Re: Problems with easy simplifications

*To*: mathgroup at smc.vnet.net*Subject*: [mg54152] Re: Problems with easy simplifications*From*: Curt Fischer <tentrillion at gmail.NOSPAM.com>*Date*: Sat, 12 Feb 2005 01:57:00 -0500 (EST)*References*: <cuhsm1$9j1$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Antonio González wrote: > I have found some weird behaviors of Mathematica (5.0) related to the > simplifications of easy expressions. > > Take, for instance the function > > H[x_, a_, b_] = If[x < a, a + b, a - b] > > If I try now to evaluate > > H[x,0,0] > > the result > > If[x < 0, 0 + 0, 0 - 0] what result were you expecting? What is the bug? You have not supplied a value for x that Mathematica could use to test whether or not x<a or not. In[1]:= h[x_,a_,b_]=If[x<a,a+b,a-b] Out[1]= If[x<a,a+b,a-b] In[2]:= h[1,2,3] Out[2]= 5 In[3]:= h[3,1,2] Out[3]= -1 > > (the values of a and b are irrelevat, a similar result is obtained, for > instance, with a=1, b= 2, or any integer, real or complex values). I > cannot force (at least in a simple way) Mathematica to make the addition > or the substraction. The action of Simplify or FullSimplify leaves the > expression unchanged while a Map of Simplify > > MapAll[Simplify, H[x, 0, 0]] > > produces > > If[x < 0, > Simplify[Simplify[0] + Simplify[0]], Simplify[Simplify[ > 0] + Simplify[Simplify[-1] Simplify[0]]]] > > Something even worse happens if a use values already defined. For instance > > c = 0; d = 0; H[x_] = If[x < c, c + d, c - d] > > produces > > If[x < 0, c + d, c - d] > > In this case, the addition is not necessary. > > c = 0; d = 0; H[x_] = If[x < c, c, d] > > leads to > > If[x < 0, c, d] If you don't want your definition for H[x_] to be evaluated _right away_, before substituting the definitions for other variables, you should use the delayed assignment operator :=. In[3]:= c=0;d=0; In[4]:= g[x_]:=If[x<c,c+d,c-d] In[5]:= g[1] Out[5]= 0 > > Similar problems arise using the function Which. > > Any explanation or help with this malfunction would be welcome. Read the Help Browser. -- Curt Fischer