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Re: Simplify with NestedLessLess?

• To: mathgroup at smc.vnet.net
• Subject: [mg106531] Re: [mg106487] Simplify with NestedLessLess?
• From: Dave Bird <dbird at ieee.org>
• Date: Fri, 15 Jan 2010 03:21:09 -0500 (EST)
• References: <201001141049.FAA19892@smc.vnet.net> <4B4F39E7.1070002@wolfram.com> <4B4FAC81.7000108@ieee.org> <4B4FB26F.7050702@wolfram.com>
• Reply-to: dbird at ieee.org

Not infinitesimals. I'm working in analog circuit design/analysis. I 
have a 3 pole symbolic circuit response (third order) which is not 
easily separable. I can use Mathematica to find the three roots of the 
response. But, the roots are, of course, very messy. I know that certain 
elements in the circuit are orders of magnitude larger than other like 
elements - capacitors in this case. For example, one small section of 
one root is

-Cf^2 L2^2 Rg^2 Vg^4+3 (4 C Rg^2 Vd^2+4 Cf Rg^2 Vd^2+2 C Rg^2 Vd Vg)

I know that C<<Cf. By careful inspection, I can see that the first term 
in the parens will drop out compared to the second term in the parens. I 
would like Mathematica to do this without my having to examine it so 
closely since there are many other like situations.

This kind of situation occurs in many other engineering situations.

Hope this helps clarify.

Thanks for the interest.

Dave




Daniel Lichtblau wrote:
> Dave Bird wrote:
>> Thanks Daniel for the observation. I forgot to add that both a, and b 
>> are real positive. That, of course would have to be added to the 
>> assumptions.
>>
>> Dave
>
> It's still not obvious what you are wanting to do. I have the idea you 
> are working in some sense with infinitesmals. If so, I doubt Simplify 
> would be the best tool for removing them; it really can only do that 
> if it is told, in some way, to replace them with zero. How might one 
> instruct Simplify to figure that out?
>
> Daniel
>
>
>> Daniel Lichtblau wrote:
>>> dbird wrote:
>>>> Please excuse if this has been answered before, but I can't find it.
>>>>
>>>> Is there some way to do a Simplify with assumptions using a 
>>>> NestedLessLess or something similar? For example:
>>>>
>>>> d=a+b
>>>> Simplify[d,NestedLessLess[a,b]]
>>>>
>>>> Answer is:
>>>> a+b
>>>>
>>>> Answer should be:
>>>> b
>>>>
>>>> Thanks,
>>>>
>>>> Dave
>>>
>>> I fail to see why the result should be b.
>>>
>>> Daniel Lichtblau
>>> Wolfram Research
>>>
>>>
>
>

• Follow-Ups:
  • Re: Re: Simplify with NestedLessLess?
    • From: Daniel Lichtblau <danl@wolfram.com>

• References:
  • Simplify with NestedLessLess?
    • From: dbird <dbird@ieee.org>