On Mon, Jan 18, 2010 at 12:32 AM, Minh Nguyen <[email protected]> wrote:
> 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
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
>
> --
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>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
--
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