New answers tagged function-construction
1
Here's how I would write your example, in a way that "jibes" with Mathematica.
(* Define the functions in terms of parameters *)
fun1[a_, b_][c_][x_] := a + b x + c
fun2[a_, b_][c_][x_] := b + a x + c
fun3[a_, b_][c_][x_] := fun1[a, b][c][x] + fun2[a, b][c][x]
(* Specify the parameters' values *)
a = 1; b = 2; c = {1, 4, 10};
(* Rather than loop, ...
0
This can be performed using the Quantum Mathematica add-on
http://homepage.cem.itesm.mx/lgomez/quantum/
You can implement any commutator (or even anti-commutator) algebra of your choice. See here for an example with the algebra of Pauli matrices. It works flawlessly and I have used it quite extensively while working with algebras or super-algebras with ...
2
You can use Fold and switch i and v in your definition of h ...
h[v_, i_] := ...
Fold[h, v, Range[3]]
(* h[h[h[v, 1], 2], 3] *)
... or switch the order directly in Fold.
h[i_, v_] := ...
Fold[h[#2, #1] &, v, Range[3]]
(* h[3, h[2, h[1, v]]] *)
9
You can see why when you break it up. Since you use 1.1 then Mathematica evaluated it numerically.
Compare
v = 1 + I
a = Abs[v]
b = Exp[I Arg[v]]
a*b
With
v = 1.10 + I
a = Abs[v]
b = Exp[I Arg[v]]
a*b
You see that Exp[I Arg[v]] now is 0.73994 + 0.672673 I
To keep things nice, as your first example, use exact number
v = 11/10 + I
a = Abs[v]
b = Exp[I Arg[...
1
Maybe the following? I didn't understand all the extra variables, so I stripped down the code more. In a complicated case, you might need Dynamic@Refresh instead of just Dynamic; see What is the point of Refresh if Dynamic has an UpdateInterval option? and related Q&A on Refresh. You'd probably have to put the output in a docked cell, since the FE ...
2
A slight variation using the Fold function (benefitting from Bob Hanlon's answer):
lorentz[x_, x0_, linewidth_] := 1/Pi (1/2 linewidth)/((x - x0)^2 + (1/2 linewidth)^2) ;
mol[J_, dB_] := dB * J (J + 1);
linewidth = 0.1;
dB = 0.1;
fCombined[x_] =
Fold[#1 + lorentz[x, mol[#2, dB], linewidth] &, 0, Range[10]] //
Together // FullSimplify
The Fold ...
3
Blank ( _ ) is only used as a pattern object; it cannot be used in a variable name
Clear["Global`*"]
lorentz[x_, x0_, linewidth_] :=
1/Pi (1/2 linewidth)/((x - x0)^2 + (1/2 linewidth)^2);
mol[J_, dB_] := dB*J (J + 1);
linewidth = 1/10;
dB = 1/10;
fCombined[x_] =
Sum[lorentz[x, mol[J, dB], linewidth], {J, 1, 10}] // Together //
...
Top 50 recent answers are included