Re: Re: Simplify with NestedLessLess?

• To: mathgroup at smc.vnet.net
• Subject: [mg106561] Re: [mg106531] Re: [mg106487] Simplify with NestedLessLess?
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sat, 16 Jan 2010 06:12:38 -0500 (EST)
• References: <201001141049.FAA19892@smc.vnet.net>

Series[-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), {C, 0,
5}] // Simplify

SeriesData[C, 0, {
Cf Rg^2 (12 Vd^2 - Cf L2^2 Vg^4), 6 Rg^2 Vd (2 Vd + Vg)}, 0, 6, 1]

Bobby

On Fri, 15 Jan 2010 02:21:09 -0600, Dave Bird <dbird at ieee.org> wrote:

> 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]]
>>>>>
>>>>> a+b
>>>>>
>>>>> b
>>>>>
>>>>> Thanks,
>>>>>
>>>>> Dave
>>>>
>>>> I fail to see why the result should be b.
>>>>
>>>> Daniel Lichtblau
>>>> Wolfram Research
>>>>
>>>>
>>
>>
>

--
DrMajorBob at yahoo.com

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