Re: Bug in Plot3D?

*To*: mathgroup at smc.vnet.net*Subject*: [mg105225] Re: Bug in Plot3D?*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Wed, 25 Nov 2009 02:30:33 -0500 (EST)

On 11/24/09 at 5:51 AM, wellsoberlin at gmail.com (SixWingedSeraph) wrote: >The two plot commands in the notebook below should give identical >outputs, but they don't. The notebook is posted at >http://abstractmath.org/MM/MmaBugQ.nb >a := 9; b := 18; There is no reason I can see to use SetDelayed here. >ff[x_, y_, z_] := x + y + z >gg[x_, y_, z_] := 2*x - 2*y - z >f[x_, y_] := z /. Solve[ff[x, y, z] == a, z] Given you are plotting this function, you definitely should be using Set ("=") instead of SetDelayed (":="). By using SetDelayed you are telling Mathematica to solve for z every time Plot supplies a new set of x, y points. This causes Mathematica to do more work than necessary to create the plot. >f[x, y] >g[x_, y_] := z /. Solve[gg[x, y, z] == b, z] >g[x, y] >Plot3D[{-x - y + 9, 2*(x - y - 9)}, {x, 6, 10}, {y, -5, 1}... >Plot3D[{f[x, y], g[x, y]}, {x, 6, 10}, {y, -5, 1}... You are not plotting the same thing in both cases. That is: In[14]:= {f[x, y], g[x, y]} Out[14]= {{-x - y + 9}, {2 (x - y - 9)}} which is not the same as {-x - y + 9, 2 (x - y - 9)} You can make things the same by redefining ff and gg to take the first solution returned by Solve or by taking the first solution when plotting