Re: Piecewise vs. /; ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg103915] Re: Piecewise vs. /; ?*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Mon, 12 Oct 2009 06:38:15 -0400 (EDT)*References*: <hashpc$qu8$1@smc.vnet.net>

Erik Max Francis wrote: > I'm defining a piecewise function: > > mmin = 0.08; > mmax = 100; > > \[Xi][m_] := Piecewise[ > {{0.035 m^-1.3, 0.08 <= m <= 0.50}, > {0.019 m^-2.2, 0.50 < m <= 1.00}, > {0.019 m^-2.7, 1.00 < m <= 100}}]; (* stars per pc^3 *) > > This works fine for plotting (which I won't show) and integrating: > > In[5]:= Integrate[\[Xi][m], {m, mmin, mmax}] > > Out[5]= 0.136978 > > If I try to define \[Xi][m] with /;, it doesn't work. This version: > > \[Xi][m_ /; 0.08 <= m <= 0.50] = 0.035 m^-1.3 ; > \[Xi][m_ /; 0.50 < m <= 1.00] = 0.019 m^-2.2; > \[Xi][m_ /; 1.00 < m <= 100] = 0.019 m^-2.7; > (* stars per pc^3 *) > > plots correctly but integrate refuses to do anything: > > In[26]:= Integrate[\[Xi]2[m], {m, mmin, mmax}] > > Out[26]= \!\( > \*SubsuperscriptBox[\(\[Integral]\), \(0.08`\), \(100\)]\(\[Xi]2[ > m] \[DifferentialD]m\)\) > > This version (putting the /; in a different place): > > \[Xi]3[m_] = 0.035 m^-1.3 /; 0.08 <= m <= 0.50; > \[Xi]3[m_] = 0.019 m^-2.2 /; 0.50 < m <= 1.00; > \[Xi]3[m_] = 0.019 m^-2.7 /; 1.00 < m <= 100; > (* stars per pc^3 *) > > neither plots properly (the plot is blank) nor integrates properly: > > In[27]:= Integrate[\[Xi]3[m], {m, mmin, mmax}] > > Out[27]= \!\( > \*SubsuperscriptBox[\(\[Integral]\), \(0.08`\), \(100\)]\(\(( > \*FractionBox[\(0.035`\), > SuperscriptBox[\(m\), \(1.3`\)]] /; > 0.08` <= m <= 0.5`)\) \[DifferentialD]m\)\) > > I was under the impression that these were equivalent; what am I missing? > Integrate operates on Mathematical expressions - which Piecewise is considered to be - not on arbitrary pieces of code, which would be an impossibly demanding and somewhat ill-defined task. David Bailey http://www.dbaileyconsultancy.co.uk