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From: Sam Takoy on 17 Jul 2010 08:16
Hi,

Suppose I have written the following block of commands for computing the
differential geometry elements on a surface of evolution given by r=F[g]
z=Z[g]. This topic not my interest, I just cooked it up for an example.

TF[m_] := Flatten[Transpose[m]]
Combine[m1_, m2_] :=
Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T
R[g_, theta_] := {F[g] Cos[theta], F[g] Sin[theta], Z[g]}
Z1[g_, theta_] := Derivative[1, 0][R][g, theta]
Z2[g_, theta_] := Derivative[0, 1][R][g, theta]
UnitN[g_, theta_] := Cross[Z1[g, theta], Z2[g, theta]] // Normalize
shift[g_, theta_] := Combine[{Z1[g, theta]} // T, {Z2[g, theta]} // T]
m[g_, theta_] := Transpose[shift[g, theta]].shift[g, theta]
M[g_, theta_] := Inverse[m[g, theta]]

M[g, theta] // MatrixForm


My question is this: could this entire block be turned into a function
"paramtrized" by F and Z. For example, denote that whole block by XXXXX.
Is there something along the lines of

DiffGeom[F_, Z_] := XXXXX
r[g_] := a Cosh[(g - H/2)/a]
z[g_] := g
DiffGeom[r, z]

In other words, once I have taught Mathematica to compute these objects
for general surfaces of revolution, I want it to apply it to a
particular surface of revolution. What's the best way to organize this?

From: Helen Read on 18 Jul 2010 01:03
On 7/17/2010 8:16 AM, Sam Takoy wrote:
>
> My question is this: could this entire block be turned into a function
> "paramtrized" by F and Z. For example, denote that whole block by XXXXX.
> Is there something along the lines of
>
> DiffGeom[F_, Z_] := XXXXX
> r[g_] := a Cosh[(g - H/2)/a]
> z[g_] := g
> DiffGeom[r, z]
>
> In other words, once I have taught Mathematica to compute these objects
> for general surfaces of revolution, I want it to apply it to a
> particular surface of revolution. What's the best way to organize this?

Use Module or Block

Look them up in the Documentation.


--
Helen Read
University of Vermont

From: Leonid Shifrin on 18 Jul 2010 01:04
Hi,

Here is a simpler working example to illustrate one possibility:

In[1]:= Clear[makeDefs];
makeDefs[p_, q_] :=
Module[{},
Clear[f, g, h];
f[x_, y_] := Sin[p[x]*q[y]];
g[x_, y_] := Cos[p[x]/q[y]];
h[x_, y_] := f[x, y] + g[x, y];]

In[3]:= makeDefs[Sin, Cos]

In[4]:= h[a, b]

Out[4]= Cos[Sec[b] Sin[a]] + Sin[Cos[b] Sin[a]]

In[5]:= makeDefs[#^2 &, #^3 &]

In[6]:= h[a, b]

Out[6]= Cos[a^2/b^3] + Sin[a^2 b^3]

Alternatively, you can pass functions as extra explicit parameters to those
functions that use them.

When you provide some sample code, I recommend to try constructing the
simplest
example illustrating your problem, and make sure it does work. Also, using
capital letters
as starting letters for your function or variable names is a bad habit.

Hope this helps.

Regards,
Leonid


On Sat, Jul 17, 2010 at 4:16 PM, Sam Takoy <sam.takoy(a)yahoo.com> wrote:

> Hi,
>
> Suppose I have written the following block of commands for computing the
> differential geometry elements on a surface of evolution given by r=F[g]
> z=Z[g]. This topic not my interest, I just cooked it up for an example.
>
> TF[m_] := Flatten[Transpose[m]]
> Combine[m1_, m2_] :=
> Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T
> R[g_, theta_] := {F[g] Cos[theta], F[g] Sin[theta], Z[g]}
> Z1[g_, theta_] := Derivative[1, 0][R][g, theta]
> Z2[g_, theta_] := Derivative[0, 1][R][g, theta]
> UnitN[g_, theta_] := Cross[Z1[g, theta], Z2[g, theta]] // Normalize
> shift[g_, theta_] := Combine[{Z1[g, theta]} // T, {Z2[g, theta]} // T]
> m[g_, theta_] := Transpose[shift[g, theta]].shift[g, theta]
> M[g_, theta_] := Inverse[m[g, theta]]
>
> M[g, theta] // MatrixForm
>
>
> My question is this: could this entire block be turned into a function
> "paramtrized" by F and Z. For example, denote that whole block by XXXXX.
> Is there something along the lines of
>
> DiffGeom[F_, Z_] := XXXXX
> r[g_] := a Cosh[(g - H/2)/a]
> z[g_] := g
> DiffGeom[r, z]
>
> In other words, once I have taught Mathematica to compute these objects
> for general surfaces of revolution, I want it to apply it to a
> particular surface of revolution. What's the best way to organize this?
>
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