1 | initial version |

Noted from John's comments, I can confirm the difference stems from the coercion and conversion stuff.

Given `script.py`

and `script.sage`

(same contents):

```
from sage.all import *
import time
def run(num):
cube = (polytopes.cube() * 37 / 45).change_ring(QQ)
for i in range(num):
hspace = Polyhedron(ieqs=[[(i+1)/(i+2), 1/(i+1), (i+2), (i+53)]]).change_ring(QQ)
intersection = hspace.intersection(cube)
tik = time.time()
run(100)
print('time elapsed: {}'.format(time.time() - tik), 's')
```

With `python script.py`

, I got `time elapsed: 8.750308990478516 s`

.

With `sage script.sage`

, I got `time elapsed: 0.6618611812591553 s`

, whose execution generated a python file `script.sage.py`

which looks like this:

```
# This file was *autogenerated* from the file profile.sage
from sage.all_cmdline import * # import sage library
_sage_const_37 = Integer(37); _sage_const_45 = Integer(45); _sage_const_1 = Integer(1); _sage_const_2 = $
from sage.all import *
import time
def run(num):
cube = (polytopes.cube() * _sage_const_37 / _sage_const_45 ).change_ring(QQ)
for i in range(num):
hspace = Polyhedron(ieqs=[[(i+_sage_const_1 )/(i+_sage_const_2 ), _sage_const_1 /(i+_sage_const_$
intersection = hspace.intersection(cube)
tik = time.time()
run(_sage_const_100 )
print('time elapsed: {}'.format(time.time() - tik), 's')
```

I then ran `python script.sage.py`

and got `time elapsed: 0.6441857814788818 s`

.

This conversion is documented in the tutorial:

When Sage loads example.sage it converts it to Python, which is then executed by the Python interpreter. This conversion is minimal; it mainly involves wrapping integer literals in Integer() floating point literals in RealNumber(), replacing ^’s by **’s, and replacing e.g., R.2 by R.gen(2). The converted version of example.sage is contained in the same directory as example.sage and is called example.sage.py.

2 | No.2 Revision |

Noted from John's comments, I can confirm the difference stems from the coercion and conversion stuff.

Given `script.py`

and `script.sage`

(same contents):

```
from sage.all import *
import time
def run(num):
cube = (polytopes.cube() * 37 / 45).change_ring(QQ)
for i in range(num):
hspace = Polyhedron(ieqs=[[(i+1)/(i+2), 1/(i+1), (i+2), (i+53)]]).change_ring(QQ)
intersection = hspace.intersection(cube)
tik = time.time()
run(100)
print('time elapsed: {}'.format(time.time() - tik), 's')
```

With `python script.py`

, I got `time elapsed: 8.750308990478516 s`

.

With `sage script.sage`

, I got `time elapsed: 0.6618611812591553 s`

, whose execution automatically generated a python file `script.sage.py`

which looks like this:

```
# This file was *autogenerated* from the file profile.sage
from sage.all_cmdline import * # import sage library
_sage_const_37 = Integer(37); _sage_const_45 = Integer(45); _sage_const_1 = Integer(1); _sage_const_2 = $
from sage.all import *
import time
def run(num):
cube = (polytopes.cube() * _sage_const_37 / _sage_const_45 ).change_ring(QQ)
for i in range(num):
hspace = Polyhedron(ieqs=[[(i+_sage_const_1 )/(i+_sage_const_2 ), _sage_const_1 /(i+_sage_const_$
intersection = hspace.intersection(cube)
tik = time.time()
run(_sage_const_100 )
print('time elapsed: {}'.format(time.time() - tik), 's')
```

I then ran `python script.sage.py`

and got `time elapsed: 0.6441857814788818 s`

.

This conversion is documented in the tutorial:

When Sage loads example.sage it converts it to Python, which is then executed by the Python interpreter. This conversion is minimal; it mainly involves wrapping integer literals in Integer() floating point literals in RealNumber(), replacing ^’s by **’s, and replacing e.g., R.2 by R.gen(2). The converted version of example.sage is contained in the same directory as example.sage and is called example.sage.py.

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