Changeset edfd36 in git for Singular/LIB/signcond.lib
 Timestamp:
 May 6, 2005, 1:17:33 PM (18 years ago)
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 (u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')
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 7acf9bf2b74329722c5db8dcbfad38aefc35a663
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 6ed9240d0e05977f97c2c93af491078329ba7b6d
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 1 edited
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Singular/LIB/signcond.lib
r6ed924 redfd36 1 // $Id: signcond.lib,v 1. 2 20050502 12:24:16Singular Exp $1 // $Id: signcond.lib,v 1.3 20050506 11:17:33 Singular Exp $ 2 2 // E. Tobis 12.Nov.2004 3 3 // last change 16. Apr. 2005 (G.M. Greuel) … … 14 14 15 15 PROCEDURES: 16 signcnd(P,I) The sign conditions realized thepolynomials of P on a V(I)16 signcnd(P,I) The sign conditions realized by polynomials of P on a V(I) 17 17 psigncnd(P,l) Pretty prints the output of signcnd (l) 18 18 firstoct(I) The number of elements of V(I) with every coordinate > 0 … … 27 27 proc firstoct(ideal I) 28 28 "USAGE: firstoct(i); i ideal 29 RETURN: number: the number of points of V(i) lying in the first o rthant29 RETURN: number: the number of points of V(i) lying in the first octant 30 30 ASSUME: i is a Groebner basis 31 31 SEE ALSO: signcnd … … 70 70 71 71 proc signcnd(ideal P,ideal I) 72 "USAGE: signcnd(P, i); ideal P,i. i must be a grobner basis72 "USAGE: signcnd(P,I); ideal P,I 73 73 RETURN: list: the sign conditions realized by the polynomials of P on V(I). 74 See the example for an explanation of the output. 75 SEE ALSO: firstoct 74 The output of signcnd is a list of two lists. Both lists have the 75 same length. That length is the number of sign conditions realized 76 by the polynomials of P on the set V(i). 77 Each element of the first list indicates a sign condition of the 78 polynomials of P. 79 Each element of the second list indicates how many elements of V(I) 80 give rise to the sign condition expressed by the same position on 81 the first list. 82 See the example for further explanation of the output. 83 ASSUME: I is a Groebner basis 84 NOTE: The procedure psigncnd performs some pretty printing of this output 85 SEE ALSO: firstoct, psigncnd 76 86 EXAMPLE: example signcnd; shows an example" 77 87 { … … 242 252 } 243 253 example 244 { 245 echo = 2; 254 { echo = 2; 246 255 ring r = 0,(x,y),dp; 247 256 ideal i = (x2)*(x+3)*x,y*(y1); 248 257 ideal P = x,y; 249 258 list l = signcnd(P,i); 250 echo = 0; 251 252 print("The output of signcnd is a list of two lists. Both lists have the 253 same"); 254 print("length. That length is the number of sign conditions realized by the"); 255 print ("polynomials of P on the set V(i). In this example, that number 256 is"); 257 print("print(size(l[1]));"); 258 print(size(l[1])); 259 print("Each element of the first list indicates a sign condition of the"); 260 print("polynomials of P. For example,"); 261 print("print(l[1][2]);"); 262 print(l[1][2]); 263 print("means P[1] > 0,P[2] = 0"); 264 print("Each element of the second list indicates how many elements of V(I)"); 265 print("give rise to the sign condition expressed by the same position on the"); 266 print("first list. For example"); 267 print("print(l[2][2]);"); 268 print(l[2][2]); 269 print("indicates that exactly 1 elemnt of V(I) gives rise to the condition"); 270 print("P[1] > 0,P[2] = 0."); 271 print("The procedure psigncnd performs some pretty printing on this output."); 259 260 size(l[1]); // = the number of sign conditions of P on V(i) 261 262 //Each element of l[1] indicates a sign condition of the polynomials of P. 263 //The following means P[1] > 0, P[2] = 0: 264 l[1][2]; 265 266 //Each element of l[2] indicates how many elements of V(I) give rise to 267 //the sign condition expressed by the same position on the first list. 268 //The following means that exactly 1 element of V(I) gives rise to the 269 //condition P[1] > 0, P[2] = 0: 270 l[2][2]; 272 271 } 273 272 /////////////////////////////////////////////////////////////////////////////// 274 273 275 274 proc psigncnd(ideal P,list l) 276 "USAGE: psigncnd(P, I); ideal P, list l275 "USAGE: psigncnd(P,l); ideal P, list l 277 276 RETURN: list: a formatted version of l 278 277 SEE ALSO: signcnd … … 438 437 /////////////////////////////////////////////////////////////////////////////// 439 438 439
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