Changeset 22c0fc9 in git
 Timestamp:
 Jun 9, 1999, 11:49:47 AM (24 years ago)
 Branches:
 (u'jengelhdatetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
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 8ef5750b7a3298e63ae583dd8949e9ec89e70622
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 6047f66a1c9dd5e774d56bb4724616bc964ab76c
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 1 edited
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Singular/LIB/primdec.lib
r6047f6 r22c0fc9 1 // $Id: primdec.lib,v 1.3 2 19990608 15:54:46 pfister Exp $1 // $Id: primdec.lib,v 1.33 19990609 09:49:47 Singular Exp $ 2 2 //////////////////////////////////////////////////////////////////////////////// 3 3 // primdec.lib // … … 11 11 //////////////////////////////////////////////////////////////////////////////// 12 12 13 version="$Id: primdec.lib,v 1.3 2 19990608 15:54:46 pfister Exp $";13 version="$Id: primdec.lib,v 1.33 19990609 09:49:47 Singular Exp $"; 14 14 info=" 15 15 LIBRARY: primdec.lib: PROCEDURE FOR PRIMARY DECOMPOSITION … … 29 29 of the ideal I 30 30 prepareAss(I); computes the radicals of the equidimensional parts of I 31 These procedures are implemented to be used in characteristic 0. 32 They work also in positive characteristic >> 0. 33 In small characteristic primdecGTZ, minAssGTZ, radical and equiRadical may not 34 terminate and primdecSY and minAssChar may not give a complete decomposition. 31 35 "; 32 36 … … 491 495 "Warning: The characteristic ist too small to use"; 492 496 "the Algorithm of Gianni/Trager/Zacharias."; 493 "The result may be incomplete."; 494 "Try primdecSY"; 495 "The result may be also imcomplete."; 497 "This may result in an infinte loop"; 496 498 } 497 499 if (reduce(i[m]t^e,prm,1) !=0) … … 4032 4034 and their associated primes 4033 4035 NOTE: Algorithm of Gianni, Traeger, Zacharias 4036 designed for characteristic 0, works also in char k >> 0, 4037 may result in an infinite loop in small characteristic 4034 4038 EXAMPLE: example primdecGTZ; shows an example 4035 4039 " … … 4053 4057 and their associated primes 4054 4058 NOTE: Algorithm of ShimoyamaYokoyama 4059 implemented for characteristic 0, works also in char k >> 0, 4060 the result may be not compltely decomposed in small characteristic 4055 4061 EXAMPLE: example primdecSY; shows an example 4056 4062 " … … 4071 4077 "USAGE: minAssGTZ(i); i ideal 4072 4078 RETURN: list = the minimal associated prime ideals of i 4073 NOTE: 4079 NOTE: designed for characteristic 0, works also in char k >> 0, 4080 may result in an infinite loop in small characteristic 4074 4081 EXAMPLE: example minAssGTZ; shows an example 4075 4082 " … … 4091 4098 "USAGE: minAssChar(i); i ideal 4092 4099 RETURN: list = the minimal associated prime ideals of i 4093 NOTE: 4100 NOTE: implemented for characteristic 0, works also in char k >> 0, 4101 the result may be not compltely decomposed in small characteristic 4102 EXAMPLE: example primdecSY; shows an example 4103 " 4104 { 4105 return(prim_dec(i,1)); 4106 } 4107 example 4108 { "EXAMPLE:"; echo = 2; 4109 ring r = 32003,(x,y,z),lp; 4110 poly p = z2+1; 4111 poly q = z4+2; 4112 ideal i = p^2*q^3,(yz3)^3,(xyz+z4)^4; 4113 list pr= primdecSY(i); 4114 pr; 4115 } 4116 /////////////////////////////////////////////////////////////////////////////// 4117 proc minAssGTZ(ideal i) 4118 "USAGE: minAssGTZ(i); i ideal 4119 RETURN: list = the minimal associated prime ideals of i 4120 NOTE: designed for characteristic 0, works also in char k >> 0, 4121 may result in an infinite loop in small characteristic 4122 EXAMPLE: example minAssGTZ; shows an example 4123 " 4124 { 4125 return(minAssPrimes(i,1)); 4126 } 4127 example 4128 { "EXAMPLE:"; echo = 2; 4129 ring r = 32003,(x,y,z),dp; 4130 poly p = z2+1; 4131 poly q = z4+2; 4094 4132 EXAMPLE: example minAssChar; shows an example 4095 4133 " … … 4113 4151 RETURN: ideal = the intersection of associated primes 4114 4152 of i of dimension of i 4115 NOTE: 4153 NOTE: designed for characteristic 0, works also in char k >> 0, 4154 may result in an infinite loop in small characteristic 4116 4155 EXAMPLE: example equiRadical; shows an example 4117 4156 " … … 4134 4173 NOTE: a combination of the algorithms of Krick/Logar 4135 4174 and Eisenbud/Huneke/Vasconcelos 4175 designed for characteristic 0, works also in char k >> 0, 4176 may result in an infinite loop in small characteristic 4136 4177 EXAMPLE: example radical; shows an example 4137 4178 "
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