This file is indexed.

/usr/share/singular/LIB/compregb.lib is in singular-data 1:4.1.0-p3+ds-2build1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
//////////////////////////////////////////////////////////////////////////////
version="version compregb.lib 4.0.0.0 Jun_2013 "; // $Id: 95e4c7dacb9b13daa2efb154f66ace0d4fef37dc $
category="General purpose";
info="
LIBRARY:  compregb.lib      experimental implementation for comprehensive Groebner systems
AUTHOR:  Akira Suzuki (http://kurt.scitec.kobe-u.ac.jp/~sakira/CGBusingGB/)
                      (<sakira@kobe-u.ac.jp>)
OVERVIEW:
see \"A Simple Algorithm to compute Comprehensive Groebner Bases using Groebner
Bases\" by Akira Suzuki and Yosuke Sato for details.

PROCEDURES:
  cgs(polys,vars,pars,R1,R2);     comprehensive Groebner systems
  base2str(G);                    pretty print of the result G

KEYWORDS: comprehensive Groebner system
";
///////////////////////////////////////////////////////////////////////////////
// global variables are the followings:
// Parameters, Variables, VMinDPoly,
// RingAll, RingVar;

///////////////////////////////////////////////////////////////////////////////
static proc setup_special_dpolys()
{
  poly VMinDPoly = Variables[size(Variables)];
  export(VMinDPoly);
}

static proc newcasebasis(poly Case, ideal Basis)
{
  list CB = Case, Basis;
  return(CB);
}

static proc contains(poly Vari, list Varis)
{
  int l = size(Varis);
  for (int i = 1; i <= l; i ++)
  {
    if (Vari == Varis[i])
    {
      return(1);
    }
  }

  return(0);
}

static proc polys_heads(list PolyL)
{
  int i, j;
  int length = size(PolyL);
  if (!length)
  {
    return(PolyL);
  }

  setring(RingVar);
  list PolyL = imap(RingAll, PolyL);
  list HCoefs = list();
  length = size(PolyL);
  for (i = 1; i <= length; i ++)
  {
    HCoefs = insert(HCoefs, leadcoef(PolyL[i]));
  }
  setring(RingAll);
  list HCoefs = imap(RingVar, HCoefs);

  list CoefL;
  ideal CoefLsub;
  poly Coef;
  for (i = 1; i <= length; i ++)
  {
    Coef = HCoefs[i];
    if (typeof(Coef) == "poly")
    {
      CoefLsub = factorize(Coef, 1);
      for (j = 1; j <= size(CoefLsub); j ++)
      {
        if (CoefLsub[j] > 1)
        {
          CoefL = insert(CoefL, CoefLsub[j]);
        }
      }
    }
  }

  for (i = 1; i <= size(CoefL); i ++)
  {
    Coef = CoefL[i];
    for (j = i + 1; j <= size(CoefL); j ++)
    {
      if (Coef == CoefL[j])
      {
        CoefL = delete(CoefL, j);
        j --;
      }
    }
  }

  return(CoefL);
}

static proc polys_restrict_v(ideal Polys)
{
  return(polys_separate_v_p(Polys)[0]);
}

static proc polys_restrict_p(ideal Polys)
{
  return(polys_separate_v_p(Polys)[1]);
}

static proc polys_separate_v_p(ideal Polys)
{
  list R_v, R_p;
  poly P;
  int length = size(Polys);

  for (int i = 1; i <= length; i ++)
  {
    P = Polys[i];
    if (P < VMinDPoly)
    {
      R_p = insert(R_p, P);
    }
    else
    {
      R_v = insert(R_v, P);
    }
  }

  return(R_v, R_p);
}

static proc cgs_main(ideal Polys)
{
  ideal F;
  list FP, FV, HFact, Bases;
  poly H;
  int i;

//    F = groebner(Polys);
  F = slimgb(Polys);

  if (F[1] == 1)
  {
    return(list());
  }

  FV, FP = polys_separate_v_p(F);

  HFact = polys_heads(FV);
  int HFL = size(HFact);

  H = 1;
  for (i = 1; i <= HFL; i ++)
  {
    H = H * HFact[i];
  }

  Bases = insert(Bases, list(H, F));

  for (i = 1; i <= HFL; i ++)
  {
    //    print("paras:" + string(FP));
    //    print("ideal:" + string(HFact[i]));
    Bases = cgs_main(F + ideal(HFact[i])) + Bases;
  }

  return(Bases);
}

proc cgs(ideal Polys, list Vars, list Paras,def RingVar,def RingAll)
"USAGE: cgs(Polys,Vars,Paras,RingVar,RingAll); Polys an ideal, Vars, the list
        of variables, Paras the list of parameters, RingVar the ring with
        Paras as parameters, RingAll the ring with Paras as variables
        (RingAll should be the current ring)
RETURN: a list L of lists L[i] of a polynomial and an ideal:
        L[i][1] the polynomial giving the condition on the parameters
        L[i][2] the Groebner basis for this case
EXAMPLE: example cgs; shows an example
"
{
  option(redSB);
  list Parameters = Paras;
  list Variables = Vars;
  poly VMinDPoly = Vars[size(Vars)];
  export(Parameters, Variables, VMinDPoly);

  export(RingVar, RingAll);
  setring(RingAll);

  list G = cgs_main(Polys);

  keepring(RingAll);
  return(G);
}
example
{ "EXAMPLE:";echo=2;
  ring RingVar=(0,a,b),(x,y,t),lp;
  ring RingAll=0,(x,y,t,a,b),(lp(3),dp);
  ideal polys=x^3-a,y^4-b,x+y-t;
  list vars=x,y,t;
  list paras=a,b;
  list G = cgs(polys,vars,paras,RingVar,RingAll);
  G;
}
proc basis2str(list B)
{
  string Str;
  ideal Factors;
  int i;

  Str = "(";
  Factors = factorize(B[1], 1);
  for (i = 1; i <= size(Factors); i ++)
  {
    Str = Str + "(" + string(Factors[i]) + ")";
  }
  Str = Str + "!=0,";

  list FV, FP;
  FV, FP = polys_separate_v_p(B[2]);
  for (i = 1; i <= size(FP); i ++)
  {
    Str = Str + string(FP[i]) + "=0,";
  }

  if (size(Str) > 1)
  {
    Str = Str[1, size(Str) - 1] + ")[";
  }
  else
  {
    Str = "()[";
  }

  if (size(FV))
  {
    for (i = 1; i <= size(FV); i ++)
    {
      Str = Str + string(FV[i]) + ",";
    }

    Str = Str[1, size(Str) - 1] + "]";
  }
  else
  {
    Str += "]";
  }

  return(Str);
}

proc bases2str(list Bases)
{
  string Str;
  int i;

  Str = "";
  for (i = 1; i <= size(Bases); i ++)
  {
    Str = Str + basis2str(Bases[i]) + newline;
  }

  return(Str);
}

/*
ring RingVar=(0,a,b),(x,y,t),lp; ring RingAll=0,(x,y,t,a,b),(lp(3),dp);
ideal polys=x^3-a,y^4-b,x+y-t; list vars=x,y,t; list paras=a,b;
list G = cgs(polys,vars,paras,RingVar,RingAll);
bases2str(G);
*/