Re: Constant function Integrate Assumption
- To: mathgroup at smc.vnet.net
- Subject: [mg47218] Re: Constant function Integrate Assumption
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Wed, 31 Mar 2004 02:57:42 -0500 (EST)
- References: <c4bdnf$6tr$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
dsr14 at Cornell.edu (Daryl Reece) wrote: > I am trying to use units within an Integration and would like > Mathematica to understand that the units (Month) are not a function of > the integration variable, but I have not had any luck with my > attempts. > > Specifically > > Integrate[UnitStep[t Months], t] > > should yield > > t UnitStep[t] Not exactly. I'll explain in a moment. > but I get the unevaluated form, because Mathematica does not know how to > assume that Month is not a function of t. Yes, you get an unevaluated form, but that's not due to Mathematica thinking that Month (or Months, whichever) might be a function of t. Consider, for example, In[1]:= Integrate[t Month, t] Out[1]= (Month t^2)/2 showing that Mathematica assumes, just as you wish, that Month is independent of t. > I've tried Assumptions, SetAttribute, Replace...to no avail. I've > also hunted extensively online (Wolfram, this group and MathGroup) > without any results, so any help would be greatly appreciated. The problem with something like Integrate[UnitStep[t Month], t] seems to be that we cannot convince Mathematica that Month is positive unless we actually specify a numerical value for it. Note first that In[2]:= Integrate[UnitStep[Pi t], t] Out[2]= t UnitStep[t] works as desired because Mathematica knows that Pi>0. We also see that In[3]:= a=-3; Integrate[UnitStep[a t], t] Out[3]= t-t UnitStep[t] is correct because Mathematica knows that a<0. Prior to your posting, I would have thought that the following would work: In[4]:= Clear[a]; Assuming[a>0,Integrate[UnitStep[a t], t]] Out[4]= Integrate[UnitStep[a t], t] but we see, alas, that it doesn't work. So can someone suggest a way to get Integrate[UnitStep[t Month], t] to evaluate to t UnitStep[t] without having to assign a specific positive value to Month? David Cantrell