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Re: Mantaining the same form

• To: mathgroup at smc.vnet.net
• Subject: [mg124148] Re: Mantaining the same form
• From: Christopher Young <cy56 at comcast.net>
• Date: Wed, 11 Jan 2012 04:21:10 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <je9624$iqs$1@smc.vnet.net> <201201090817.DAA12948@smc.vnet.net> <CAEtRDSf32tqmVNXnAL8urpzv_na5H8YRSHou9HkN3S5zaBckJA@mail.gmail.com>

Thanks a lot, this is a big help. It's going to take me a while to 
understand why the Hold functions don't actually do anything, or give 
any warning, if the attributes don't include a Hold.


On Jan 9, 2012, at 8:57 AM, Bob Hanlon wrote:

> Include in attributes of functions either HoldAll or HoldFirst or
> HoldRest as appropriate
>
> SetAttributes[{exprHeld, exprForm}, HoldAll];
>
> exprHeld[e_]:=Hold[e]
>
> exprForm[e_]:=HoldForm[e]
>
>
> exprHeld[(Sin[2 x]*Tan[y])/(x*Sec[y]^2)]
>
> Hold[(Sin[2 x] Tan[y])/(x Sec[y]^2)]
>
>
> exprForm[(Sin[2 x]*Tan[y])/(x*Sec[y]^2)]
>
> (Sin[2 x] Tan[y])/(x Sec[y]^2)
>
>
> {%,%%}//ReleaseHold
>
> {(Cos[y] Sin[2 x] Sin[y])/x,(Cos[y] Sin[2 x] Sin[y])/x}
>
>
> Bob Hanlon
>
> On Mon, Jan 9, 2012 at 3:17 AM, Chris Young <cy56 at comcast.net> wrote:
>> On 2012-01-07 10:16:36 +0000, Miguel Gil said:
>>
>>> At a function in which one parameter is an expression "expr",
>>> Mathematica 8.0 evaluates or simplifies the value of "expr" when it is
>>> introduced.
>>> How is that Mathematica keep the same form of the "expr" introduced?.
>>>
>>> Example:
>>>
>>> In []: MyFunction [expr_]: = expr;
>>> MyFunction [(Sin [2x], Tan [y]) / (x * Sec [y]^2)]
>>>
>>> Out []: (Cos [y]^2 (Sin [2x], Tan [y]) / x
>>>
>>> I want to get the same expression (Sin [2x], Tan [y]) / (x * Sec [y]^2)
>>>
>>> Clearly, the input expression and modified expression are equivalent,
>>> but are not equal.
>>> For example, if we were to apply the rule of L'Hopital or the theorem
>>> Schwarz  the results would be erroneous.
>>
>> I tried everything I could think of, but couldn't write any function
>> that would just pass on the expression unchanged:
>>
>> In[264]:= exprHeld[e_] := Hold[e]
>>
>> In[265]:= exprHeld[(Sin[2 x] * Tan[y])/(x * Sec[y]^2)]
>> Out[265]= Hold[(Cos[y] Sin[2 x] Sin[y])/x]
>>
>> In[266]:= holdAll[e_] := HoldAll[e]
>>
>> holdAll[(Sin[2 x] * Tan[y])/(x * Sec[y]^2)]
>> Out[267]= HoldAll[(Cos[y] Sin[2 x] Sin[y])/x]
>>
>> In[268]:= holdComplete[e_] := HoldComplete[e]
>>
>> In[269]:= holdComplete[(Sin[2 x] * Tan[y])/(x * Sec[y]^2)]
>> Out[269]= HoldComplete[(Cos[y] Sin[2 x] Sin[y])/x]
>>
>>
>> In[270]:= uneval[e_] := Unevaluated[e];
>>
>> In[271]:= uneval[(Sin[2 x] * Tan[y])/(x * Sec[y]^2)]
>> Out[271]= (Cos[y] Sin[2 x] Sin[y])/x
>>
>> In[272]:= Hold[Unevaluated[(Sin[2 x] * Tan[y])/(x * Sec[y]^2)]]
>> Out[272]= Hold[Unevaluated[(Sin[2 x] Tan[y])/(x Sec[y]^2)]]
>>
>> In[273]:= holdUneval[e_] := Hold[Unevaluated[e]]
>>
>> In[274]:= holdUneval[(Sin[2 x] * Tan[y])/(x * Sec[y]^2)]
>>
>> Out[274]= Hold[Unevaluated[(Cos[y] Sin[2 x] Sin[y])/x]]
>>
>> In[278]:= ToString[HoldComplete @ ((Sin[2 x] * Tan[y])/(x * Sec[y]^2)),
>> InputForm]
>> Out[278]= "HoldComplete[(Sin[2*x]*Tan[y])/(x*Sec[y]^2)]"
>>
>> In[279]:= heldString[e_] := ToExpression[
>>   ToString[HoldComplete @ e, InputForm],
>>   InputForm];
>>
>> In[280]:= heldString[(Sin[2 x] * Tan[y])/(x * Sec[y]^2)]
>>
>> Out[280]= HoldComplete[(Cos[y] Sin[2 x] Sin[y])/x]
>>

Chris Young
cy56 at comcast.net

• References:
  • Re: Mantaining the same form
    • From: Chris Young <cy56@comcast.net>