@c ---content LibInfo---
@comment This file was generated by doc2tex.pl from d2t_singular/paramet_lib.doc
@comment DO NOT EDIT DIRECTLY, BUT EDIT d2t_singular/paramet_lib.doc INSTEAD
@c library version: (1.11.2.1,2002/10/21)
@c library file: ../Singular/LIB/paramet.lib
@cindex paramet.lib
@cindex paramet_lib
@table @asis
@item @strong{Library:}
paramet.lib
@item @strong{Purpose:}
   Parametrization of Varieties
@item @strong{Author:}
Thomas Keilen, keilen@@mathematik.uni-kl.de

@end table

@strong{Procedures:}
@menu
* parametrize:: parametrizes a prime ideal via the normalization
* parametrizepd:: calculates the prim.dec. and parametrizes the components
* parametrizesing:: parametrizes an isolated plane curve singularity
@end menu
@table @asis
@item @strong{Overview:}
A library to compute parametrizations of algebraic varieties (if possible)
with the aid of a normalization, or a primary decomposition, resp. to compute
a parametrization of a plane curve singularity with the aid of a
Hamburger-Noether expansion.

@end table
@c inserted refs from d2t_singular/paramet_lib.doc:30
@ifinfo
@menu
See also:
* hnoether_lib::
* normal_lib::
* primdec_lib::
@end menu
@end ifinfo
@iftex
@strong{See also:}
@ref{hnoether_lib};
@ref{normal_lib};
@ref{primdec_lib}.
@end iftex
@c end inserted refs from d2t_singular/paramet_lib.doc:30

@c ---end content LibInfo---

@c ------------------- parametrize -------------
@node parametrize, parametrizepd,, paramet_lib
@subsubsection parametrize
@cindex parametrize
@c ---content parametrize---
Procedure from library @code{paramet.lib} (@pxref{paramet_lib}).

@table @asis
@item @strong{Usage:}
parametrize(I); I ideal in an arbitrary number of variables,
whose radical is prime, in a ring with global ordering

@item @strong{Create:}
If the parametrization is successful, the basering will be changed to
the parametrization ring, that is to the ring PR=0,(s,t),dp;
respectively PR=0,t(1..d),dp;, depending on the dimension of the
parametrized variety.

@item @strong{Return:}
a list containing the parametrization ideal resp. the original ideal,
the number of variables needed for the parametrization resp. 0, and
1 resp. 0 depending on whether the parametrization was successful
or not

@cindex parametrization
@cindex normalization
@end table
@strong{Example:}
@smallexample
@c computed example parametrize d2t_singular/paramet_lib.doc:65 
LIB "paramet.lib";
ring RING=0,(x,y,z),dp;
ideal I=z2-y2x2+x3;
parametrize(I);
@expansion{} [1]:
@expansion{}    _[1]=s2-t2
@expansion{}    _[2]=s
@expansion{}    _[3]=s2t-t3
@expansion{} [2]:
@expansion{}    2
@expansion{} [3]:
@expansion{}    1
@c end example parametrize d2t_singular/paramet_lib.doc:65
@end smallexample
@c inserted refs from d2t_singular/paramet_lib.doc:72
@ifinfo
@menu
See also:
* normal::
* parametrizepd::
* primdecGTZ::
* radical::
@end menu
@end ifinfo
@iftex
@strong{See also:}
@ref{normal};
@ref{parametrizepd};
@ref{primdecGTZ};
@ref{radical}.
@end iftex
@c end inserted refs from d2t_singular/paramet_lib.doc:72

@c ---end content parametrize---

@c ------------------- parametrizepd -------------
@node parametrizepd, parametrizesing, parametrize, paramet_lib
@subsubsection parametrizepd
@cindex parametrizepd
@c ---content parametrizepd---
Procedure from library @code{paramet.lib} (@pxref{paramet_lib}).

@table @asis
@item @strong{Usage:}
parametrizepd(I); I ideal in a polynomial ring with global ordering

@item @strong{Create:}
If the parametrization is successful, the basering will be changed to
the parametrization ring, that is to the ring PR=0,(s,t),dp;
respectively PR=0,t(1..d),dp;, depending on the dimension of the
parametrized variety.

@item @strong{Return:}
a list of lists, where each entry contains the parametrization
of a primary component of I resp. 0, the number of variables
resp. 0, and 1 resp. 0 depending on whether the parametrization
of the component was successful or not

@cindex parametrization
@cindex normalization
@end table
@strong{Example:}
@smallexample
@c computed example parametrizepd d2t_singular/paramet_lib.doc:106 
LIB "paramet.lib";
ring RING=0,(x,y,z),dp;
ideal I=(x2-y2z2+z3)*(x2-z2-z3),(x2-y2z2+z3)*yz;
parametrizepd(I);
@expansion{} [1]:
@expansion{}    [1]:
@expansion{}       _[1]=s2t-t3
@expansion{}       _[2]=s
@expansion{}       _[3]=s2-t2
@expansion{}    [2]:
@expansion{}       2
@expansion{}    [3]:
@expansion{}       1
@expansion{} [2]:
@expansion{}    [1]:
@expansion{}       _[1]=0
@expansion{}       _[2]=s
@expansion{}       _[3]=0
@expansion{}    [2]:
@expansion{}       1
@expansion{}    [3]:
@expansion{}       1
@expansion{} [3]:
@expansion{}    [1]:
@expansion{}       _[1]=s3-s
@expansion{}       _[2]=0
@expansion{}       _[3]=s2-1
@expansion{}    [2]:
@expansion{}       1
@expansion{}    [3]:
@expansion{}       1
@c end example parametrizepd d2t_singular/paramet_lib.doc:106
@end smallexample
@c inserted refs from d2t_singular/paramet_lib.doc:113
@ifinfo
@menu
See also:
* normal::
* parametrize::
* primdecGTZ::
@end menu
@end ifinfo
@iftex
@strong{See also:}
@ref{normal};
@ref{parametrize};
@ref{primdecGTZ}.
@end iftex
@c end inserted refs from d2t_singular/paramet_lib.doc:113

@c ---end content parametrizepd---

@c ------------------- parametrizesing -------------
@node parametrizesing,, parametrizepd, paramet_lib
@subsubsection parametrizesing
@cindex parametrizesing
@c ---content parametrizesing---
Procedure from library @code{paramet.lib} (@pxref{paramet_lib}).

@table @asis
@item @strong{Usage:}
parametrizesing(f); f a polynomial in two variables, ordering ls or ds

@item @strong{Create:}
If the parametrization is successful, the basering will be changed to
the parametrization ring, that is to the ring 0,(x,y),ls;

@item @strong{Return:}
a list containing the parametrizations of the different branches of the
singularity at the origin resp. 0, if f was not of the desired kind

@cindex parametrization
@cindex curve singularities
@end table
@strong{Example:}
@smallexample
@c computed example parametrizesing d2t_singular/paramet_lib.doc:143 
LIB "paramet.lib";
ring RING=0,(x,y),ls;
poly f=(x^2-y^3)*(x^2-y^2-y^3);
parametrizesing(f);
@expansion{} [1]:
@expansion{}    _[1]=x
@expansion{}    _[2]=x-1/2x2
@expansion{} [2]:
@expansion{}    _[1]=x
@expansion{}    _[2]=-x-1/2x2
@expansion{} [3]:
@expansion{}    _[1]=x3
@expansion{}    _[2]=x2
@c end example parametrizesing d2t_singular/paramet_lib.doc:143
@end smallexample
@c inserted refs from d2t_singular/paramet_lib.doc:150
@ifinfo
@menu
See also:
* develop::
* hnexpansion::
* hnoether_lib::
@end menu
@end ifinfo
@iftex
@strong{See also:}
@ref{develop};
@ref{hnexpansion};
@ref{hnoether_lib}.
@end iftex
@c end inserted refs from d2t_singular/paramet_lib.doc:150

@c ---end content parametrizesing---
