Changeset f42f106 in git
- Timestamp:
- Jul 21, 1999, 11:55:35 AM (25 years ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- 9139a2542fdbd4dd772ac6494d00af0985a1d7a4
- Parents:
- bb9d6dea650af33c4445435cce27a639c58d4a08
- File:
-
- 1 edited
-
Singular/LIB/spcurve.lib (modified) (16 diffs)
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Singular/LIB/spcurve.lib
rbb9d6d rf42f106 1 // $Id: spcurve.lib,v 1. 6 1999-07-20 08:47:19 SingularExp $1 // $Id: spcurve.lib,v 1.7 1999-07-21 09:55:35 anne Exp $ 2 2 // (anne, last modified 31.5.99) 3 3 ///////////////////////////////////////////////////////////////////////////// 4 4 5 version="$Id: spcurve.lib,v 1. 6 1999-07-20 08:47:19 SingularExp $";5 version="$Id: spcurve.lib,v 1.7 1999-07-21 09:55:35 anne Exp $"; 6 6 info=" 7 LIBRARY: spcurve.lib PROCEDURES FOR CM CODIMENSION 2 SINGULARITIES8 AUTHOR: Anne Fruehbis-Krueger, anne@mathematik.uni-kl.de7 LIBRARY: spcurve.lib PROCEDURES FOR CM CODIMENSION 2 SINGULARITIES 8 AUTHOR: Anne Fruehbis-Krueger, anne@mathematik.uni-kl.de 9 9 last modified: 31.5.99 10 SEE ALSO: sing_lib, deform_lib 10 11 11 12 PROCEDURES: … … 31 32 32 33 proc isCMcod2(ideal kurve) 33 "USAGE: isCMcod2(i); i an ideal 34 RETURN: presentation matrix of i, if i is Cohen-Macaulay of codimension2 35 a zero matrix otherwise 36 EXAMPLE: example isCMcod2; shows an example" 34 "USAGE: @code{isCMcod2(i)}; @code{i} ideal 35 RETURN: presentation matrix of @code{i}, if @code{i} is Cohen-Macaulay of codimension 2 36 @* a zero matrix otherwise 37 EXAMPLE: @code{example isCMcod2}; shows an example 38 " 37 39 { 38 40 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 62 64 63 65 proc CMtype(ideal kurve) 64 "USAGE: CMtype(i); i an ideal, CM of codimension 2 65 RETURN: Cohen-Macaulay type of i (integer) 66 (-1, if i is not Cohen-Macaulay of codimension 2) 67 EXAMPLE: example CMtype; shows an example" 66 "USAGE: @code{CMtype(i)}; @code{i} ideal, CM of codimension 2 67 RETURN: Cohen-Macaulay type of @code{i} (integer) 68 @*(-1, if i is not Cohen-Macaulay of codimension 2) 69 EXAMPLE: @code{example CMtype}; shows an example 70 " 68 71 { 69 72 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 98 101 99 102 proc matrixT1(matrix M ,int n) 100 "USAGE: matrixT1(M,n); M matrix, ninteger101 ASSUME: Mis a presentation matrix of an ideal i, CM of codimension 2;102 consider i as a family of ideals in a ring in the first n103 "USAGE: @code{matrixT1(M,n)}; @code{M} matrix, @code{n} integer 104 ASSUME: @code{M} is a presentation matrix of an ideal i, CM of codimension 2; 105 @* consider i as a family of ideals in a ring in the first @code{n} 103 106 variables where the remaining variables are considered as 104 107 parameters 105 RETURN: list consisting of the k x (k+1) matrix M and a module K_M such that 106 T1=Mat(k,k+1;R)/K_M is the space of first order deformations of i 107 EXAMPLE: example matrixT1; shows an example" 108 RETURN: list consisting of the k x (k+1) matrix @code{M} and a 109 module @math{K_M} such that @math{T1=Mat(k,k+1;R)/K_M} is the space 110 of first order deformations of i 111 EXAMPLE: @code{example matrixT1}; shows an example 112 " 108 113 { 109 114 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 190 195 191 196 proc semiCMcod2(matrix M, module t1) 192 "USAGE: semiCMcod2(M,t1); M matrix, t1 module 193 ASSUME: M is a presentation matrix of an ideal i, CM of codimension 2, 194 and t1 is a presentation of the space of first order deformations 195 of i ((M,t1) as returned by the procedure matrixT1) 197 "USAGE: @code{semiCMcod2(M,t1)}; @code{M} matrix, @code{t1} module 198 ASSUME: @code{M} is a presentation matrix of an ideal i, CM of codimension 2, 199 and @code{t1} is a presentation of the space of first order 200 deformations of i (@code{(M,t1)} as returned by the procedure 201 @code{matrixT1}) 196 202 CREATE: new basering with name rneu 197 203 RETURN: ideal in rneu describing the semiuniversal deformation of i 198 204 NOTE: The current basering should not contain any variables named 199 205 A(j) where j is some integer! 200 EXAMPLE: example semiCMcod2; shows an example" 206 EXAMPLE: @code{example semiCMcod2}; shows an example 207 " 201 208 { 202 209 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 269 276 270 277 proc discr(ideal kurve, int n) 271 "USAGE: discr(sem,n); sem ideal, ninteger272 ASSUME: semis the versal deformation of an ideal of codimension 2273 the first n variables of the ring are treated as variables278 "USAGE: @code{discr(sem,n)}; @code{sem} ideal, @code{n} integer 279 ASSUME: @code{sem} is the versal deformation of an ideal of codimension 2 280 @*the first n variables of the ring are treated as variables 274 281 all the others as parameters 275 282 RETURN: ideal describing the discriminant 276 283 NOTE: This is not a powerful algorithm! 277 EXAMPLE: example discr; shows an example" 284 EXAMPLE: @code{example discr}; shows an example 285 " 278 286 { 279 287 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 323 331 324 332 proc qhmatrix(matrix M) 325 "USAGE: qhmatrix(M); Ma k x (k+1) matrix333 "USAGE: @code{qhmatrix(M)}; @code{M} a k x (k+1) matrix 326 334 RETURN: list, consisting of an integer vector containing the weights of 327 335 the variables of the basering and an integer matrix giving the 328 weights of the entries of M, if Mis quasihomogeneous;329 zero integer vector and zero integer matrix, if Mis not336 weights of the entries of @code{M}, if @code{M} is quasihomogeneous; 337 @*zero integer vector and zero integer matrix, if @code{M} is not 330 338 quasihomogeneous, i.e. does not allow row and column weights 331 EXAMPLE: example qhmatrix; shows an example" 339 EXAMPLE: @code{example qhmatrix}; shows an example 340 " 332 341 { 333 342 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 503 512 504 513 proc relweight(matrix N, intmat W, intvec a) 505 "USAGE: relweight(N,W,a); N matrix, W intmat, a intvec 506 ASSUME: N is a non-zero matrix 507 W is an integer matrix of the same size as N 508 a is an integer vector giving the weights of the variables 509 RETURN: integer, max(a-weighted order(N_ij) - W_ij | all entries ij) 510 string \"ERROR\" if sizes do not match 511 EXAMPLE: example relweight; shows an example" 514 "USAGE: @code{relweight(N,W,a)}; @code{N} matrix, @code{W} intmat, @code{a} intvec 515 ASSUME: @code{N} is a non-zero matrix 516 @* @code{W} is an integer matrix of the same size as @code{N} 517 @* @code{a} is an integer vector giving the weights of the variables 518 RETURN: integer, @math{max(a-weighted order(N_ij) - W_ij | all entries ij)} 519 @* string \"ERROR\" if sizes do not match 520 EXAMPLE: @code{example relweight}; shows an example 521 " 512 522 { 513 523 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 564 574 565 575 proc posweight(matrix M, module t1, int choose, list #) 566 "USAGE: posweight(M,t1,n[,s]); M matrix, t1 module, n int, sstring567 n=0 : all deformations of non-negative weight568 n=1 : only non-constant deformations of non-negative weight569 n=2 : all deformations of positive weight570 As an optional parameter the name of a new ring may be576 "USAGE: @code{posweight(M,t1,n[,s])}; @code{M} matrix, @code{t1} module, @code{n} int, @code{s} string 577 @*@code{n}=0 : all deformations of non-negative weight 578 @*@code{n}=1 : only non-constant deformations of non-negative weight 579 @*@code{n}=2 : all deformations of positive weight 580 @*As an optional parameter the name of a new ring may be 571 581 specified. 572 ASSUME: M is a presentation matrix of a Cohen-Macaulay codimension 2 573 ideal and t1 is its T1 space in matrix notation 582 ASSUME: @code{M} is a presentation matrix of a Cohen-Macaulay codimension 2 583 ideal and @code{t1} is a presentation of its T1 space in matrix 584 notation 574 585 CREATE: new basering (default name: rneu); a different name for this ring 575 586 may be given as a 4th parameter … … 579 590 NOTE: The current basering should not contain any variables named 580 591 T(i) where i is some integer! 581 EXAMPLE: example posweight; shows an example" 592 EXAMPLE: @code{example posweight}; shows an example 593 " 582 594 { 583 595 //--------------------------------------------------------------------------- … … 725 737 726 738 proc KSpencerKernel(matrix M,list #) 727 "USAGE: KSpencerKernel(M[,s][,v]); M matrix, s string, vintvec728 optional parameters (please specify in this order, if both are739 "USAGE: @code{KSpencerKernel(M[,s][,v])}; @code{M} matrix, @code{s} string, @code{v} intvec 740 @*optional parameters (please specify in this order, if both are 729 741 present): 730 * s= first of the names of the new rings731 e.g. \"R\" leads to ring names R and R1732 * vof size n(n+1) leads to the following module ordering733 gen(v[1]) > gen(v[2]) > ... > gen(v[n(n+1)])734 where the matrix entry ij corresponds to gen((i-1)*n+j)735 ASSUME: M is a quasihomogeneous n x (n+1) matrix where the n minors define736 an isolated space curve singularity742 @* * @code{s} = first of the names of the new rings 743 @* e.g. \"R\" leads to ring names R and R1 744 @* * @code{v} of size n(n+1) leads to the following module ordering 745 @* @code{gen(v[1]) > gen(v[2]) > ... > gen(v[n(n+1)])} 746 @* where the matrix entry ij corresponds to @code{gen((i-1)*n+j)} 747 ASSUME: @code{M} is a quasihomogeneous n x (n+1) matrix where the n minors 748 define an isolated space curve singularity 737 749 CREATE: 2 new rings (default names: rneu and reneu) 738 750 different ring names may be specified as a 2nd parameter … … 745 757 * setting an intvec with 5 entries and name watchProgress 746 758 shows the progress of the computations: 747 watchProgress[1]>0 => option(prot) in groebner commands 748 watchProgress[2]>0 => trace output for highcorner 749 watchProgress[3]>0 => output of deformed matrix 750 watchProgress[4]>0 => result of elimination step 751 watchProgress[4]>1 => trace output of multiplications with xyz 752 and subsequent reductions 753 watchProgress[5]>0 => matrix representing the kernel 754 using print 755 EXAMPLE: example KSpencerKernel; shows an example" 759 @* watchProgress[1]>0 => option(prot) in groebner commands 760 @* watchProgress[2]>0 => trace output for highcorner 761 @* watchProgress[3]>0 => output of deformed matrix 762 @* watchProgress[4]>0 => result of elimination step 763 @* watchProgress[4]>1 => trace output of multiplications with xyz 764 @* and subsequent reductions 765 @* watchProgress[5]>0 => matrix representing the kernel 766 @* using print 767 EXAMPLE: @code{example KSpencerKernel}; shows an example 768 " 756 769 { 757 770 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 912 925 if (defined(newname)>1) 913 926 { 914 list li=posweight(M,mo, 0,newname+"1");927 list li=posweight(M,mo,2,newname+"1"); 915 928 def rneu=basering; 916 929 } 917 930 else 918 931 { 919 list li=posweight(M,mo, 0);932 list li=posweight(M,mo,2); 920 933 } 921 934 if (size(li)<=1) … … 1101 1114 1102 1115 proc mod2id(matrix M,intvec vpos) 1103 "USAGE: mod2id(M,vpos); M matrix, vposintvec1104 ASSUME: vpos is an integer vector such that gen(i)corresponds1105 to var(vpos[i])1106 the basering contains variables var(vpos[i]) which do not occur1107 in M1116 "USAGE: @code{mod2id(M,vpos)}; @code{M} matrix, @code{vpos} intvec 1117 ASSUME: @code{vpos} is an integer vector such that @code{gen(i)} corresponds 1118 to @code{var(vpos[i])} 1119 @*the basering contains variables @code{var(vpos[i])} which do not 1120 occur in @code{M} 1108 1121 NOTE: this procedure should be used in the following situation: 1109 1122 one wants to pass to a ring with new variables, say e(1),..,e(s), 1110 1123 which correspond to the components gen(1),..,gen(s) of the 1111 module Msuch that e(i)*e(j)=0 for all i,j1124 module @code{M} such that e(i)*e(j)=0 for all i,j 1112 1125 the new ring should already exist and be the current ring 1113 RETURN: ideal i in which each gen(i) from the module is replaced by 1114 var(vpos[i]) and all monomials var(vpos[i])*var(vpos[j]) have 1115 been added to the generating set of i 1116 EXAMPLE: example mod2id; shows an example" 1126 RETURN: ideal i in which each gen(i) from the module is replaced by 1127 @code{var(vpos[i])} and all monomials @code{var(vpos[i])*var(vpos[j])} 1128 have been added to the generating set of i 1129 EXAMPLE: @code{example mod2id}; shows an example 1130 " 1117 1131 { 1118 1132 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 1150 1164 1151 1165 proc id2mod(ideal i,intvec vpos) 1152 "USAGE: id2mod(I,vpos); I ideal, vposintvec1166 "USAGE: @code{id2mod(I,vpos)}; @code{I} ideal, @code{vpos} intvec 1153 1167 NOTE: * use this procedure only makes sense if the ideal contains 1154 all var(vpos[i])*var(vpos[j])as monomial generators and1168 all @code{var(vpos[i])*var(vpos[j])} as monomial generators and 1155 1169 all other generators are linear combinations of the 1156 var(vpos[i])over the ring in the other variables1157 * this is the inverse procedure to mod2id and should be applied1158 only to ideals created by mod2id using the same intvec vpos1159 (possibly after a standard basis computation)1160 RETURN: module corresponding to the ideal by replacing var(vpos[i])by1161 gen(i) and omitting all generators var(vpos[i])*var(vpos[j])1162 EXAMPLE: example id2mod; shows an example"1170 @code{var(vpos[i])} over the ring in the other variables 1171 @* * this is the inverse procedure to @code{mod2id} and should be 1172 applied only to ideals created by @code{mod2id} using the same 1173 intvec @code{vpos} (possibly after a standard basis computation) 1174 RETURN: module corresponding to the ideal by replacing @code{var(vpos[i])} by 1175 gen(i) and omitting all generators @code{var(vpos[i])*var(vpos[j])} 1176 EXAMPLE: @code{example id2mod}; shows an example" 1163 1177 { 1164 1178 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1) … … 1195 1209 1196 1210 proc subrInterred(ideal mon, ideal sm, intvec iv) 1197 "USAGE: subrInterred(mon,sm,iv);1198 sm: ideal in a ring r with n + s variables,1211 "USAGE: @code{subrInterred(mon,sm,iv)}; 1212 @*@code{sm}: ideal in a ring r with n + s variables, 1199 1213 e.g. x_1,..,x_n and t_1,..,t_s 1200 mon: ideal with monomial generators (not divisible by1214 @*@code{mon}: ideal with monomial generators (not divisible by 1201 1215 one of the t_i) such that sm is contained in the module 1202 k[t_1,..,t_s]*mon[1]+..+k[t_1,..,t_s]*mon[size(mon)]1203 iv: intvec listing the variables which are supposed to be used1204 as x_i1216 @code{k[t_1,..,t_s]*mon[1]+..+k[t_1,..,t_s]*mon[size(mon)]} 1217 @*@code{iv}: intvec listing the variables which are supposed to be 1218 used as x_i 1205 1219 RETURN: interreduced system of generators of sm seen as a submodule 1206 of k[t_1,..,t_s]*mon[1]+..+k[t_1,..,t_s]*mon[size(mon)] 1207 EXAMPLE: example subrInterred; shows an example" 1220 of @code{k[t_1,..,t_s]*mon[1]+..+k[t_1,..,t_s]*mon[size(mon)]} 1221 EXAMPLE: @code{example subrInterred}; shows an example 1222 " 1208 1223 { 1209 1224 int p = printlevel-voice+3; // p=printlevel+1 (default: p=1)
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