201 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 ...
64 views

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

When I request with Reduce, Mathematica returns: ...
43 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 ...
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 ...
2k 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 ...
882 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 ...
1k 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 ...
736 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: ...
256 views

### How do I solve 1 - (1 - (A x)^2)^(3/2) - B(1 - Cos[x]) == 0?

1 - (1 - (A x)^2)^(3/2) - B(1 - Cos[x]) == 0 A and B are constant. What is the analytic ...
214 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 ...
111 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: ...
196 views

### Why is EigenValues returning Root expressions?

This is the code I have: ...
218 views

### Count and plot the number of solutions in an interval

I have equations depending on one or more parameters and I want to find and plot regions in the parameter space in which there is a specific number of solutions. For definiteness let's consider a ...