GRÖBNER is capable of computing Gröbner bases for sets of polynomials that are
subsets of , for various fields .
is called the *coefficient domain*, are
called the *ring variables* and have to be entered at run-time.

If *Coefficient Domain* is chosen from the general setup menu the
actual setting for can be chosen from the following menu:

================================================= Current setting is: rational_numbers ================================================= Rational Numbers ........ RN Rational Functions ...... RF Finite Field Zp ......... FF Galois Field ............ GF Floting Point Numbers ... FPN Leave Unmodified ........ <return>

First, the *current setting* of the coefficient domain is displayed,
the following choices are possible then:

**RN**- chooses
*rational numbers*as coefficient domain, i.e. . **RF**- chooses
*rational functions*as coefficient domain, i.e. . is called the*rational function base domain*and can be chosen from an immediately following menu:**RN**- chooses ,
**FF**- chooses .
*p*is called the*characteristic*of the finite field and must be entered at run-time.

*field variables*and have to be entered at run-time. **FF**- chooses
*finite fields*of the form as coefficient domain, i.e. .*p*is called the*characteristic*of the finite field and must be entered at run-time. **GF**- chooses
*finite fields*of the form as coefficient domain, i.e. .*p*is called the*characteristic*of the finite field and*n*is called the*degree*of the field extension. Both*p*and*n*have to be entered at run-time.is isomorphic to , where

*q*is an irreducible polynomial over of degree*n*. This isomorphism is used to represent elements of as univariate polynomials over of degree less than*n*. The actual name of the variable*x*has to be entered at run-time.In order to perform arithmetic in ,

*p*and*q*are required. At run-time*p*has to be entered first. In case*p*=2 the degree of the field extension,*n*, has to be entered. For*n*<10 irreducible polynomials over of degree*n*are predefined. For or an irreducible polynomial over of degree*n*must be supplied at run-time.Although is a special case of , namely

*n*=1, we implemented finite fields of the form seperately, since arithmetic can be done more efficiently. **FPN**- Chooses
*floating point numbers*as coefficient domain, i.e. . This is an experimental implementaion of floating point coefficients.

**Note:** The menu for setting up the coefficient domain can also
be accessed directly by calling the program `coef_setup`.

See Section 2.1 for the influence of the chosen coefficient domain.

Wed Sep 2 09:42:51 MDT 1998