/usr/share/singular/LIB/rwalk.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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 | /////////////////////////////////////////////////
version="version rwalk.lib 4.0.0.0 Jun_2014 "; // $Id: d757f4f4f51ea22f0792a8197f08acc393ef1894 $
category="Commutative Algebra";
info="
LIBRARY: rwalk.lib Groebner Walk Conversion Algorithms
AUTHOR: Stephan Oberfranz
PROCEDURES:
prwalk(ideal,int,int[,intvec,intvec]); standard basis of ideal via Random Perturbation Walk algorithm
rwalk(ideal,int[,intvec,intvec]); standard basis of ideal via Random Walk algorithm
frandwalk(ideal,int[,intvec,intvec]); standard basis of ideal via Random Fractal Walk algorithm
KEYWORDS: walk, groebner;Groebnerwalk
SEE ALSO: grwalk_lib; swalk_lib
";
/***********************************
* Argument string for Random Walk *
***********************************/
static proc OrderStringalp_NP(string Wpal,list #)
{
int n= nvars(basering);
string order_str = "dp";
int nP = 1;
//Default: if size(#)=0, the Groebnerwalk algorithm and its developments compute
//a Groebner basis from "dp" to "lp"
intvec curr_weight = system("Mivdp",n); //define (1,1,...,1)
intvec target_weight = system("Mivlp",n); //define (1,0,...,0)
// check if the target ring has a weighted lp ordering
list rl = ringlist(basering);
if (rl[3][1][1] == "a" and rl[3][2][1] == "lp") {
target_weight = rl[3][1][2];
}
if(size(#) != 0)
{
if(size(#) == 1)
{
if(typeof(#[1]) == "intvec") {
curr_weight = #[1];
if(Wpal == "al"){
order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)";
}
else {
order_str = "(Wp("+string(#[1])+"),C)";
}
}
else {
if(typeof(#[1]) == "int"){
nP = #[1];
}
else {
if(typeof(#[1]) == "string")
{
if(#[1] == "Dp") {
order_str = "Dp";
}
else {
order_str = "dp";
}
}
else {
print("// ** the input must be \"(ideal, intvec)\" or ");
print("// ** \"(ideal, string)\" or ");
print("// ** \"(ideal, string,intvec)\" or ");
print("// ** \"(ideal, intvec,intvec)\".");
print("// ** a lex. GB will be computed from \"dp\" to \"lp\".");
}
}
}
}
else {
if(size(#) == 2) {
if(typeof(#[1]) == "intvec" and typeof(#[2]) == "int") {
curr_weight = #[1];
order_str = "(Wp("+string(#[1])+"),C)";
if(Wpal == "al") {
order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)";
}
if(Wpal == "M") {
order_str = "(M("+string(#[1])+"),C)";
}
}
else {
if(typeof(#[1]) == "intvec" and typeof(#[2]) == "intvec") {
curr_weight = #[1];
target_weight = #[2];
order_str = "(Wp("+string(#[1])+"),C)";
if(Wpal == "al") {
order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)";
}
if(Wpal == "M"){
order_str = "(M("+string(#[1])+"),C)";
}
}
else {
if(typeof(#[1]) == "string" and typeof(#[2]) == "intvec") {
target_weight = #[2];
if(#[1] == "Dp") {
order_str = "Dp";
}
else {
order_str = "dp";
}
}
else {
print("// ** the input must be \"(ideal, intvec)\" or ");
print("// ** \"(ideal, string)\" or ");
print("// ** \"(ideal, string,intvec)\" or ");
print("// ** \"(ideal, intvec,intvec)\".");
print("// ** a lex. GB will be computed from \"dp\" to \"lp\".");
}
}
}
}
else {
if(size(#) == 3) {
if(typeof(#[1]) == "intvec" and typeof(#[2]) == "intvec" and
typeof(#[3]) == "int") {
curr_weight = #[1];
target_weight = #[2];
nP = #[3];
order_str = "(Wp("+string(#[1])+"),C)";
if(Wpal == "al") {
order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)";
}
if(Wpal == "M") {
order_str = "(M("+string(#[1])+"),C)";
}
}
else {
if(typeof(#[1]) == "string" and typeof(#[2]) == "intvec" and
typeof(#[3]) == "int") {
target_weight = #[2];
nP = #[3];
if(#[1] == "Dp") {
order_str = "Dp";
}
else {
order_str = "dp";
}
}
else {
print("// ** the input must be \"(ideal,intvec,intvec,int)\"");
print("// ** and a lex. GB will be computed from \"dp\" to \"lp\"");
}
}
}
else {
print("// ** The given input is wrong");
print("// ** and a lex. GB will be computed from \"dp\" to \"lp\"");
}
}
}
}
list result;
result[1] = nP;
result[2] = order_str;
result[3] = curr_weight;
result[4] = target_weight;
return(result);
}
/****************
* Random Walk *
****************/
proc rwalk(ideal Go, int radius, int pert_deg, list #)
"SYNTAX: rwalk(ideal i, int radius);
if size(#)>0 then rwalk(ideal i, int radius, intvec v, intvec w);
intermediate Groebner bases are not reduced if reduction = 0
TYPE: ideal
PURPOSE: compute the standard basis of the ideal, calculated via
the Random walk algorithm from the ordering
\"(a(v),lp)\", \"dp\", \"Dp\" or \"M\"
to the ordering \"(a(w),lp)\", \"(a(1,0,...,0),lp)\" or \"M\".
SEE ALSO: std, stdfglm, groebner, gwalk, pwalk, fwalk, twalk, awalk1, awalk2
KEYWORDS: Groebner walk
EXAMPLE: example rwalk; shows an example"
{
//-------------------- Initialize parameters ------------------------
int n= nvars(basering);
list OSCTW = OrderStringalp_NP("al",#);
if(size(#)>1)
{
if(size(#[2]) == n*n)
{
OSCTW= OrderStringalp_NP("M", #);
}
}
else
{
OSCTW= OrderStringalp_NP("al", #);
}
string ord_str = OSCTW[2];
intvec curr_weight = OSCTW[3]; // original weight vector
intvec target_weight = OSCTW[4]; // target weight vector
kill OSCTW;
//-------------------- Initialize parameters ------------------------
int reduction=1;
int printout=0;
def xR = basering;
execute("ring ostR = "+charstr(xR)+",("+varstr(xR)+"),"+ord_str+";");
def old_ring = basering;
ideal G = fetch(xR, Go);
G = system("Mrwalk", G, curr_weight, target_weight, radius, pert_deg, reduction, printout);
setring xR;
kill Go;
keepring basering;
ideal result = fetch(old_ring, G);
attrib(result,"isSB",1);
return (result);
}
example
{
"EXAMPLE:"; echo = 2;
// compute a Groebner basis of I w.r.t. lp.
ring r = 32003,(z,y,x), lp;
ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
int radius = 1;
int perturb_deg = 2;
rwalk(I,radius,perturb_deg);
}
/*****************************************
* Perturbation Walk with random element *
*****************************************/
proc prwalk(ideal Go, int radius, int o_pert_deg, int t_pert_deg, list #)
"SYNTAX: rwalk(ideal i, int radius);
if size(#)>0 then rwalk(ideal i, int radius, intvec v, intvec w);
TYPE: ideal
PURPOSE: compute the standard basis of the ideal, calculated via
the Random Perturbation Walk algorithm from the ordering
\"(a(v),lp)\", \"dp\", \"Dp\" or \"M\"
to the ordering \"(a(w),lp)\", \"(a(1,0,...,0),lp)\" or \"M\".
SEE ALSO: std, stdfglm, groebner, gwalk, pwalk, fwalk, twalk, awalk1, awalk2
KEYWORDS: Groebner walk
EXAMPLE: example prwalk; shows an example"
{
//-------------------- Initialize parameters ------------------------
list OSCTW = OrderStringalp_NP("al", #);
int nP = OSCTW[1];
string ord_str = OSCTW[2];
intvec curr_weight = OSCTW[3]; // original weight vector
intvec target_weight = OSCTW[4]; // target weight vector
kill OSCTW;
//-------------------- Initialize parameters ------------------------
int reduction=1;
int printout=0;
def xR = basering;
execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
def old_ring = basering;
ideal G = fetch(xR, Go);
G = system("Mprwalk", G, curr_weight, target_weight, radius, o_pert_deg, t_pert_deg,
nP, reduction, printout);
setring xR;
kill Go;
keepring basering;
ideal result = fetch(old_ring, G);
attrib(result,"isSB",1);
return (result);
}
example
{
"EXAMPLE:"; echo = 2;
// compute a Groebner basis of I w.r.t. lp.
ring r = 32003,(z,y,x), lp;
ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
int radius = 1;
int o_perturb_deg = 2;
int t_perturb_deg = 2;
prwalk(I,radius,o_perturb_deg,t_perturb_deg);
}
/************************************
* Fractal Walk with random element *
************************************/
proc frandwalk(ideal Go, int radius, list #)
"SYNTAX: frwalk(ideal i, int radius);
frwalk(ideal i, int radius, intvec v, intvec w);
TYPE: ideal
PURPOSE: compute the standard basis of the ideal w.r.t. the
lexicographical ordering or a weighted-lex ordering,
calculated via the Random Fractal walk algorithm.
SEE ALSO: std, stdfglm, groebner, gwalk, pwalk, twalk, awalk1, awalk2
KEYWORDS: The fractal walk algorithm
EXAMPLE: example frandwalk; shows an example"
{
// we use ring with ordering (a(...),lp,C)
list OSCTW = OrderStringalp_NP("al", #);
string ord_str = OSCTW[2];
intvec curr_weight = OSCTW[3]; /* current weight vector */
intvec target_weight = OSCTW[4]; /* target weight vector */
kill OSCTW;
def xR = basering;
execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
def old_ring = basering;
//print("//** help ring = " + string(basering));
ideal G = fetch(xR, Go);
int reduction=1;
int printout=0;
G = system("Mfrwalk", G, curr_weight, target_weight, radius, reduction, printout);
setring xR;
//kill Go;
keepring basering;
ideal result = fetch(old_ring, G);
attrib(result,"isSB",1);
return (result);
}
example
{
"EXAMPLE:"; echo = 2;
ring r = 0,(z,y,x), lp;
ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
int reduction = 0;
frandwalk(I,2);
}
|