Suggestions for more compact code

*To*: mathgroup at smc.vnet.net*Subject*: [mg48783] Suggestions for more compact code*From*: mathma18 at hotmail.com (Narasimham G.L.)*Date*: Wed, 16 Jun 2004 04:54:55 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I wish to avoid writing independent variable repetitively, reducing the bulk and appearance of written programs in Mathematica; :).. May I avail the liberty,even with my relatively new acquaintance to Mathematica, to make a small suggestion for the code? Of course, I do understand the code is written keeping generalities/versatality in mind, but as is well known in NDSolve and other so many Function usages that Mathematica is so well known for, a single independent variable like x or time t is most often used. For plotting Cornu's Spiral from its differential equation, one writes in the normal way: --- NDSolve[{ph'[s] == s,ph[0] == 0}, ph,{s,-8,8}]; ph2[u_]=ph[u]/.First[%]; Plot[ph2[s],{s, -8,8}] ; NDSolve[{x'[s] == Simplify[Cos[ph2[s]]],x[0] == 0}, x,{s, -8,8}]; x2[v_]=x[v]/.First[%]; Plot[x2[s],{s,-8,8}]; NDSolve[{y'[s] == Simplify[Sin[ph2[s]]],y[0] == 0}, y,{s, -8,8}]; y2[w_]=y[w]/.First[%]; Plot[y2[s],{s,-8,8}]; ParametricPlot[{x2[s],y2[s]},{s,-8,8}]; ---- " Suggested declaration for Functions of single argument: Variables[{ph,ph2,x,x2,y,y2},[s]] " " Suggested command for single Dummy independent variable/argument: x2[]=x[]/.First[%]" ---- By above shorter notation, it might be possible to write: NDSolve[{ph' == s,ph[0] == 0},ph,{s,-8,8}]; ph2[]=ph[]/.First[%]; Plot[ph2,{s, -8,8}] ; NDSolve[{x' == Simplify[Cos[ph2]],x[0] == 0},x,{s, -8,8}]; x2[]=x[]/.First[%]; Plot[x2,{s,-8,8}]; NDSolve[{y' == Simplify[Sin[ph2]],y[0] == 0},y,{s, -8,8}]; y2[]=y[]/.First[%]; Plot[y2,{s,-8,8}]; ParametricPlot[{x2,y2},{s,-8,8}]; -------- Best Regards, Narasimham.