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1
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0answers
56 views

Solutions given by WolframAlpha [closed]

When I try to solve, the following equation over the integers using WolframAlpha: $$x^2(1+x)=y(3y-1)\tag1$$ WolframAlpha gives me the following solutions $(x,y)$: $$(-1,0),(0,0),(1,1),(4,-5),(6,-9)\...
3
votes
2answers
118 views

Using the solve function for big numbers, getting a failure now

When I try to solve: Solve[y^2==441+48*x*(1+x)(-13+16*x)&&1100*10^9<=y<=1200*10^9&&x>=2,{y,x},Integers] My code runs for 169 seconds and ...
0
votes
1answer
36 views

Solving a fifth order polynomial with changing values of coefficients [closed]

I have a fifth order polynomial in x whose coefficients depend on a certain variable k. Now, I want to find the real roots of that polynomial for each value of k, say from 0.1 to 2 in steps of 0.05 ...
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)...
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 $f(x)$ ...
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 ...
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...
3
votes
3answers
125 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 ...
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
3answers
81 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 ...
0
votes
4answers
78 views

Solve for coefficients to express polynomial in terms of another polynomial

If I have a polynomial, say $p(x) = 6x^3 - x^2 + x$, and I want to express that in terms of a sum of other polynomials, how may I do that in Mathematica? Specifically I would like to say that $$p(x) = ...
1
vote
2answers
94 views

Finding roots of equation in table form

I would like to find roots of legendre polynomial NRoots[LegendreP[4, x]== 0, x] , I'm getting ...
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
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 ...
1
vote
1answer
38 views

How to check if 0 polynomial lies in span of some polynomials?

I have lot of polynomials like this ...
0
votes
1answer
32 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 ...
2
votes
2answers
185 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 ...
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
81 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 ...
5
votes
2answers
924 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 ...
9
votes
2answers
315 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: ...
3
votes
0answers
82 views
3
votes
1answer
217 views

Factorization of a fractional multivariate polynomial

Suppose I have given a fractional multivariate polynomial ...
1
vote
2answers
45 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
106 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): ...
0
votes
2answers
134 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 ...
0
votes
1answer
69 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 ...
2
votes
1answer
86 views

Range of contour plot for polynomial

...
0
votes
1answer
53 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
56 views

Solve polynomial system

I am trying to solve ...
0
votes
0answers
267 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
251 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: ...
-1
votes
1answer
71 views
1
vote
2answers
133 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
223 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 ...
6
votes
1answer
241 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 ...
41
votes
3answers
12k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
1
vote
1answer
111 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 ...
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 ...
1
vote
1answer
176 views

Solving and plotting a non-linear and polynomial equations of degree 3 and higher

I'm doing the following and cannot plot the function, could anyone spot a problem please ...
1
vote
2answers
215 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 ...
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),...
2
votes
1answer
86 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
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 ...
7
votes
1answer
310 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
163 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 ...
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 ...