What is the pattern in the following polynom: (how to generate them)
1: 12 n^2 + 12 n + 1
2: 300 n^3 + 450 n^2 + 160 n + 5
3: 840 n^4+1680 n^3+1030 n^2+190 n+3
4: 1260 n^5+3150 n^4+2730 n^3+945 n^2+107 n+1
5: 27720 n^6+83160 n^5+93030 n^4+47460 n^3+10689 n^2+819 n+5
1: 6n + 5
2: 150 n^2 + 200 n + 55
3: 420 n^33 + 770 n^2 + 410 n + 57
4: 630 n^4+1470 n^3+1155 n^2+343 n+29
5: 13860 n^5 + 39270 n^4 + 40740 n^3 + 18711 n^2 + 3591 n+205
In the Belgium lottery they pick 6 numbers out of 42 ( there can't be 2 equals numbers being picked out )
Now for my maple homework , i must do some exercices in maple
1 ) Simulate the lottery
2 ) If you partici
I would like to declare spin states; spin up (alpha) and spin down (beta)
such that they form an orthogonal basis not necessarily using Dirac Ket notaion. I am using the Physics package and Linear Algebra
When I try to use the Dirac Ket notation, I have noncommuting issues with the Cartesian basis
Cart := Vector[column](3, [Ket(X), Ket(Y), Ket(Z)]);
Spin := Vector[column](2, [Ket(alpha), Ket(beta)]);
<p>sys := [diff(v(s, n), n)+diff(u(s, n), s)+diff(xi(s, n), s)+A*n*(diff(c(s), s)) = 0, A1*(diff(xi(s, n), n))+diff(v(s, n), s)-c(s)+A2*v(s, n)+A3*c(s) = 0, diff(u(s, n), s)+2*A2*u(s, n) = A2*(xi(s, n)+A*n*c(s))-A1*(diff(xi(s, n), s))-A2*n*c(s)] The dependent variables are v,u and xi and the boundary conditions are: bc := {u(0, n) = 0, v(s, -1) = 0, v(s, 1)} other things: -1<=n<=1. I tried ans := pdsolve(sys, bc, xi(s, n), u(s, n), v(s, n)) i also tried ans := pdsolve(sys, bc) I keep getting error messages about the dependent variables.
