Changeset 80b3cd in git
- Timestamp:
- Aug 3, 1999, 3:01:02 PM (25 years ago)
- Branches:
- (u'spielwiese', '5b153614cbc72bfa198d75b1e9e33dab2645d9fe')
- Children:
- 46e39d5cb05fa4ee94268859b7b06dfdb5e76678
- Parents:
- 0914249ec3414c61666a68fde6a8c2bb3babd2d2
- File:
-
- 1 edited
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Singular/LIB/primdec.lib
r091424 r80b3cd 1 // $Id: primdec.lib,v 1.4 3 1999-08-03 11:43:09obachman Exp $1 // $Id: primdec.lib,v 1.44 1999-08-03 13:01:02 obachman Exp $ 2 2 /////////////////////////////////////////////////////////////////////////////// 3 3 // primdec.lib // … … 11 11 /////////////////////////////////////////////////////////////////////////////// 12 12 13 version="$Id: primdec.lib,v 1.4 3 1999-08-03 11:43:09obachman Exp $";13 version="$Id: primdec.lib,v 1.44 1999-08-03 13:01:02 obachman Exp $"; 14 14 info=" 15 15 LIBRARY: primdec.lib: PROCEDURES FOR PRIMARY DECOMPOSITION … … 17 17 Wolfram Decker, email: decker@math.uni-sb.de (SY) 18 18 Hans Schoenemann, email: hannes@mathematik.uni-kl.de (SY) 19 last change: 99/07/2320 19 21 20 PROCEDURES: 22 primdecGTZ(I); complete primary decomposition via Gianni,Trager,Zacharias23 primdecSY(I );complete primary decomposition via Shimoyama-Yokoyama24 minAssGTZ(I); the minimal associated primes via Gianni,Trager,Zacharias25 minAssChar(I );the minimal associated primes using characteristic sets26 testPrimary( ..); tests the result of the primary decomposition27 radical(I); computes the radical of the ideal I28 equiRadical(I); the radical of the equidimensional part of the ideal I29 prepareAss(I); list of radicals of the equidimensional components of I21 primdecGTZ(I); complete primary decomposition via Gianni,Trager,Zacharias 22 primdecSY(I...); complete primary decomposition via Shimoyama-Yokoyama 23 minAssGTZ(I); the minimal associated primes via Gianni,Trager,Zacharias 24 minAssChar(I...); the minimal associated primes using characteristic sets 25 testPrimary(L,k); tests the result of the primary decomposition 26 radical(I); computes the radical of the ideal I 27 equiRadical(I); the radical of the equidimensional part of the ideal I 28 prepareAss(I); list of radicals of the equidimensional components of I 30 29 31 30 REMARK: 32 33 34 35 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. 36 35 "; 37 36 … … 552 551 for(k=2;k<=r;k++) 553 552 { 554 keepprime[size(l)/2+k-1]=interred(keepprime[i]+ideal(act[1][k]));553 keepprime[size(l)/2+k-1]=interred(keepprime[i]+ideal(act[1][k])); 555 554 } 556 555 keepprime[i]=interred(keepprime[i]+ideal(act[1][1])); … … 875 874 if(lead(primary[2*@k-1][@n])/var(zz)!=0) 876 875 { 877 jmap1[zz]=-1/leadcoef(primary[2*@k-1][@n])*primary[2*@k-1][@n]876 jmap1[zz]=-1/leadcoef(primary[2*@k-1][@n])*primary[2*@k-1][@n] 878 877 +2/leadcoef(primary[2*@k-1][@n])*lead(primary[2*@k-1][@n]); 879 878 jmap2[zz]=primary[2*@k-1][@n]; … … 1582 1581 int j,k,odim,ndim,count; 1583 1582 attrib(@pr[1],"isSB",1); 1584 1583 if(#[1]==77) 1584 { 1585 odim=dim(@pr[1]); 1586 count=1; 1587 intvec pos; 1588 pos[size(@pr)]=0; 1589 for(j=2;j<=size(@pr);j++) 1590 { 1591 attrib(@pr[j],"isSB",1); 1592 ndim=dim(@pr[j]); 1593 if(ndim>odim) 1594 { 1595 for(k=count;k<=j-1;k++) 1596 { 1597 pos[k]=1; 1598 } 1599 count=j; 1600 odim=ndim; 1601 } 1602 if(ndim<odim) 1603 { 1604 pos[j]=1; 1605 } 1606 } 1607 for(j=1;j<=size(@pr);j++) 1608 { 1609 if(pos[j]!=1) 1610 { 1611 @res[j]=decomp(@pr[j],2); 1612 } 1613 else 1614 { 1615 @res[j]=empty; 1616 } 1617 } 1618 } 1619 else 1620 { 1585 1621 ser=ideal(1); 1586 1622 for(j=1;j<=size(@pr);j++) … … 1595 1631 // } 1596 1632 } 1633 } 1597 1634 1598 1635 @res=union(@res); … … 3993 4030 /////////////////////////////////////////////////////////////////////////////// 3994 4031 3995 proc primdecSY(ideal i )4032 proc primdecSY(ideal i, list #)) 3996 4033 "USAGE: primdecSY(i); i ideal, c int 3997 4034 if c=0, the given ordering of the variables is used. … … 4048 4085 Otherwise, the system tries to find an optimal ordering, 4049 4086 which in some cases may considerably speed up the algorithm 4087 RETURN: list = the minimal associated prime ideals of i 4050 4088 NOTE: implemented for characteristic 0, works also in char k >> 0, 4051 4089 the result may be not compltely decomposed in small characteristic … … 4071 4109 "USAGE: equiRadical(i); i ideal 4072 4110 RETURN: ideal, intersection of associated primes of i of maximal dimension 4073 NOTE: designed for characteristic 0, works also in char k > 0 if it termi-4074 nates, may result in an infinite loop in small characteristic4111 NOTE: designed for characteristic 0, works also in char k > 0 if it 4112 terminates, may result in an infinite loop in small characteristic 4075 4113 EXAMPLE: example equiRadical; shows an example 4076 4114 "
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