Re: MatchQ

*To*: mathgroup at smc.vnet.net*Subject*: [mg8641] Re: [mg8542] MatchQ*From*: Raya Khanin <raya at mech.ed.ac.uk>*Date*: Fri, 12 Sep 1997 04:10:54 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I thought this conversation about MatchQ[] and Complex numbers might be interesting. Raya Khanin University of Edinburgh On Mon, 8 Sep 1997, David Withoff wrote: > Hello, > > > Thanks a lot for your explanation. > > I've indeed tried an example > > > > MatchQ[E^(2*I*b), E^(I*freq_)] > > > > which gave me False. > > > > Do not you agree that there is no principal > > difference between > > > > E^(2*I*b) and E^(a*I*b) and in both cases > > > > MatchQ[E^(2*I*b), E^(I*freq_)] and MatchQ[E^(a*I*b), E^(I*freq)] > > > > should give True? Certainly, we do not know anything about > > a in E^(a*I*b) (it can be Complex number), but we do not anything > > about b or freq_ in the pattern either. > > > > > The match fails because Complex[0, 2] doesn't match Complex[0, 1]. > > > > Should not it be included in the future versions of MatchQ > > that > > > > Complex[0, 2] does match Complex[0, 1]*2, > > or for any real c Complex[0, c] does match Complex[0,1]*c > > > > Thanks, > > Raya Khanin > > University of Edinburgh > > Here is a related example. > > In[2]:= MatchQ[2*3, 2*x_] > > Out[2]= False > > This match fails because 2*3 evaluates to 6, which does not match > the pattern, even though 6 could be factored into 2 times 3, which > would match: > > In[3]:= MatchQ[Hold[2*3], Hold[2*x_]] > > Out[3]= True > > The pattern matcher does not factor integers in an effort to find > a factoring that will match the pattern. > > The same principle applies to an integer that happens to be part > of a complex number. This match fails: > > In[4]:= MatchQ[Complex[0, 2], Complex[0, 1]*x_] > > Out[4]= False > > because the pattern matcher is not designed to factor Complex[0, 2] > into 2*Complex[0, 1]. > > There is a distinct conflict between the way that complex numbers are > seen in written mathematics, and the way that complex numbers are stored > in a computer. In written mathematics, complex numbers are usually > given as the sum of a real part and the product of an imaginary part > and some notation for the square root of minus one. Complex numbers > are almost never stored that way on a computer. In nearly all computer > programs, complex numbers are stored in a separate data structure > that does not involve sums or products. > > It has occasionally been suggested that complex numbers be handled > as a special case in the pattern matcher, to accommodate the way > that complex numbers are seen in written mathematics, and it is > possible that such a change will be made in some future version > of Mathematica. It is worth pointing out, however, that this > change is not easy to make, and furthermore that there are some > common examples that would break as a result of such a change. > > Dave Withoff > Wolfram Research >