Simon, et al.,
The script is working for you but not for me. The answer you get for
the variety is
{y: 5, z: 7, u: 5, x: 1}
{y: 7, z: 8, u: 6, x: 3}
{y: 8, z: 1, u: 5, x: 3}
{y: 2, z: 5, u: 4, x: 4}
This is correct, which is why you see zeros. But when I run the
script, the answer I get for the variety is
{y: 5, z: 7, u: 5, x: 1}
{y: 7, z: 8, u: 6, x: 3}
{y: 8, z: 1, u: 5, x: 3}
{y: 2, z: 5, u: 4, x: 4}
{y: 13, z: -72, u: -7, x: 4} # Bad
{y: 10, z: -28, u: 0, x: 1} # Bad
Here's a bad output line that I see when I run the script:
z^2 - 849/91*z - 30/13*y - 48/91*x + 2582/91({y: 13, z: -72, u: -7, x:
4}): 5852
I ran my script using the following console command line:
j...@stroomer-imac-2 ~/grobner_experiments
$ sage bugcase.sage
Here's my sage version:
$ sage --version
Sage Version 4.1.1, Release Date: 2009-08-14
I am running on an iMac, OS X 10.6.2, 2.16 Intel Core 2 Duo.
Jeff
On Jan 18, 1:47 am, William Stein <wst...@gmail.com> wrote:
> On Mon, Jan 18, 2010 at 12:32 AM, Minh Nguyen <nguyenmi...@gmail.com> wrote:
> > Hi Jeff,
>
> > On Mon, Jan 18, 2010 at 3:27 PM, Jeff Stroomer <jstroom...@hotmail.com>
> > 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
>
> The whole point of putting
>
> #! /usr/bin/env sage
>
> at the top of the file is so that one can type
>
> [mv...@mod mvngu]$ ./variety.sage
>
> after say doing
>
> [mv...@mod mvngu]$ chmod +x variety.sage
>
> William
>
>
>
> > {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
>
> > --
> > To post to this group, send email to sage-support@googlegroups.com
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>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org
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