Re: Sign Declaration

*To*: mathgroup at smc.vnet.net*Subject*: [mg80105] Re: [mg80028] Sign Declaration*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 12 Aug 2007 07:26:23 -0400 (EDT)*References*: <200708110602.CAA02393@smc.vnet.net>

On 11 Aug 2007, at 08:02, Mr Ajit Sen wrote: > Dear MathGroup, > > Given the list A= {a,b,c,d,e,f,g,h}, I'd like to > tell > Mathematica (5.2) that a,b,...,e are +ve, and f,g,h are -ve. > > I'm using the following > > Table[Sign[A[[i]]]^=1,{i,5}]; > > Table[Sign[A[[i]]]^=-1,{i,6,8}]; > > > My queries are : > > 1. Is it possible to combine the above into 1 > Table[]? > For example: In[1]:= A = {a, b, c, d, e, f, g, h}; In[2]:= Do[Sign[A[[i]]] ^= Sign[5.5 - i], {i, 8}] In[3]:= Sign /@ A Out[3]= {1, 1, 1, 1, 1, -1, -1, -1} (you can use Table instead of Do if you prefer it). > 2. How do I achieve the same thing with the construct > > x/:Sign[x]=1 > in Table ? Why do you keep insisting on using Table? Here is one way using Function and Map: A = {a, b, c, d, e}; Block[{x}, x /: Sign[x] = 1; Function[v, UpValues[v] = UpValues[x] /. x -> v] /@ A;] Sign /@ A {1, 1, 1, 1, 1} I think I would just use > > 3. Any more efficient ways of doing those sign > declarations? > It depends on what sort of efficiency you are talking about. If you want o be able to easily add positive and negative symbols I would suggest a different approach. Use a heads, e.g. Pos and Neg to distinguish positive and negative symbols and define: Pos /: Sign[Pos[x_]] = 1; Neg /: Sign[Neg[x_]] = -1; Then Sign /@ Join[Pos /@ {a, b, c, d, e}, Neg /@ {f, g, h}] {1, 1, 1, 1, 1, -1, -1, -1} and you can easily creat as many positive or negative symbols as you like by simply mapping Pos or Neg on arbitrary lists. Andrzej Kozlowski

**References**:**Sign Declaration***From:*Mr Ajit Sen <senra99@yahoo.co.uk>