Two-Dimensional Vector Field Plots

## Description

Plotting a vector field for $\mathbf F(x,y) = (\cos x, \sin y)$ with Sage.

## Sage Cell

#### Code

```
x,y = var('x y')
f = cos(x)
g = sin(y)
plot_vector_field((f,g), (x,-3,3), (y,-3,3))
```

## Options

To plot vectors of the same length, divide by the length of each vector at each point.

To plot a vector field without a frame, use the option `frame = False`. The default is `frame = True`.

To change the number of plot points, use `plot_points`. The default is `plot_points=10`.

```
x,y = var('x y')
f = cos(x)
g = sin(y)
plot_vector_field((f,g), (x,-3,3), (y,-3,3))
```

```
x,y = var('x y')
f = cos(x)
g = sin(y)
n = sqrt(f^2 + g^2)
plot_vector_field((f/n,g/n), (x,-3,3), (y,-3,3))
```

```
x,y = var('x y')
x,y = var('x y')
f = cos(x)
g = sin(y)
plot_vector_field((f,g), (x,-3,3), (y,-3,3), frame = False)
```

```
x,y = var('x y')
f = cos(x)
g = sin(y)
plot_vector_field((f,g), (x,-3,3), (y,-3,3), plot_points=10)
```

## Tags

Primary Tags: two-dimensional plots, multivariable calculus

Secondary Tags: two-dimensional vector field plots

## Related Cells

None

## Attribute

Permalink:

Author: T. Judson

Date: 21 Jul 2017 11:38

Submitted by: Tom Judson