source: git/Singular/LIB/locnormal.lib

spielwiese
Last change on this file was 22ebd9, checked in by Hans Schoenemann <hannes@…>, 5 months ago
doc: ref to modnormal.lib, locnormal.lib -> normal.lib
  • Property mode set to 100644
File size: 5.1 KB
Line 
1//////////////////////////////////////////////////////////////////////////////
2version="version locnormal.lib 4.3.1.0 Jul_2022 "; // $Id$
3category="Commutative Algebra";
4info="
5LIBRARY: locnormal.lib   Normalization of affine domains using local methods
6AUTHORS:  J. Boehm        boehm@mathematik.uni-kl.de
7          W. Decker       decker@mathematik.uni-kl.de
8          S. Laplagne     slaplagn@dm.uba.ar
9          G. Pfister      pfister@mathematik.uni-kl.de
10          S. Steidel      steidel@mathematik.uni-kl.de
11          A. Steenpass    steenpass@mathematik.uni-kl.de
12
13OVERVIEW:
14
15Suppose A is an affine domain over a perfect field.@*
16This library implements a local-to-global strategy for finding the normalization
17of A. Following [1], the idea is to stratify the singular locus of A, apply the
18normalization algorithm given in [2] locally at each stratum, and put the local
19results together. This approach is inherently parallel.@*
20Furthermore we allow for the optional modular computation of the local results
21as provided by modnormal.lib. See again [1] for details.
22
23REFERENCES:
24
25[1] Janko Boehm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Stefan Steidel,
26Andreas Steenpass: Parallel algorithms for normalization, http://arxiv.org/abs/1110.4299, 2011.
27
28[2] Gert-Martin Greuel, Santiago Laplagne, Frank Seelisch: Normalization of Rings,
29Journal of Symbolic Computation 9 (2010), p. 887-901
30
31KEYWORDS:
32normalization; local methods; modular methods
33
34SEE ALSO: normal_lib
35
36PROCEDURES:
37locNormal(I, [...]);  normalization of R/I using local methods
38
39";
40
41LIB "normal.lib";
42LIB "sing.lib";
43LIB "modstd.lib";
44
45///////////////////////////////////////////////////////////////////////////
46//
47//   All procedures here have been moved to normal.lib
48//
49///////////////////////////////////////////////////////////////////////////
50
51
52///////////////////////////////////////////////////////////////////////////
53//
54//                            EXAMPLES
55//
56///////////////////////////////////////////////////////////////////////////
57/*
58// plane curves
59
60ring r24 = 0,(x,y,z),dp;
61int k = 2;
62poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1));
63f = subst(f,z,2x-y+1);
64ring s24 = 0,(x,y),dp;
65poly f = imap(r24,f);
66ideal i = f;
67
68locNormal(i);
69//modNormal(i,1);
70
71
72ring r24 = 0,(x,y,z),dp;
73int k = 3;
74poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1));
75f = subst(f,z,2x-y+1);
76ring s24 = 0,(x,y),dp;
77poly f = imap(r24,f);
78ideal i = f;
79
80locNormal(i);
81//modNormal(i,1,"noVerification");
82
83
84ring r24 = 0,(x,y,z),dp;
85int k = 4;
86poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1));
87f = subst(f,z,2x-y+1);
88ring s24 = 0,(x,y),dp;
89poly f = imap(r24,f);
90ideal i = f;
91
92locNormal(i);
93//modNormal(i,1,"noVerification");
94
95
96ring r24 = 0,(x,y,z),dp;
97int k = 5;
98poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1));
99f = subst(f,z,2x-y+1);
100ring s24 = 0,(x,y),dp;
101poly f = imap(r24,f);
102ideal i = f;
103
104locNormal(i);
105
106
107
108ring s24 = 0,(x,y),dp;
109int a=7;
110ideal i = ((x-1)^a-y^3)*((x+1)^a-y^3)*((x)^a-y^3)*((x-2)^a-y^3)*((x+2)^a-y^3)+y^15;
111
112locNormal(i);
113//modNormal(i,1);
114
115
116ring s24 = 0,(x,y),dp;
117int a=7;
118ideal i = ((x-1)^a-y^3)*((x+1)^a-y^3)*((x)^a-y^3)*((x-2)^a-y^3)*((x+2)^a-y^3)+y^15;
119
120locNormal(i);
121//modNormal(i,1);
122
123ring s24 = 0,(x,y),dp;
124int a=7;
125ideal i = ((x-1)^a-y^3)*((x+1)^a-y^3)*((x)^a-y^3)*((x-2)^a-y^3)*((x+2)^a-y^3)+y^15;
126
127locNormal(i);
128//modNormal(i,1,"noVerification");
129
130
131
132
133ring r=0,(x,y),dp;
134ideal i=9127158539954x10+3212722859346x8y2+228715574724x6y4-34263110700x4y6
135-5431439286x2y8-201803238y10-134266087241x8-15052058268x6y2+12024807786x4y4
136+506101284x2y6-202172841y8+761328152x6-128361096x4y2+47970216x2y4-6697080y6
137-2042158x4+660492x2y2-84366y4+2494x2-474y2-1;
138
139locNormal(i);
140//modNormal(i,1);
141
142
143// surfaces in A3
144
145
146ring r7 = 0,(x,y,t),dp;
147int a=11;
148ideal i = x*y*(x-y)*(x+y)*(y-1)*t+(x^a-y^2)*(x^10-(y-1)^2);
149locNormal(i);
150//modNormal(i,1,"noVerification");
151
152ring r7 = 0,(x,y,t),dp;
153int a=12;
154ideal i = x*y*(x-y)*(x+y)*(y-1)*t+(x^a-y^2)*(x^10-(y-1)^2);
155locNormal(i);
156//modNormal(i,1,"noVerification");
157
158
159ring r7 = 0,(x,y,t),dp;
160int a=13;
161ideal i = x*y*(x-y)*(x+y)*(y-1)*t+(x^a-y^2)*(x^10-(y-1)^2);
162
163locNormal(i);
164modNormal(i,1,"noVerification");
165
166
167ring r22 = 0,(x,y,z),dp;
168ideal i = z2-(y2-1234x3)^2*(15791x2-y3)*(1231y2-x2*(x+158))*(1357y5-3x11);
169
170locNormal(i);
171//modNormal(i,1,"noVerification");
172
173
174ring r22 = 0,(x,y,z),dp;
175ideal i = z2-(y2-1234x3)^3*(15791x2-y3)*(1231y2-x2*(x+158))*(1357y5-3x11);
176
177locNormal(i);
178//modNormal(i,1,"noVerification");
179
180
181ring r23 = 0,(x,y,z),dp;
182ideal i = z5-((13x-17y)*(5x2-7y3)*(3x3-2y2)*(19y2-23x2*(x+29)))^2;
183
184locNormal(i);
185//modNormal(i,1,"noVerification");
186
187
188// curve in A3
189
190ring r23 = 0,(x,y,z),dp;
191ideal i = z3-(19y2-23x2*(x+29))^2,x3-(11y2-13z2*(z+1));
192
193locNormal(i);
194//modNormal(i,1,"noVerification");
195
196
197ring r23 = 0,(x,y,z),dp;
198ideal i = z3-(19y2-23x2*(x+29))^2,x3-(11y2-13z2*(z+1))^2;
199
200locNormal(i);
201//modNormal(i,1,"noVerification");
202
203// surface in A4
204
205ring r23 = 0,(x,y,z,w),dp;
206ideal i = z2-(y3-123456w2)*(15791x2-y3)^2, w*z-(1231y2-x*(111x+158));
207
208
209locNormal(i);
210//modNormal(i,1,"noVerification");
211*/
212
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