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MathGroup Archive 2007

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Re: set versus set-delay

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75218] Re: set versus set-delay
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Sat, 21 Apr 2007 23:03:04 -0400 (EDT)
  • References: <f09h44$19r$1@smc.vnet.net>

You should also have added that there some cases that Set is
preferable.

For example compare the timings...

In[1]:=
g2[a_] := Integrate[(x^2 + 4*x + 6)^3/(x^2 + 2*x^2 + 6)^7, {x, 0, a}]

In[2]:=
Timing[Plot[g2[a], {a, 1, 10}]]
(*graphics to be displayed*)
Out[2]=
{6.766*Second, Graphics[]}

In[3]:=
g3[a_] = Integrate[(x^2 + 4*x + 6)^3/(x^2 + 2*x^2 + 6)^7, {x, 0, a}]

Out[3]=
(20800 + (-1331200 + 2291520*a - 675840*a^2 + 5202400*a^3 - 46080*a^4
+ 4115232*a^5 + 1693296*a^7 + 363460*a^9 + 32070*a^11 +
16035*Sqrt[2]*(2 + a^2)^6*ArcTan[a/Sqrt[2]])/(2 + a^2)^6)/67184640

In[4]:=
Timing[Plot[g3[a], {a, 1, 10}]]
(*graphics to be displayed*)
Out[4]=
{0.014999999999998792*Second, Graphics[]}

Dimitris

=CF/=C7 siewsk at bp.com =DD=E3=F1=E1=F8=E5:
> Informative Article
> ===================
>
> SET versus SETDELAY
>
>
> Newbie are always told to use SETDELAY instead of SET when they create
> a mathematica function.
>
> The objective of this article is to explain the differnce between SET
> and SETDELAY using ordinary language (what linguistics call vernacular
> language)
>
> The main differences between those two are:
>
> SET       means    CALCULATE FIRST THEN CHANGE
> SETDELAY  means    CHANGE FIRST THEN CALCULATE
>
>
> To explain, consider the following two functions f ang g
>
> f[x_] = Expand[(x+7)^2]           (* Using SET       *)
> g[x_]:= Expand[(x+7)^2]          (* Using SETDELAY  *)
>
> The two functions are identical except f uses SET while g uses
> SETDELAY. In normal usage there is no difference in the two functions.
> However they produce their results using different steps.
>
> ================
> SET
> ================
>
> Consider f[4]
>
> (Step 1.  CALCULATE FIRST )
>
> f[x] = Expand[(x+7)^2]
>
> f[x] = x^2 + 14 x + 49
>
> (Step 2. THEN CHANGE )
>
> f[x->4] = x^2 + 14 x + 49
>
> f[4] <- 4^2 + 14 * 4 + 49
>
> f[4] <- 121
>
>
> ================
> SETDELAY
> ================
>
> Consider g[4]
>
> (Step 1.  CHANGE FIRST )
>
> g[x] := Expand[(x+7)^2]
>
> g[x->4] := Expand[(x+7)^2]
>
> g[4] <- Expand[(4+7)^2]
>
> (Step 2. THEN CALCULATE )
>
> g[4] <- Expand[(11)^2]
>
> g[4] <- Expand[121]
>
> g[4] <- 121



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