Prev: Solving systems of differential equations
Next: how to find a function
From: SixWingedSeraph on 24 Nov 2009 05:52
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;

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]

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},
BoxRatios -> {4, 6, 24}, ViewPoint -> {4.5, 3, 20},
MeshStyle -> Gray,
AxesLabel -> {x, y, z}, PlotStyle -> {{Red, Opacity[0.7]},
{Green, Opacity[0.7]}}, ColorFunction -> White]

Plot3D[{f[x, y], g[x, y]}, {x, 6, 10}, {y, -5, 1},
BoxRatios -> {4, 6, 24}, ViewPoint -> {4.5, 3, 20},
MeshStyle -> Gray,
AxesLabel -> {x, y, z}, PlotStyle -> {{Red, Opacity[0.7]},
{Green, Opacity[0.7]}}, ColorFunction -> White]


From: Bob Hanlon on 25 Nov 2009 02:34

Change your definitions for f and g to

f[x_, y_] := z /. Solve[ff[x, y, z] == a, z][[1]]

g[x_, y_] := z /. Solve[gg[x, y, z] == b, z][[1]]



Bob Hanlon

---- SixWingedSeraph <wellsoberlin(a)gmail.com> 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;

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]

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},
BoxRatios -> {4, 6, 24}, ViewPoint -> {4.5, 3, 20},
MeshStyle -> Gray,
AxesLabel -> {x, y, z}, PlotStyle -> {{Red, Opacity[0.7]},
{Green, Opacity[0.7]}}, ColorFunction -> White]

Plot3D[{f[x, y], g[x, y]}, {x, 6, 10}, {y, -5, 1},
BoxRatios -> {4, 6, 24}, ViewPoint -> {4.5, 3, 20},
MeshStyle -> Gray,
AxesLabel -> {x, y, z}, PlotStyle -> {{Red, Opacity[0.7]},
{Green, Opacity[0.7]}}, ColorFunction -> White]



From: Bill Rowe on 25 Nov 2009 02:39
On 11/24/09 at 5:51 AM, wellsoberlin(a)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


From: Sjoerd C. de Vries on 25 Nov 2009 02:39
As defined here, the functions f and g are a list. You should use the
first part of it instead.

Cheers -- Sjoerd

On Nov 24, 12:52 pm, SixWingedSeraph <wellsober...(a)gmail.com> wrote:
> The two plot commands in the notebook below should give identical
> outputs, but they don't. The notebook is posted athttp://abstractmath.org/MM/MmaBugQ.nb
>
> a := 9; b := 18;
>
> 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]
>
> 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},
> BoxRatios -> {4, 6, 24}, ViewPoint -> {4.5, 3, 20},
> MeshStyle -> Gray,
> AxesLabel -> {x, y, z}, PlotStyle -> {{Red, Opacity[0.7]},
> {Green, Opacity[0.7]}}, ColorFunction -> White]
>
> Plot3D[{f[x, y], g[x, y]}, {x, 6, 10}, {y, -5, 1},
> BoxRatios -> {4, 6, 24}, ViewPoint -> {4.5, 3, 20},
> MeshStyle -> Gray,
> AxesLabel -> {x, y, z}, PlotStyle -> {{Red, Opacity[0.7]},
> {Green, Opacity[0.7]}}, ColorFunction -> White]


 | 
Pages: 1
Prev: Solving systems of differential equations
Next: how to find a function