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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 ...
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. <...
0
votes
2answers
149 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
249 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
160 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
136 views

Coefficients of Knuth's “Convolution Polynomials”

Donald E. Knuth gives in his paper Convolution Polynomials the code ...
4
votes
0answers
356 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
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 ...
11
votes
1answer
2k 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
414 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
115 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
3k 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 ...
0
votes
1answer
94 views

Polynomial root [closed]

How can I find the root of a polynomial with FindRoot? I do not understand what to put in the 2nd argument. I want to find the values that cancel this polynomial: <...
2
votes
1answer
122 views

Transformation of variables in function in mathematica

How do i change variables of function in mathematica ? for example of f(p,q) = p^3 + q^3, from p,q to x= p-q and y = p+q, so that the function now becomes f(x,y) ?
0
votes
0answers
92 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 ...
3
votes
1answer
217 views

Factorization of a fractional multivariate polynomial

Suppose I have given a fractional multivariate polynomial ...
2
votes
1answer
148 views

Can Root function be replaced by the roots from the Solve function? [duplicate]

I am using Mathematica to integrate a complicated expression however the integration gives an answer containing these there terms ...
2
votes
1answer
75 views

solving a system of polynomial functions with arbitrary length

I am trying to solve a system of polynomial functions: $$x^T T_1 X = x_1 , \\ x^T T_2 x = x_2,\\ \vdots\\x^T T_l x =x_l$$ where $\{T_i\}$ is a given set of $l \times l$ matrices And I require a ...
5
votes
1answer
128 views

Can I absolutely rely on CountRoots and RootIntervals?

I have some polynomials of high degree with coefficients of the form a + b Sqrt[5] where a, b...
0
votes
1answer
337 views

Solving a system of simultaneous polynomial equations [closed]

This is the first time I have used Mathematica, so please bear with me. I'm trying to solve a system of $10$ nonlinear polynomial equations in $10$ unknowns, which I denote by $a, b, c, d, e, f, g, h, ...
4
votes
2answers
1k views

find roots with specified coefficients

Please assume we have an equation which we want to obtain its roots. We can use ...
1
vote
1answer
77 views

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 ...
5
votes
2answers
926 views

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 ...
3
votes
2answers
349 views

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 ...
0
votes
2answers
422 views

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 ...
1
vote
3answers
152 views

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 ...
2
votes
2answers
443 views

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 ...
0
votes
0answers
567 views

Finding closed-form Eigenvalues of a particular Matrix

MWE ...
0
votes
1answer
420 views

Solving for Polynomial roots

This simple Solve gives the roots of a quadratic: Solve[a x^2 + b x + c == 0, x] However, if I factor the polynomial in terms ...
5
votes
1answer
372 views

Is there a package to find ALL exact roots of a polynomial, if they exist?

There are polynomials with roots not expressible with radicals but expressible as trigonometric or other functions, for which Solve[] only returns ...
3
votes
1answer
347 views

How to efficiently find only the rational roots of a rational complex polynomial?

I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this? My best effort on an example polynomial: ...
4
votes
1answer
222 views

Does Solve[] find ALL the exact roots of rational polynomials?

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. But is the ...
2
votes
0answers
428 views

Solving for coefficients of a polynomial? [closed]

I'm sure I'm doing something wrong here, but I'm damned if I can figure out what. I'm trying to find a cubic function that passes through (0, 270), (1, 312), (2,230), (3,0), but the first way I tried ...
1
vote
0answers
147 views

Rearrange generic expression into a quartic polynomial [closed]

I'm rather new to mathematica. I'm attempting to express: $$\sqrt{x} = \frac{\gamma \sqrt{y}}{-i(\Delta - g \sqrt{1 - (\frac{\tau}{4lhx})^2})+\frac{\gamma}{2}}$$ as $$0 = Ax^4 + Bx^3 + Cx^2 + Dx + E,$...
4
votes
1answer
140 views

How many solutions do you get from simultaneous polynomial equations?

I have the following four simultaneous polynomial equations ...
4
votes
2answers
645 views

The exact real solutions of a cubic polynomial?

Such an 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 <...
1
vote
0answers
48 views

How can I use x->Root outputs from Solve? [duplicate]

Do not understand the meaning of the output given by Mathematica to this equation: ...
4
votes
1answer
2k views

How to equate coefficient of two polynomials? [closed]

Given two polynomials, How can I equate coefficients of them in Mathematica? For instance a + b x + (c+d) x^2 + (e+f)x^3 == 0
3
votes
1answer
764 views

How do I find the analytical roots of this polynomial? [closed]

I want to find the analytical roots of this polynomial - x - a^3*x*(a^2*x*(a*x*(x - 1) + 1)*(x - 1) + 1)*(a*x*(x - 1) + 1)*(x - 1) ...
0
votes
2answers
295 views

Finding all complex polynomial roots in a specified range efficiently

I need to find the roots of a rational polynomial that are near i. In the following code, I try that two different ways. First, I use a constraint to only find roots in the right region. Second, I ...
2
votes
1answer
133 views

Does the function Solve determine if a polynomial is NOT solvable by radicals?

If I input: ...
3
votes
6answers
395 views

Avoiding a For-loop when finding the solution to a set of polynomial equations

There are several examples and questions regarding Map, but I couldn't find what I need. This is a minimal working example. I have two functions $\qquad f=x^4+y^...
3
votes
4answers
531 views

NSolve didn't get the answer for my equations within 24 hours

I have two polynomials as function of $wa$ and $wb$ , I am going to show those polynomials. This is the expression for $GS65$: ...
10
votes
3answers
527 views

Wrong results from NSolve on coupled polynomials. WorkingPrecision -> Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
3
votes
1answer
473 views

How to solve coupled multi-variable polynomials?

The following code generates two polynomials $q_1$ and $q_2$ in complex variables p and c: ...
1
vote
1answer
268 views

Conditions for real roots of a cubic polynomial with complicated, yet constant, parameter values

Can anyone find conditions on the following parameters $\sigma_{\ell}$, $\mu_{\ell}$, $d_{\ell}$ and $\sigma_M$ such that the cubic: $$ (d_{\ell}-d_{\ell}\sigma_M)\ell^3 + (2d_{\ell}+\mu_{\ell}-\...
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 ...
15
votes
2answers
519 views

How can I get the solutions of $x^n-x-t=0$ in hypergeometric form?

$x^3-x-t=0$ has three roots that can be expressed in hypergeometric form, for example $$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} {...
3
votes
3answers
434 views

FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
0
votes
2answers
248 views

Don't understand results from solving easy polynomial equations

I am alarmed by the behavior of Mathematica (9.0) when given the following simple set of equations to solve: ...