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FindRoot not recognising replaced symbol in nested function

Archie Watts-Farmer, Carnot Ltd
Posted 5 years ago

Hi All,

I have the following example FindRoot function as part of a Nest function.

Clear[del]
del[x_] := Module[{y, dP, res, OP},
  res := {y} /. FindRoot[y^2 + 2 y - x, {y, 0}];
  OP := res[[1]];
  dP := OP + 1;
  Nest[(# + dP/#)/2 &, 1.5, 2]
  ]
del[name] /. name -> 3

Mathematica doesn't recognise the "name" symbol and returns the following error:

"FindRoot::nlnum: The function value {0. -1. name} is not a list of numbers with dimensions {1} at {y$21486} = {0.}.

ReplaceAll::reps: {FindRoot[y$21486^2+2 y$21486-name,{y$21486,0}]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing."

If you set Nest to apply zero times or replace it with a function that doesn't repeat the code works fine. It also works if you replace FindRoot with a simple assignment for symbol "OP". However, it doesn't work if you use Solve instead of FindRoot. Can anyone shine any light on this?

Many thanks for any help.

Attachments:
Replace.nb
POSTED BY: Archie Watts-Farmer
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Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Crossposted here.
POSTED BY: Rohit Namjoshi

Hi,

there is a clue in the error message.

{FindRoot[y214862+2y21486-name,{y$21486,0}]}

FindRoot attempts to find a root numerically. As you see the error message says that it fails to do so, because there is the variable y (with the $21486, because of the localisation of Module), and the variable: name. That cannot work. Solve uses other methods and in particular symbolic solutions which makes it work in this case (it doesn't care that name is substituted later.

This is basically a combination of (i) when are the variables substituted by numbers and (ii) do you use symbolics or numerics, I would think.

Best wishes, Marco
POSTED BY: Marco Thiel

Many thanks for the comprehensive explanation Marco.
POSTED BY: Archie Watts-Farmer
POSTED BY: Archie Watts-Farmer

Hi,

this works:

Clear[del]
del[x_] := 
 Module[{y, dP, res, OP}, 
  res := {y} /. FindRoot[y^2 + 2 y - x, {y, 0}];
  OP := res[[1]];
  dP := OP + 1;
  Nest[(# + dP/#)/2 &, 1.5, 2]]
del[name /. name -> 3]

Of course,

del[3]

is more concise.

Cheers,

Marco
POSTED BY: Marco Thiel
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