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Re: Re: Simplify with NestedLessLess?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106557] Re: [mg106531] Re: [mg106487] Simplify with NestedLessLess?
*From*: Daniel Lichtblau <danl at wolfram.com>
*Date*: Sat, 16 Jan 2010 06:11:51 -0500 (EST)
*References*: <201001141049.FAA19892@smc.vnet.net> <4B4F39E7.1070002@wolfram.com> <4B4FAC81.7000108@ieee.org> <4B4FB26F.7050702@wolfram.com> <201001150821.DAA29881@smc.vnet.net>
Dave Bird 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
> [...]
Yes, that clarifies. This is along the lines of what I had meant by
infinitesmals; you want to drop terms of certain order in certain
settings. One respondant suggested using Series and then Normal to
remove terms in that way. I think that is probably a good way to go
about it, and I have seen that approach in the past.
In the setting of your example above, what you might do is replace each
small variable such as C by C*t (and if, say, L2 was much smaller than
C, maybe use L2*t^2). For a series expansion in powers of t, dropping
all terms beyond a certain point. If the "large" terms have varying
orders of magnitude, that could be emulated by multiplying them by
powers of 1/t.
Another approach would use polynomial reduction. Short examples of each
method can be found at the location below.
http://forums.wolfram.com/mathgroup/archive/2007/Dec/msg00476.html
Daniel Lichtblau
Wolfram Research
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