Re: (Newbie question): New types of numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg66556] Re: [mg66545] (Newbie question): New types of numbers*From*: "Carl K. Woll" <carlw at wolfram.com>*Date*: Sat, 20 May 2006 04:46:51 -0400 (EDT)*References*: <200605190740.DAA12871@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

craigugoretz at gmail.com wrote: > Hello, > > I am new to Mathematica, but I have a potentially complex problem > to solve. My goal is get Mathematica to understand a new type of > number called a "neutrosophic number". Neutrosophic numbers have a > similar form to complex numbers, except that I^2 = I instead of I^2=-1. > Is it possible to add a new type for the neutrosophic numbers in > addition to the four types that Mathematica currently supports > (Integer, Real, Rational, Complex per Appendix A.1.5 in the help > browser for Mathematica 5.1)? If so, what bases would I need to cover > to make the implementation possible for user defined operators (to be > developed) and the system operators '+' and '*' (to begin with). If it > is not possible to create new types of numbers, is there a way to "fake > it"? One possible example may involve intercepting input from the main > evaluation loop and coercing it somehow. > > Sincerely, > Craig > Ugoretz One possibility is to create your own data structure and give rules for multiplication, addition and powers of the data structure: neuro /: neuro[a_, b_] neuro[c_, d_] := neuro[a c, a d + b c + b d] neuro /: neuro[a_, b_]^n_Integer := neuro[a^n, ((a + b))^n - a^n] neuro /: neuro[a_, b_] + neuro[c_, d_] := neuro[a + c, b + d] neuro /: x_ neuro[a_, b_] := neuro[a x, b x] neuro /: x_ + neuro[a_, b_] := neuro[a + x, b] For example: In[17]:= neuro[0, 1] neuro[0, 1] Out[17]= neuro(0, 1) In[18]:= a + b neuro[0, 1] Out[18]= neuro(a, b) In[19]:= neuro[a, b] neuro[c, d] Out[19]= neuro(a c, b c + a d + b d) In[20]:= neuro[a, b]^3 Out[20]= neuro(a^3, ((a + b))^3 - a^3) One can also create formatting rules so that neuro[a,b] displays as a+b *n* where *n* is your I element. Carl Woll Wolfram Research

**References**:**(Newbie question): New types of numbers***From:*"craigugoretz@gmail.com" <craigugoretz@gmail.com>