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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 $f(x)$ ...
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
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
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
3
votes
0answers
82 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
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 ...
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): ...
2
votes
1answer
85 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: ...
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 ...
-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
222 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
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: ...
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 ...
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 ...
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 ...
6
votes
1answer
240 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
308 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 ...
2
votes
3answers
159 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
31 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
234 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
146 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
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 ...
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 ...
1
vote
2answers
133 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
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. <...