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Wolfram Language

Back reference of variable in Module?

Hongyi Zhao

Posted 1 year ago

See the following example: In[904]:= (* The Abelian group of order 3 has these elements: *) A3={IdentityMatrix[2],RotationMatrix[2 \[Pi]/3],RotationMatrix[4 \[Pi]/3]}; f1//ClearAll; f1[m_?MatrixQ]:=Module[{n=1,e=IdentityMatrix[Length[m]]}, NestWhile[(n++;Dot[#,m])&,m,#!=e&];n] f2//ClearAll; f2[m_?MatrixQ]:=Module[{ d=Length[m], n=1, e=IdentityMatrix[d] }, NestWhile[(n++;Dot[#,m])&,m,#!=e&];n] f1/@A3 f2/@A3 Out[909]= {1, 3, 3} Out[910]= {1, 1, 1} So, how to do the back reference of variable in Module? Regards, Zhao

See the following example:

In[904]:= (*
The Abelian group of order 3 has these elements:
*)
A3={IdentityMatrix[2],RotationMatrix[2 \[Pi]/3],RotationMatrix[4 \[Pi]/3]};

f1//ClearAll;
f1[m_?MatrixQ]:=Module[{n=1,e=IdentityMatrix[Length[m]]},
NestWhile[(n++;Dot[#,m])&,m,#!=e&];n]

f2//ClearAll;
f2[m_?MatrixQ]:=Module[{
d=Length[m],
n=1,
e=IdentityMatrix[d]
},
NestWhile[(n++;Dot[#,m])&,m,#!=e&];n]

f1/@A3
f2/@A3

Out[909]= {1, 3, 3}

Out[910]= {1, 1, 1}

So, how to do the back reference of variable in Module?

Regards, Zhao

POSTED BY: Hongyi Zhao

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Hongyi Zhao

Posted 1 year ago

Your last method should be changed into the following for using with the example I posted here: In[27]:= (Block permits references to earlier scoped symbols. If a symbol is never reassigned a value then a combination of With and Module can be used e.g. ) f3//ClearAll; f3[m_?MatrixQ] := With[{d = Length[m]}, Module[{n=1,e = IdentityMatrix[d]}, NestWhile[(n++;Dot[#,m])&,m,#!=e&];n ]] f3/@A3 Out[29]= {1, 3, 3}

Your last method should be changed into the following for using with the example I posted here:

In[27]:= (*Block permits references to earlier scoped symbols. If a symbol is never reassigned a value then a combination of With and Module can be used e.g.
*)
f3//ClearAll;
f3[m_?MatrixQ] := 
 With[{d = Length[m]}, 
  Module[{n=1,e = IdentityMatrix[d]}, 
  NestWhile[(n++;Dot[#,m])&,m,#!=e&];n
  ]]

f3/@A3 

Out[29]= {1, 3, 3}

POSTED BY: Hongyi Zhao

Rohit Namjoshi

Posted 1 year ago

Because of the way `Module` evaluates the list of symbols it is not possible to refer to earlier scoped symbols. I usually specify what names should be lexically scoped and set them in the body e.g. f2[m_?MatrixQ]:=Module[{d, n, e}, d = Length[m]; n = 1; e = IdentityMatrix[d]; ... ] `Block` permits references to earlier scoped symbols. If a symbol is never reassigned a value then a combination of `With` and `Module` can be used e.g. f2[m_?MatrixQ] := With[{d = Length[m], n = 1}, Module[{e = IdentityMatrix[d]}, ...]]

POSTED BY: Rohit Namjoshi

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