Re: Suggestions for more compact code

*To*: mathgroup at smc.vnet.net*Subject*: [mg48998] Re: Suggestions for more compact code*From*: mathma18 at hotmail.com (Narasimham G.L.)*Date*: Mon, 28 Jun 2004 04:13:41 -0400 (EDT)*References*: <cap3tt$cbm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

A single independent variable for functions is often useful. A notation where paranthesis [t] or [t_] is omitted (as understood) is helpful, especially in Simulation. An example using Advanced Continuous Simulation Language (ACSL of MGA software, excellent for non-linear differential equations,transfer functions, automatic statement sorting etc. among others) is compared here with Mathematica in four corrosponding code lines: -- yi=2 ; equn = 0 == y'[t] - t / y[t] +Sin[t]; NDSolve[{equn,y[0] == yi},y,{t,-5,5}]; y2[u_]=y[u]/.First[%]; Plot[y2[t],{t,0,5}]; -- constant yi=2. yd=t/y - sin(t) y=integ(yd,yi) $ termt(t.ge.5) $ end prepar t , y $ plot y -- One can see how "lean" the latter is when adopting a single time independent variable.Or is there an artifice/statement available already, without having to repeat [t]? mathma18 at hotmail.com (Narasimham G.L.) wrote in message news:<cap3tt$cbm$1 at smc.vnet.net>... > 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.