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MathGroup Archive 1998

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Multiplying piecewise functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14547] Multiplying piecewise functions
  • From: sergio at scisun.sci.ccny.cuny.edu
  • Date: Thu, 29 Oct 1998 04:33:39 -0500
  • Organization: Deja News - The Leader in Internet Discussion
  • Sender: owner-wri-mathgroup at wolfram.com

(*
 Hello fellows:

 Using Mathematica of course, would it be possible
 to get, after multiplying two or more piecewise
 functions defined using Which, a single (one Which)
 expression which can be integrated later.? For instance,
 let's say one has:
*)
Clear[f]
f[x_] := Which[ -1 <= x < 5,
                            100*x^2 + 1,
                       5<=x,
                            x^3,
                       True,
                            10*x - 200 ]; Clear[g]
g[x_] := Which[ -10 <= x < 10,
                              x^4 + 100,
                      10 <= x,
                              x^3,
                         True,
                              -100*x ];
	(* The product of this functions is given by: *) Clear[FG];
FG[x_] := Evaluate[f[x]*g[x]] ;

	(* QUESTION: How can I instruct Mathematica to write
           it in something similar to: *) Clear[fg]
fg[x_] := Which[ x < -10,
                            (10*x - 200)*(-100*x),
             -10 <=  x < -1,
                            (10*x - 200)*(x^4 + 100),
                -1 <= x < 5,
                            (100*x^2 + 1)*(x^4 + 100),
                5 <= x < 10,
                            x^3*(x^4 + 100),
                   10 <= x ,
                            x^3*x^3 ];

	(* The equivalence of FG[x] and fg[x] can be
           asserted from: *)

Clear[p1,p2];
pFG = Plot[FG[x],{x,-20,20},PlotRange -> All,
                     Frame -> True,
                 PlotStyle -> {AbsoluteThickness[3],Hue[0.1]},
                 FrameLabel -> {"","","This is f[x]*g[x]",""}]

pfg = Plot[fg[x],{x,-20,20},PlotRange -> All,
                     Frame -> True,
                 PlotStyle -> {AbsoluteThickness[5],Hue[0.4]},
                 FrameLabel -> {"","","This is fg[x]",""}]

Show[pfg,pFG,Frame -> True,
               FrameLabel -> {"","","This is fg[x] and FG[x]",""}]

val = Table[Random[Real,{-100,100}],{30}]; Print["using x =
Random[Real,{-100,100}] -> fg[x]-FG[x]] = ",
                                         Map[fg,val]-Map[FG,val]] (*
Sergio
Email: sergio at scisun.sci.ccny.cuny.edu *)

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