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Computing heights of ideals
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1909		 Page 1 of 1
Author:  sfstatemichael [ Mon Feb 21, 2011 3:40 am ]
Post subject:  Computing heights of ideals
Hello,

I am getting an error when trying to compute the height of an ideal. Following the example in the online manual, I establish my ring (0,(x,y),dp) and input my ideal, I, and then the function: heightZ(I).

Any guidance would be greatly appreciated.

Thanks,
Michael
Author:  sfstatemichael [ Mon Feb 21, 2011 4:46 am ]
Post subject:  Re: Computing heights of ideals
Ok, so I was successful in computing the ideal! turns out I needed to include in the beginning the "LIB primdecint.lib";

in the case for Laurent Polynomials, how does one notate positive and negative powers using mulivariables x1,x2,x3,...
Author:  gorzel [ Tue Feb 22, 2011 11:30 pm ]
Post subject:  Re: Computing heights of ideals
Follow closely the code given in the example for heightZ
http://www.singular.uni-kl.de/Manual/la ... tm#SEC1832

As shown in the example, this procs needs the primdecint.lib
to be loaded. Put the quotation marks at the right place.

Instead of rational numbers i.e. r =0,(x,y,z),dp;
you should choose here integers for the coefficients.

To your questions:

The exponent for variables have to be non-negative. Thus
Laurent polynomials in ringvariables can not be defined.

Negative exponents are only allowed for parameters.
This means, if you are working over a function field, then
the coefficients can be rational functions.

However, the funtion heightZ can not be applied to those expressions.

If you want to work with x1,x2,x3,x4, then define a ring
with these variables. Note that you have to put the * and ^ now.

Code:
> ring rZZ = integers,(x1,x2,x3,x4),dp;
> ideal I = 13*x1^2,17*x2^4;
Author:  sfstatemichael [ Sat Jun 18, 2011 7:37 am ]
Post subject:  Re: Computing heights of ideals
Can I compute over the rational polynomial ring?
Author:  sfstatemichael [ Sat Jun 18, 2011 11:36 pm ]
Post subject:  Re: Computing heights of ideals
Also, I'm working in Sage, and I'm trying to compute the height of very large ideals using singular. I get an error message stating:

TypeError: Singular error:
? nesting too deep
? error occurred in or before crypto.lib::gcdN line 152: `parameter number a; parameter number b; `
? leaving crypto.lib::gcdN
skipping text from `)` error at token `)`
? leaving crypto.lib::gcdN
? leaving crypto.lib::gcdN

Any thoughts?
Author:  hannes [ Mon Jun 27, 2011 11:52 am ]
Post subject:  Re: Computing heights of ideals
The problem is the very trivial implementation of gcdN in crypto.lib.
This is a library to explain algorithms and should not have been used in the first place in primdecint.lib.

A workaround is:
edit crypto.lib and sustitute the body of gcdN by:
return(gcd(a,b));
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