J.C. Kantor ([email protected])

In [1]:

```
from IPython.display import YouTubeVideo
YouTubeVideo("KrrZB5LvXF4",560,315,start=0,end=144,rel=0)
```

Out[1]:

Assuming you have mastered the solution of linear equations with paper and pencil, let's see how to find solutions using the python symbolic algebra library Sympy.

Sympy is an example of a Python 'library'. The first step in using the library is to import it into the current workspace. It is customary to import into the workspace with the namespace `sym`

to avoid name clashes with variables and functions.

In [2]:

```
import sympy as sym
```

`sym.var()`

constructs symbolic variables given a list of variable names.

In [3]:

```
sym.var(['n1','n2'])
```

Out[3]:

`sym.Eq()`

accepts two arguments, each a symbolic expression expressing the left and right hand sides of an equation. For this problem there are two equations to be solved simultaneously, so we construct both and store them in a python list.

In [4]:

```
eqns = [
sym.Eq(n1 + n2, 100),
sym.Eq(0.7*n1 + 0.2*n2, 30)
]
print eqns
```

The last step is solve the equations using `sym.solve()`

.

In [5]:

```
soln = sym.solve(eqns)
print soln
```

In [6]:

```
# import sympy
import sympy as sym
# Step 1. Create symbolic variables.
sym.var(['n1','n2'])
# Step 2. Create a list of equations using the symbolic variables
eqns = [
sym.Eq(n1 + n2, 100),
sym.Eq(0.7*n1 + 0.2*n2, 30)
]
# Step 3. Solve and display solution
soln = sym.solve(eqns)
print soln
```

In [7]:

```
from IPython.display import YouTubeVideo
YouTubeVideo("KrrZB5LvXF4",560,315,start=144,end=166,rel=0)
```

Out[7]:

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```