Get all parameters

Questions
, ,
1 
(* Capture Recapture History *)

myCHcc[K_] := Table[IntegerDigits[n, 2, K], {n, 1, 2^K - 1}]

(* Capture Recapture Probability *)

myindprobCC[CH_]:=Module[{K,ind,fi,li,d,ans},


	(* Get $K$ *)
	K = Length[ CH ];
	
	(* None Zero Positions *)
	ind = Position[ CH, _?(# != 0 &) ];
	fi = ind[[1]][[1]];
	li = ind[[-1]][[1]];
	
	(* Get probabilities *)
	
	ans =
  Sum[
   Product[ Subscript[\[Phi], j], {j, fi, d - 1}]
   *
   (1 - Subscript[\[Phi], d])
   *
   Product[
    Subscript[p,j]^CH[[j]]
    *
    (1-Subscript[p,j])^(1 - CH[[j]]),
    {j, fi + 1, d}
   ],
   {d, li, K}
  ]
]


xij = myCHcc[3]
ans = Map[myindprobCC, xij]

I have been a long time Maple user, so sorry if the questions are a bit basic.

Now,how I do get all the parameters in “ans”?
What I hope to have is a derivative matrix (Jacobian) from the vector “ans”.

In Maple, there is a function called “indets”

http://www.maplesoft.com/support/help/Maple/view.aspx?path=indets

So, quickly, I can apply the “D” fucntion to the “ans” with respect to the “parameters”.
Is there a similar function in Mathematica?

This is just a simple “ans” that I am testing, so the solution from an earlier post for me

https://wolfram.discourse.group/t/1791/1

does not work in this case.

Also, just a side to this piece of code,
is there a “proper” way to get the integer from the line

fi = ind[[1]][[1]];

the [[1]][[1]] seems “unnecessary” to me. So I wonder is this the correct way to do it.

Thanks,

2

Seems like Variables is suitable for this.

Variables[ans]

(* Out[67]= {Subscript[p, 2], Subscript[p, 3], Subscript[\[Phi], 1], \
Subscript[\[Phi], 2], Subscript[\[Phi], 3]} *)

In[70]:= jac = Outer[D, ans, Variables[ans]]

(* {{0, 0, 0,
  0, -1}, {0, -Subscript[\[Phi], 2] (1 - Subscript[\[Phi], 3]),
  0, -1 + (1 - Subscript[p, 3]) (1 - Subscript[\[Phi], 3]), -(1 -
      Subscript[p, 3]) Subscript[\[Phi], 2]}, {0,
  Subscript[\[Phi], 2] (1 - Subscript[\[Phi], 3]), 0,
  Subscript[p,
   3] (1 - Subscript[\[Phi], 3]), -Subscript[p, 3] Subscript[\[Phi],
   2]}, {-Subscript[\[Phi],
     1] (1 - Subscript[\[Phi], 2]) - (1 - Subscript[p,
      3]) Subscript[\[Phi], 1] Subscript[\[Phi],
    2] (1 - Subscript[\[Phi], 3]), -(1 - Subscript[p,
      2]) Subscript[\[Phi], 1] Subscript[\[Phi],
   2] (1 - Subscript[\[Phi],
     3]), -1 + (1 - Subscript[p, 2]) (1 - Subscript[\[Phi], 2]) + (1 -
       Subscript[p, 2]) (1 - Subscript[p, 3]) Subscript[\[Phi],
    2] (1 - Subscript[\[Phi],
      3]), -(1 - Subscript[p, 2]) Subscript[\[Phi],
    1] + (1 - Subscript[p, 2]) (1 - Subscript[p, 3]) Subscript[\[Phi],
     1] (1 - Subscript[\[Phi], 3]), -(1 - Subscript[p, 2]) (1 -
     Subscript[p, 3]) Subscript[\[Phi], 1] Subscript[\[Phi],
   2]}, {-Subscript[p, 3] Subscript[\[Phi], 1] Subscript[\[Phi],
   2] (1 - Subscript[\[Phi], 3]), (1 - Subscript[p,
     2]) Subscript[\[Phi], 1] Subscript[\[Phi],
   2] (1 - Subscript[\[Phi], 3]), (1 - Subscript[p, 2]) Subscript[p,
   3] Subscript[\[Phi],
   2] (1 - Subscript[\[Phi], 3]), (1 - Subscript[p, 2]) Subscript[p,
   3] Subscript[\[Phi],
   1] (1 - Subscript[\[Phi], 3]), -(1 - Subscript[p, 2]) Subscript[p,
   3] Subscript[\[Phi], 1] Subscript[\[Phi],
   2]}, {Subscript[\[Phi],
    1] (1 - Subscript[\[Phi], 2]) + (1 - Subscript[p,
      3]) Subscript[\[Phi], 1] Subscript[\[Phi],
    2] (1 - Subscript[\[Phi], 3]), -Subscript[p, 2] Subscript[\[Phi],
   1] Subscript[\[Phi], 2] (1 - Subscript[\[Phi], 3]),
  Subscript[p, 2] (1 - Subscript[\[Phi], 2]) +
   Subscript[p, 2] (1 - Subscript[p, 3]) Subscript[\[Phi],
    2] (1 - Subscript[\[Phi], 3]), -Subscript[p, 2] Subscript[\[Phi],
    1] + Subscript[p, 2] (1 - Subscript[p, 3]) Subscript[\[Phi],
    1] (1 - Subscript[\[Phi], 3]), -Subscript[p,
    2] (1 - Subscript[p, 3]) Subscript[\[Phi], 1] Subscript[\[Phi],
   2]}, {Subscript[p, 3] Subscript[\[Phi], 1] Subscript[\[Phi],
   2] (1 - Subscript[\[Phi], 3]),
  Subscript[p, 2] Subscript[\[Phi], 1] Subscript[\[Phi],
   2] (1 - Subscript[\[Phi], 3]),
  Subscript[p, 2] Subscript[p, 3] Subscript[\[Phi],
   2] (1 - Subscript[\[Phi], 3]),
  Subscript[p, 2] Subscript[p, 3] Subscript[\[Phi],
   1] (1 - Subscript[\[Phi], 3]), -Subscript[p, 2] Subscript[p, 3]
    Subscript[\[Phi], 1] Subscript[\[Phi], 2]}} *)
3

That’s perfect! Thanks! I am one more step closer to getting everything from Maple to Mathematica.

Just to note,

D[ans, {Variables[ans]}]

is good enough for me, rather than using the Outer function

Outer[D, ans, Variables[ans]]