Hi Jeff,
On Mon, Jan 18, 2010 at 3:27 PM, Jeff Stroomer <[email protected]> wrote:
<SNIP>
> #! /usr/bin/env sage
This line caught my attention. Is your code meant to be put in a
separate Python script (with extension ".py") or in a Sage script
(with extension ".sage")? For example, I created a Python script with
your code and gave it execute permission:
[mv...@mod mvngu]$ ls -g variety.py
-rwxr-xr-x 1 mvngu 579 2010-01-18 00:20 variety.py
[mv...@mod mvngu]$ cat variety.py
#! /usr/bin/env sage
import sys, os
from sage.all import *
R = PolynomialRing(QQ, 4, names = 'u,z,y,x', order = 'lex')
u,z,y,x = R.gens()
G = [
x^2 + 6/91*z + 6/13*y - 409/91*x + 66/91,
y*x - 6/91*z - 45/13*y - 410/91*x + 1572/91,
y^2 + 66/91*z - 129/13*y - 222/91*x + 2000/91,
z*x - 277/91*z - 4/13*y - 607/91*x + 2049/91,
z*y - 53/7*z - 5*y - 12/7*x + 313/7,
z^2 - 849/91*z - 30/13*y - 48/91*x + 2582/91,
u - 17/91*z - 4/13*y - 9/91*x - 187/91,
]
I = ideal(G)
V = I.variety()
for v in V:
print v
for g in G:
print ' %s(%s): %s' % (g, v, g.subs(v))
Running it as a Python script doesn't work:
[mv...@mod mvngu]$ sage -python variety.py
Traceback (most recent call last):
File "variety.py", line 10, in <module>
x^2 + 6/91*z + 6/13*y - 409/91*x + 66/91,
File "element.pyx", line 532, in
sage.structure.element.Element.__xor__ (sage/structure/element.c:4528)
RuntimeError: Use ** for exponentiation, not '^', which means xor
in Python, and has the wrong precedence.
[mv...@mod mvngu]$ sage variety.py
Traceback (most recent call last):
File "variety.py", line 10, in <module>
x^2 + 6/91*z + 6/13*y - 409/91*x + 66/91,
File "element.pyx", line 532, in
sage.structure.element.Element.__xor__ (sage/structure/element.c:4528)
RuntimeError: Use ** for exponentiation, not '^', which means xor
in Python, and has the wrong precedence.
Now I renamed "variety.py" to "variety.sage" (with same code, but
different file extension). Running "variety.sage" as a Sage script
works fine with Sage 4.3:
[mv...@mod mvngu]$ cat variety.sage
#! /usr/bin/env sage
import sys, os
from sage.all import *
R = PolynomialRing(QQ, 4, names = 'u,z,y,x', order = 'lex')
u,z,y,x = R.gens()
G = [
x^2 + 6/91*z + 6/13*y - 409/91*x + 66/91,
y*x - 6/91*z - 45/13*y - 410/91*x + 1572/91,
y^2 + 66/91*z - 129/13*y - 222/91*x + 2000/91,
z*x - 277/91*z - 4/13*y - 607/91*x + 2049/91,
z*y - 53/7*z - 5*y - 12/7*x + 313/7,
z^2 - 849/91*z - 30/13*y - 48/91*x + 2582/91,
u - 17/91*z - 4/13*y - 9/91*x - 187/91,
]
I = ideal(G)
V = I.variety()
for v in V:
print v
for g in G:
print ' %s(%s): %s' % (g, v, g.subs(v))
[mv...@mod mvngu]$ sage variety.sage
{y: 5, z: 7, u: 5, x: 1}
6/91*z + 6/13*y + x^2 - 409/91*x + 66/91({y: 5, z: 7, u: 5, x: 1}): 0
-6/91*z + y*x - 45/13*y - 410/91*x + 1572/91({y: 5, z: 7, u: 5, x: 1}): 0
66/91*z + y^2 - 129/13*y - 222/91*x + 2000/91({y: 5, z: 7, u: 5, x: 1}): 0
z*x - 277/91*z - 4/13*y - 607/91*x + 2049/91({y: 5, z: 7, u: 5, x: 1}): 0
z*y - 53/7*z - 5*y - 12/7*x + 313/7({y: 5, z: 7, u: 5, x: 1}): 0
z^2 - 849/91*z - 30/13*y - 48/91*x + 2582/91({y: 5, z: 7, u: 5, x: 1}): 0
u - 17/91*z - 4/13*y - 9/91*x - 187/91({y: 5, z: 7, u: 5, x: 1}): 0
{y: 7, z: 8, u: 6, x: 3}
6/91*z + 6/13*y + x^2 - 409/91*x + 66/91({y: 7, z: 8, u: 6, x: 3}): 0
-6/91*z + y*x - 45/13*y - 410/91*x + 1572/91({y: 7, z: 8, u: 6, x: 3}): 0
66/91*z + y^2 - 129/13*y - 222/91*x + 2000/91({y: 7, z: 8, u: 6, x: 3}): 0
z*x - 277/91*z - 4/13*y - 607/91*x + 2049/91({y: 7, z: 8, u: 6, x: 3}): 0
z*y - 53/7*z - 5*y - 12/7*x + 313/7({y: 7, z: 8, u: 6, x: 3}): 0
z^2 - 849/91*z - 30/13*y - 48/91*x + 2582/91({y: 7, z: 8, u: 6, x: 3}): 0
u - 17/91*z - 4/13*y - 9/91*x - 187/91({y: 7, z: 8, u: 6, x: 3}): 0
{y: 8, z: 1, u: 5, x: 3}
6/91*z + 6/13*y + x^2 - 409/91*x + 66/91({y: 8, z: 1, u: 5, x: 3}): 0
-6/91*z + y*x - 45/13*y - 410/91*x + 1572/91({y: 8, z: 1, u: 5, x: 3}): 0
66/91*z + y^2 - 129/13*y - 222/91*x + 2000/91({y: 8, z: 1, u: 5, x: 3}): 0
z*x - 277/91*z - 4/13*y - 607/91*x + 2049/91({y: 8, z: 1, u: 5, x: 3}): 0
z*y - 53/7*z - 5*y - 12/7*x + 313/7({y: 8, z: 1, u: 5, x: 3}): 0
z^2 - 849/91*z - 30/13*y - 48/91*x + 2582/91({y: 8, z: 1, u: 5, x: 3}): 0
u - 17/91*z - 4/13*y - 9/91*x - 187/91({y: 8, z: 1, u: 5, x: 3}): 0
{y: 2, z: 5, u: 4, x: 4}
6/91*z + 6/13*y + x^2 - 409/91*x + 66/91({y: 2, z: 5, u: 4, x: 4}): 0
-6/91*z + y*x - 45/13*y - 410/91*x + 1572/91({y: 2, z: 5, u: 4, x: 4}): 0
66/91*z + y^2 - 129/13*y - 222/91*x + 2000/91({y: 2, z: 5, u: 4, x: 4}): 0
z*x - 277/91*z - 4/13*y - 607/91*x + 2049/91({y: 2, z: 5, u: 4, x: 4}): 0
z*y - 53/7*z - 5*y - 12/7*x + 313/7({y: 2, z: 5, u: 4, x: 4}): 0
z^2 - 849/91*z - 30/13*y - 48/91*x + 2582/91({y: 2, z: 5, u: 4, x: 4}): 0
u - 17/91*z - 4/13*y - 9/91*x - 187/91({y: 2, z: 5, u: 4, x: 4}): 0
--
Regards
Minh Van Nguyen
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