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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 ...
11
votes
3answers
7k views

First positive root

Simple question but problem with NSolve. I need help how to extract first positive root? For example: ...
11
votes
3answers
2k views

How can we plot the complex roots of an equation?

If we'd like to display the $n$ roots of a polynomial on the complex plane as points, how can we do this? For example, if we have the equation $x^3 + x^2 + x + 1$, how can we plot the 3 roots as ...
9
votes
3answers
2k views

Checking if the roots of a function are real

I'm trying to determine if the roots of a function are real. How would you do that? (In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
4
votes
3answers
893 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 \end{...
15
votes
5answers
3k views

How to get exact roots of this polynomial?

The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
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} {...
7
votes
1answer
2k views

How to substitute the following conditions into an expression?

I have an expression: $p=a\;b\; x + b^2\; y + a\;c\; z$. I want to substitute $a\;b=1$, $b^2 = 2$ and $a\;c = 4$ to obtain $p = x + 2y + 4z$. How can I tell Mathematica to do that? I dont know how to ...
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 ...
15
votes
3answers
666 views

What are Root objects with multiple polynomials?

In Mathematica 9 a new flavor of Root object with multiple polynomials was introduced. For example, ...
13
votes
1answer
435 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...
13
votes
1answer
406 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an explicit ...
9
votes
1answer
252 views

The third argument of the Root function

Consider the roots of an arbitrary indecomposable polynomial: sol = Solve[x^5 + 2 x + 1 == 0, x] The returned expression is ...
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 ...
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 ...
6
votes
2answers
505 views

Why doesn't Roots work on a certain quartic polynomial equation?

Bug introduced in 9.0 or earlier and fixed in 10.0 In everything that follows I am using Roots to get the solutions to the equations. I start off with this ...
1
vote
2answers
707 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
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 ...
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 ...
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
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 ...
3
votes
2answers
671 views

Tweaking Solve for systems of polynomial equations

I am trying to solve the following system of $6$ quadratic equations in $6$ variables: ...
9
votes
6answers
1k views

Can Mathematica tell me if a polynomial has all real roots?

I am trying on this polynomial, ...
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 ...
4
votes
2answers
644 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 <...
3
votes
1answer
217 views

Factorization of a fractional multivariate polynomial

Suppose I have given a fractional multivariate polynomial ...
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 ...
6
votes
2answers
692 views

NSolve missing solutions in Mathematica 10

Running Mathematica 8.0.4 and 10.0.0 on a Windows 8.1 machine. Processed the same code with both kernels: ...
4
votes
1answer
221 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 ...
4
votes
2answers
599 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
3
votes
1answer
472 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: ...
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
2answers
348 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 ...
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. ...
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
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)\...
0
votes
0answers
567 views

Finding closed-form Eigenvalues of a particular Matrix

MWE ...
0
votes
1answer
417 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 ...