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MathGroup Archive 2006

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Re: Unevaluated values of a[[i]]+b[[j]]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65234] Re: Unevaluated values of a[[i]]+b[[j]]
  • From: albert <awnl at arcor.de>
  • Date: Sun, 19 Mar 2006 03:19:10 -0500 (EST)
  • References: <dvgs5h$9oc$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Alexandre Costa wrote:

> Dear group,
> Suppose a have a = {3,4,4} and b = {4,3,8}.
> I want to see the Unevaluated numerics values of  a[[i]]*b[[j]],
> a[[i]]+b[[j]], a[[i]]/b[[j]], a[[i]] - b[[j]].
> 
> The NonCommutativeMultiply operator (**)  solves the case of 
> a[[i]]*b[[j]]. But suppose I want to extend that NonCommutativeMultiply
> operator (**) to others operations: +, -, / , i.e., see the Unevaluated
> numeric values of a[[i]]+b[[j]], a[[i]]/b[[j]], a[[i]] - b[[j]]. Does
> anybody have a clue how to do this ?
> 
> Suppose I have the expression for the roots of the quadratic equation: -
> b[[index]]^2 + Sqrt[delta]/2*a[[index]]
> How can I see at once all the numeric values unevaluated on that
> expression.
> 
> In short words, I have lenghtly expressions(with
> sums,subtraction,divisions and multiplications and powers) and I want to
> check each numeric value of each term in the original unevaluated formula
> containing elements such as a[[index]] . I was thinking in a operator or
> function to solve all this issue. Any help is very welcome,
> Thanks,
> Alex

Here is what I can offer, it's neither optimized for speed nor elegance, but
it does what I think you want in a rather straightforward way by replacing
the parts you want to see evaluated. You might want to improve on this:

SetAttributes[ShowNumericSymbolsEvaluated, HoldFirst]

ShowNumericSymbolsEvaluated[expr_] := Module[{eee, numbers}, 
   eee = HoldForm[expr]; 
   positions = Position[eee,x_Symbol /; NumericQ[x]];
   Scan[
     (eee = ReplacePart[eee, eee[[Sequence @@ #1]], #1]) & , 
     positions
   ]; 
   eee
];

Now:

In[22]:= ShowNumericSymbolsEvaluated[
           b[[index]]^2 +(Sqrt[delta]/2)*a[[index]]
         ]

Out[22]= HoldForm[b[[3]]^2 + (1/2)*Sqrt[0.2]*a[[3]]]

(the HoldForm is not shown when working in the FrontEnd)


If you want to also see the list-entries evaluated use this:

SetAttributes[ShowNumericSymbolsEvaluatedEvenMore, HoldFirst]

ShowNumericSymbolsEvaluatedEvenMore[expr_] := Module[{eee, numbers},
   eee = ShowNumericSymbolsEvaluated[expr]; 
   positions = Position[eee, HoldPattern[
       (x_Symbol)[[i___Integer]] /; NumericQ[x[[i]]]]
   ];
   Scan[
     (eee = ReplacePart[eee, eee[[Sequence @@ #1]], #1]) & , 
     positions
   ]; 
   eee
]

In[23]:= ShowNumericSymbolsEvaluatedEvenMore[
           b[[index]]^2 +(Sqrt[delta]/2)*a[[index]]
         ]

Out[23] = HoldForm[0.3^2 + (Sqrt[0.2]*0.3)/2]

hth,

albert


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