1 | initial version |

The reason is that when you use `[3..5]`

, the iterator produces Sage Integers:

```
sage: for r1 in [3..5]:
....: print type(r1)
<type 'sage.rings.integer.Integer'>
<type 'sage.rings.integer.Integer'>
<type 'sage.rings.integer.Integer'>
```

while when you use `range(3,6)`

, the iterator produces Python ints:

```
sage: for r1 in range(3,6):
print type(r1)
<type 'int'>
<type 'int'>
<type 'int'>
```

Now when you write `r2 / r1`

, if one of them is a Sage Integer, you get a rational nomber. If both are Python ints, then you get an int, that is the rounded fraction:

```
sage: ZZ(3)/int(2)
3/2
sage: int(3)/ZZ(2)
3/2
sage: ZZ(3)/ZZ(2)
3/2
sage: int(3)/int(2)
1
```

Hence, when both `r1`

and `r2`

are produced by 'range()`, with`

r2 < r1`, the value of`

r2/r1* (pi ^ pi))`will be`

0`, hence your plot starts and ends with the same value, which explains the error.

To solve the problem, you can use `srange()`

function, which produces Sage integers instead of Pythoin ints, this will solve your problem.

2 | No.2 Revision |

The reason is that when you use `[3..5]`

, the iterator produces Sage Integers:

```
sage: for r1 in [3..5]:
....: print type(r1)
<type 'sage.rings.integer.Integer'>
<type 'sage.rings.integer.Integer'>
<type 'sage.rings.integer.Integer'>
```

while when you use `range(3,6)`

, the iterator produces Python ints:

```
sage: for r1 in range(3,6):
print type(r1)
<type 'int'>
<type 'int'>
<type 'int'>
```

Now when you write `r2 / r1`

, if one of them is a Sage Integer, you get a rational nomber. If both are Python ints, then you get an int, that is the rounded fraction:

```
sage: ZZ(3)/int(2)
3/2
sage: int(3)/ZZ(2)
3/2
sage: ZZ(3)/ZZ(2)
3/2
sage: int(3)/int(2)
1
```

Hence, when both `r1`

and `r2`

are produced by ~~'range()~~`, with`

`range()`

, with `r2 < r1`

of `, the value `

~~of~~`r2/r1* (pi ^ pi))`

0`, be ` will `

~~be~~`0`

, hence your plot starts and ends with the same value, which explains the error.

To solve the problem, you can use `srange()`

function, which produces Sage integers instead of Pythoin ints, this will solve your problem.