John is right. I'll paraphrase his answer for the benefit of future users.

Let's dissect this :

```
var('u_5 u beta')
```

This is equivalent to `u_5, u, beta)=SR.var("u_5 u beta)`

. In particular, this

create a *symbolic variable* $\beta$ (a Python object defined by Sage), a *symbolic variable $u_5$ and a *symbolic variable* $u$, then

sets Python variables :

+`beta`

pointing to $beta$,

y = u - u_5 + beta*(exp(u)-u-4)

This create a *symbolic expression*, a Python structure defuined by Sage, containing, among others, pointers to $beta$, $u_5$ and $u$.

```
beta = 1.0
u_5 = -4.0
```

This binds `the Python varables beta`

and `u_5`

to the numerical values 1.0 and -4 respectively. The links to $beta$ and $u_5$ are lost. Thr expression bound to `p`

*is *unchanged** : the pointers to $beta$ and $u_5$ still point to the respective symbolic variables.

```
p = y.subs(u==u_5)
```

This create a new symbolic expression where the pointer to $u$ us replaced by the value of the Python variable `u_5`

, which is now the numeric value -4.0. The pointers to $beta$ and $u_5$ are unmodified.

```
p
```

This prints the new symbolic expression, which still contains (pointers to) symbolic variables.what you wnt to do is probably :

```
sage: y.subs(u==u_5).subs([beta==1, u_5==-4])
e^(-4)
```

or, more probably :

```
sage: y.subs(u==u_5).subs([beta==1, u_5==-4]).n()
0.0183156388887342
```

This can be abbreviated as :

```
sage: y.subs(u==u_5)(beta=1, u_5=-4).n()
0.0183156388887342
```

See the documentation for details, and the initial chapters of this marvelous book, which I cannot recommend too much.

Note that :

```
sage: y.subs([u==u_5, beta==1, u_5==-4])
e^u_5
```

in which the substitutions are executed in a different order, resulting in a different value.

HTH,

I just posted an answer to this at https://stackoverflow.com/questions/7....

I allowed myself to reformat your code in order to make it readable.