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>*Reply-to*: drmajorbob at yahoo.com

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]] >>>>> >>>>> Answer is: >>>>> a+b >>>>> >>>>> Answer should be: >>>>> b >>>>> >>>>> Thanks, >>>>> >>>>> Dave >>>> >>>> I fail to see why the result should be b. >>>> >>>> Daniel Lichtblau >>>> Wolfram Research >>>> >>>> >> >> > -- DrMajorBob at yahoo.com

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