Re: Boolean 0/1 function -- Conditional definitions and Thread

*To*: mathgroup <mathgroup at yoda.physics.unc.edu>*Subject*: Re: Boolean 0/1 function -- Conditional definitions and Thread*From*: HAY at leicester.ac.uk*Date*: Thu, 5 NOV 92 15:38:27 GMT

Following up Robby Villegas's observation about using Thread here is a a little number featuring it. Many variations are possible. Let xlist = {a,b,c,d}; condns = Thread[LessEqual[Drop[xlist,-1], y, Drop[xlist,1]]] {a <= y <= b, b <= y <= c, c <= y <= d} fvalues = Thread[f[y,Drop[xlist,-1]]] {f[y, a], f[y, b], f[y, c]} Thread[If@@{condns, fvalues, 0}] {If[a <= y <= b, f[y, a], 0], If[b <= y <= c, f[y, b], 0], If[c <= y <= d, f[y, c], 0]} Plus@@% If[a <= y <= b, f[y, a], 0] + If[b <= y <= c, f[y, b], 0] + If[c <= y <= d, f[y, c], 0] The construction If@@{....} is needed since If has the attribute HoldAll; so we get Thread[If[condns, fvalues, 0]] If[condns, fvalues, 0] Re Robby's warning > fvalues = Thread[ f[y, xlist] ] > as long as 'y' isn't a list itself (if it's a number, say). We can get round this problem by using the extra slots in Thread Thread[ f[{1,4}, xlist], List, -1 ] {f[{1, 4}, a], f[{1, 4}, b], f[{1, 4}, c], f[{1, 4}, d]} Allan Hayes hay at leicester.ac.uk