers
36 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),...
0
votes
0answers
36 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 ...
0
votes
0answers
208 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 ...
0
votes
0answers
91 views

Roots of cubic polynomial when a coefficient is an infinite list

I would like to have an expression of the roots of a cubic equation of the type $x^3+ \gamma x^2 + kx = f(k)$ where $\gamma \in [0,1]$, $k$ is an integer and where $f(k) = \{|k|,|k|+2, |k|+4,...\}$. I ...
0
votes
0answers
567 views

Finding closed-form Eigenvalues of a particular Matrix

MWE ...
-1
votes
1answer
71 views