How to define vector function in Mathematica

[nikolafmf]

How you define vector function in Mathematica?

For example, f is a vector function and f=(xy,yz,zx). How to define this in Mathematica and then how to calculate the value of the components of f for any number x, y, and z?

For scalar functions it goes as this:

f[x_]:=x^2
f[4]

Any idea for vectors?

 

[Bill Simpson]

Can you use this to get you started?

You could define this to be just what your definition said:

f[v_List]:={v[[1]]*v[[2]],v[[2]]*v[[3]],v[[3]]*v[[1]]}

The {} around your result says your f is returning a vector and you calculate each element of that vector.

Or you can use tricky coding that just happens to do the same thing in this particular case.

In[1]:= f[v_List]:=RotateLeft[v]*v;

In[2]:= f[{x,y,z}]
Out[2]= {x y,y z,x z}

In[3]:= f[{3,Pi,-2}]
Out[3]= {3 Pi,-2 Pi,-6}

 

[Bill Simpson]

You could define this to be just what your definition said:

f[v_List]:={v[[1]]*v[[2]],v[[2]]*v[[3]],v[[3]]*v[[1]]}

Or you could define this as

f[{x_,y_,z_}]:={x y,y z,z x}

if that would be easier to understand

There are at least a dozen different ways of doing almost anything in Mathematica

 

[nikolafmf]

Thank you very much :)

Buy the way, is there any way to delete your post here before first reply in a case you have already found the answer?

 

[alphy]

In Mathematica, a vector function can be defined using the "Function" command or by using a list of functions. For the given example, the vector function f can be defined as follows:

f[x_, y_, z_] := {x*y, y*z, z*x}

To calculate the value of the components of f for any given values of x, y, and z, we can simply use the defined function and input the desired values. For example, to calculate the value of f for x=2, y=3, and z=4, we can use the following command:

f[2, 3, 4]

This will return the vector {6, 12, 8}, which corresponds to the components of f for the given values. This method can be used for any number of components in the vector function.

Alternatively, we can also define the vector function using a list of functions, as follows:

f[x_, y_, z_] := {x*y, y*z, z*x}

This method would give the same result as the previous one. To calculate the value of the components of f, we can use the same command as before:

f[2, 3, 4]

Both of these methods are valid ways to define a vector function in Mathematica. It is important to note that the arguments in the function definition should match the number of components in the vector function.

In conclusion, defining a vector function in Mathematica is similar to defining a scalar function, but with the addition of multiple components. By using the appropriate syntax and inputting the desired values, we can easily calculate the components of the vector function for any given inputs.