288 views

### What do the hashtags represent in the result of Solve, and how should I use them? [duplicate]

There is a function that I'm trying to get the inverse of. My function is a simple polynomial: Tn[T_] := 4/9 T^3/Tc^2 + 5/9 T Now I tried to find ...
78 views

### Mathematica returns different results when requested by Reduce, Solve [duplicate]

When I request with Reduce, Mathematica returns: ...
44 views

### Eigenvalues of a matrix, rhombus/hash sign [duplicate]

I wanted calculate the eigenvalues of A = {{0, 1, 0, 0}, {a, b, c, 0}, {0, 0, 0, 1}, {d, 0, e, f}} Then assigned the parameters a value ...
39 views

### How do I interpret the Roots syntax when I am finding the eigenvalues of a matrix [duplicate]

Here is an example of my problem: I am somewhat confused by the syntax of this. I am guessing that the #1 is specifying the start of another root? Why then does one of the roots = u + with nothing ...
19 views

### How can I obtain absolute result for Root[ # ] symbol [duplicate]

I'm using mathematica 8.0. When I calculate NDSolve`ImplicitRungeKuttaGaussCoefficients[10, Infinity] function, it gives me some symbolic results. I trided //N and //FuıllSimplify operation as in How ...
2k views

### What is the difference between Reduce and Solve?

Solve and Reduce both can be used for solving equations. Just by working with them, I know there are some differences between ...
3k views

### Can Reduce *really* not solve for x here?

Sometimes I get the feeling I'm just flailing blindly with Mathematica. Is solving for $x$ in the equation $$\frac{\cosh (x/2)}{x} = \sqrt{2}$$ really beyond the scope of Mathematica? I try to ...
1k views

### How to find the sum all even numbers of this sequence?

I have a sequence $(u_{n})$ $$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$ I want to list the first $20$ terms of this sequence ...
2k views

### What does # mean in Mathematica?

I asked Mathematica to compute the following Solve[c (1-x)^2-x^(1/4) == 0, x] and it returned this: x = Root[#1^8 c^4 - 8 #1^7 c^4 + 28 #1^6 c^4 - 56 #1^5 ...
875 views

### Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong?

If I ask Mathematica to find the eigenvectors and eigenvalues of the matrix: ...
374 views

### How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0$$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
241 views

### integral, explicit form

I want to estimate the ratio of integrals:  \frac{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_1 \left(\frac{4}{T^3}+1\right)}}{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_0 ...
125 views

### Unexpected complex roots from solving a cubic

I am new to Mathematica and there is a behavior that I don't understand. When I insert the code: Solve[-(x - 2)^3 + 10 x - 10 == 0, x] I obtain: ...