# Plotting 2d vector fields – how to delay function evaluation

I want to plot, for example, the following 2d vector field: $$\vec{F}(x,y)= \begin{cases} (0.1,0.1), & \text{for }r\le d_{min}\newline \frac{\vec{r}}{r^3}, & \text{otherwise}. \end{cases}$$ In one SageMath cell I have defined corresponding Python function:

```
reset()
dmin = 0.03
def my_vector_field_2D(x,y):
vector_field = vector([0.1,0.1])
r = vector([x,y])
if r.norm()>dmin:
vector_field = 1/ r.norm()^3 * r
return vector_field
```

In another cell, I use function `plot_vector_field`

to plot the field:

```
var('x','y')
plot_vector_field(my_vector_field_2D(x,y),(x,-0.3,0.3),(y,-0.3,0.3))
```

However, function my_vector_field_2D(x,y) is evaluated before it is given to the function `plot_vector_field`

and because in this evaluation my_vector_field_2D receives instead of numbers symbolic variables `x`

and `y`

, expression `r.norm()>dmin`

is always `False`

. As a result, my_vector_field_2D(x,y) is evalueted to: (0.100000000000000, 0.100000000000000). So the plotted filed is actually $\vec{F}(x,y)=(0.1,0.1)$ everywhere and that is not what I want.

How can I prevent this function evaluation?

I tried something that works with the `plot`

function (provide the `plot`

function with just the name of a function that you want to plot (without parameters) in order to prevent function evaluation):

```
plot_vector_field(my_vector_field_2D,(-0.3,0.3),(-0.3,0.3))
```

But here this method does not work: **TypeError**: 'function' object is not iterable.

**My first why question**: Why this does not work? It works for `plot`

function and also for `contour_plot`

function and probably for some other plot functions.

Then I found in the SageMath documentation that “when plotting non-symbolic functions, they should be wrapped in `lambda`

”. So I tried:

```
plot_vector_field(lambda x,y:my_vector_field_2D(x,y),(-0.3,0.3),(-0.3,0.3))
```

And the same error popped up: **TypeError**: 'function' object is not iterable.

But this works:

```
plot_vector_field((lambda x,y:my_vector_field_2D(x,y)[0],lambda x,y:my_vector_field_2D(x,y)[1]),(-0.3,0.3),(-0.3,0.3))
```

**My second why question**: Why do I need two `lambda`

functions or why do I need to manually decompose vector returned by my_vector_field_2D function into its two components?