Changeset dbe481 in git
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 Jul 20, 2015, 11:47:44 AM (8 years ago)
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Singular/LIB/classify_aeq.lib
rb33f5c0 rdbe481 7 7 AUTHORS: Faira Kanwal Janjua fairakanwaljanjua@gmail.com 8 8 Gerhard Pfister pfister@mathematik.unikl.de 9 Khawar Mehmood khawar1073@gmail.com NEU 9 10 10 11 OVERVIEW: A library for classifying the simple singularities … … 22 23 [4] Bruce, J.W.,Gaffney, T.J.: Simple singularities of mappings (C, 0) >(C2,0). 23 24 J. London Math. Soc. (2) 26 (1982), 465474. 24 25 [5] Ishikawa,G; Janeczko,S.: The Complex Symplectic Moduli Spaces of Unimodal Parametric Plane Curve NEU Singularities. Insitute of Mathematics of the Polish Academy of Sciences,Preprint 664(2006) 25 26 PROCEDURES: 26 27 sagbiAlg(G); Compute the Sagbibasis of the Algebra. … … 662 663 663 664 //////////////////////////////////////////////////////////////////////////////// 664 proc sagbiAlg(ideal I )665 proc sagbiAlg(ideal I,list #) 665 666 "USAGE": sagbiAlg(I); I ideal 666 667 RETURN: An ideal.The sagbi bases of I. … … 676 677 677 678 if(size(I)==0){return(I);} 678 int b=ConductorBound(I); 679 680 // int b=200; 679 if(size(#)==0) 680 { 681 int b=ConductorBound(I); 682 // int b=200; 681 683 // b=correctBound(I,b); 684 } 685 else 686 { 687 int b=#[1]; 688 } 682 689 ideal S=interReduceSagbi(I,b) ; 683 690 // b=correctBound(S,b); … … 699 706 return(S); 700 707 } 701 702 708 example 703 709 { … … 709 715 sagbiAlg(I); 710 716 } 711 717 //////////////////////////////////////////////////////////////////////////////// NEU 718 proc reducedSagbiAlg(ideal I,list #) 719 { 720 721 I=sagbiAlg(I,#); 722 intvec L=semiGroup(I)[3]; 723 if(size(#)==0) 724 { 725 int b=findConductor(L); 726 } 727 else 728 { 729 int b=#[1]; 730 } 731 int i; 732 poly q; 733 for(i=1;i<=size(I);i++) 734 { 735 q=I[i]lead(I[i]); 736 q=sagbiNF(q,I,b); 737 I[i]=lead(I[i])+q; 738 } 739 return(I); 740 } 741 example 742 { 743 "EXAMPLE:"; echo=2; 744 ring R=0,t,ds; 745 ideal I=t4+2t9,t9+t10+19/18t113t12+t13t14; 746 reducedSagbiAlg(I); 747 } 748 //////////////////////////////////////////////////////////////////////////////// NEU 749 proc classifyAEQunimodal(ideal I) 750 "USAGE": classifyAEQunimodal(I); I ideal generated by 2 polynomials 751 RETURN: An ideal.Ideal is one of the singularity in the list of Ishikawa and Jenczko [5] 752 EXAMPLE: example classifyAEQunimodal; shows an example 753 " 754 { 755 def R=basering; 756 ring @S=0,t,ds; 757 ideal I=fetch(R,I); 758 ideal J; 759 poly g; 760 if(size(I)>=3){ERROR("not a plane curve");} 761 I=simplify(I,2); //deletes zeroâs i I 762 I=simplify(I,1); //creates monic generators in I 763 if(ord(I[1])>ord(I[2])){poly q=I[2];I[2]=I[1];I[1]=q;} 764 if((ord(I[1])>=6)(ord(I[1])<=3)){return("not in the unimodal list");} 765 //compute estimate of the term with the modulus 766 int c=ord(sagbiNF(I[2],ideal(I[1]),10)); 767 if(c==10) 768 { 769 if(ord(I[1])!=4){return("not in the unimodal list");} 770 c=ord(I[2][2])+2; 771 } 772 else 773 { 774 c=0; 775 intvec v=ord(I[1]),ord(I[2]); 776 if(v==intvec(5,6)){c=14;} 777 if(v==intvec(5,7)){c=18;} 778 if(v==intvec(5,8)){c=22;} 779 if(v==intvec(4,9)){c=19;} 780 if(v==intvec(4,11)){c=25;} 781 if(c==0){return("not in the unimodal list");} 782 } 783 while(size(I[1])>1) 784 { 785 I=jet(subst(I,t,tnumber(1)/number(ord(I[1]))*leadcoef(I[1][2])*t^(ord(I[1][2])ord(I[1])+1)),c); 786 } 787 ideal G=I; 788 G[2]=sagbiNF(G[2],ideal(G[1]),c); 789 ideal M=sagbiMod(diff(G,t),G); 790 list K=semiMod(M,G); 791 792 if(K[1]==intvec(4,9)) 793 { 794 if(K[4]==intvec(3,8)){J=t4,t9;} 795 if(K[4]==intvec(3,8,22)){J=t4,t9+t19;} 796 if(K[4]==intvec(3,8,18)){J=t4,t9+t15;} 797 if(K[4]==intvec(3,8,14)){J=t4,t9+t11;} 798 if(K[4]==intvec(3,8,13)) 799 { 800 G=reducedSagbiAlg(G,15); 801 if(ord(G[2][4])==14) 802 { 803 //kill the term t14 by some transformation 804 G=subst(G,t,tleadcoef(G[2][4])/9*t^6); 805 G=jet(G,15); 806 G[1]=sagbiNF(G[1],ideal(G[2]),15); 807 //arrange the first element to be t4 808 while(size(G[1])>1) 809 { 810 G=subst(G,t,t1/4*(G[1]lead(G[1]))/t^3); 811 G=jet(G,15); 812 } 813 } 814 G[2]=sagbiNF(G[2],ideal(G[1]),15); 815 //arrange the coefficient of t10 to become 1 816 number m=leadcoef(G[2]lead(G[2])); 817 G[2]=m^9*subst(G[2],t,1/m*t); 818 J=G; 819 } 820 if(K[4]==intvec(3,8,13,18)) 821 { 822 G=reducedSagbiAlg(G,11); 823 number m=leadcoef(G[2]lead(G[2])); 824 G[2]=m^9*subst(G[2],t,1/m*t); 825 J=G; 826 } 827 } 828 if(K[1]==intvec(4,11)) 829 { 830 if(K[4]==intvec(3,10)){J=t4,t11;} 831 if(K[4]==intvec(3,10,28)){J=t4,t11+t25;} 832 if(K[4]==intvec(3,10,24)){J=t4,t11+t21;} 833 if(K[4]==intvec(3,10,20)){J=t4,t11+t17;} 834 if(K[4]==intvec(3,10,16)) 835 { 836 G=reducedSagbiAlg(G,14); 837 number m=leadcoef(G[2]lead(G[2])); 838 number l=leadcoef(G[2][3]); 839 //lambda^2=l^2/m^3 840 J=G; 841 } 842 if(K[4]==intvec(3,10,17)) 843 { 844 G=reducedSagbiAlg(G,21); 845 if(ord(G[2][4])==18) 846 { 847 //kill the term t18 by some transformation 848 G=subst(G,t,tleadcoef(G[2][4])/11*t^8); 849 G=jet(G,21); 850 G[1]=sagbiNF(G[1],ideal(G[2]),21); 851 //arrange the first element to be t4 852 while(size(G[1])>1) 853 { 854 G=subst(G,t,t1/4*(G[1]lead(G[1]))/t^3); 855 G=jet(G,21); 856 } 857 } 858 G[2]=sagbiNF(G[2],ideal(G[1]),21); 859 //arrange the coefficient of t14 to become 1 860 number m=leadcoef(G[2]lead(G[2])); 861 number l=leadcoef(G[2][4]); 862 //lambda^2=l^3/m^10 863 J=G; 864 865 866 } 867 if(K[4]==intvec(3,10,17,24)) 868 { 869 G=reducedSagbiAlg(G,18); 870 //arrange the coefficient of t14 to become 1 871 number m=leadcoef(G[2]lead(G[2])); 872 G[2]=t11+t14+leadcoef(G[2][3])/m^2*t17; 873 J=G; 874 } 875 } 876 if((size(K[1])==3)&&(K[1][1]==4)&&(K[1][2]==10)) 877 { 878 int l=(K[1][3]19) div 2; 879 G=reducedSagbiAlg(G,2*l+12); 880 number m=leadcoef(G[2]lead(G[2])); 881 number s=leadcoef(G[2][3]); 882 //lambda^(2l1)=s^(2l1)/m^(2l+1) 883 J=G; 884 } 885 if(K[1]==intvec(5,6)) 886 { 887 if(K[4]==intvec(4,5)){J=t5,t6;} 888 if(K[4]==intvec(4,5,18)){J=t5,t6+t14;} 889 if(K[4]==intvec(4,5,13)){J=t5,t6+t9;} 890 if(K[4]==intvec(4,5,12)) 891 { 892 G=reducedSagbiAlg(G,9); 893 if(ord(G[2][2])==7) 894 { 895 //kill the term t7 by some transformation 896 G=subst(G,t,tleadcoef(G[2][2])/6*t^2); 897 G=jet(G,10); 898 G[1]=sagbiNF(G[1],ideal(G[2]),9); 899 //arrange the first element to be t4 900 while(size(G[1])>1) 901 { 902 G=subst(G,t,t1/5*(G[1]lead(G[1]))/t^4); 903 G=jet(G,9); 904 } 905 } 906 G[2]=sagbiNF(G[2],ideal(G[1]),9); 907 //arrange the coefficient of t8 to become 1 908 number m=leadcoef(G[2]lead(G[2])); 909 number l=leadcoef(G[2][3]); 910 //lambda^2=l^2/m^3 911 J=G; 912 913 } 914 } 915 if(K[1]==intvec(5,7)) 916 { 917 if(K[4]==intvec(4,6)){J=t5,t7;} 918 if(K[4]==intvec(4,6,22)){J=t5,t7+t18;} 919 if(K[4]==intvec(4,6,17)){J=t5,t7+t13;} 920 if(K[4]==intvec(4,6,12)) 921 { 922 G=reducedSagbiAlg(G,11); 923 if(ord(G[2][3])==9) 924 { 925 //kill the term t9 by some transformation 926 G=subst(G,t,tleadcoef(G[2][3])/7*t^3); 927 G=jet(G,11); 928 G[1]=sagbiNF(G[1],ideal(G[2]),11); 929 //arrange the first element to be t4 930 while(size(G[1])>1) 931 { 932 G=subst(G,t,t1/5*(G[1]lead(G[1]))/t^4); 933 G=jet(G,11); 934 } 935 } 936 G[2]=sagbiNF(G[2],ideal(G[1]),11); 937 //arrange the coefficient of t8 to become 1 938 number m=leadcoef(G[2]lead(G[2])); 939 G[2]=m^7*subst(G[2],t,1/m*t); 940 J=G; 941 } 942 if(K[4]==intvec(4,6,15)) 943 { 944 G=reducedSagbiAlg(G,14); 945 if(ord(G[2][2])==9) 946 { 947 //kill the term t9 by some transformation 948 G=subst(G,t,tleadcoef(G[2][2])/7*t^3); 949 G=jet(G,14); 950 G[1]=sagbiNF(G[1],ideal(G[2]),14); 951 //arrange the first element to be t4 952 while(size(G[1])>1) 953 { 954 G=subst(G,t,t1/5*(G[1]lead(G[1]))/t^4); 955 G=jet(G,14); 956 } 957 } 958 G[2]=sagbiNF(G[2],ideal(G[1]),14); 959 //arrange the coefficient of t11 to become 1 960 number m=leadcoef(G[2]lead(G[2])); 961 number l=leadcoef(G[2][3]); 962 //lambda^2=l^2/m^3 963 J=G; 964 } 965 966 } 967 if(K[1]==intvec(5,8)) 968 { 969 if(K[4]==intvec(4,7)){J=t5,t8;} 970 if(K[4]==intvec(4,7,26)){J=t5,t8+t22;} 971 if(K[4]==intvec(4,7,21)){J=t5,t8+t17;} 972 if(K[4]==intvec(4,7,13)) 973 { 974 G=reducedSagbiAlg(G,12); 975 if(ord(G[2][3])==11) 976 { 977 //kill the term t11 by some transformation 978 G=subst(G,t,tleadcoef(G[2][3])/8*t^4); 979 G=jet(G,12); 980 G[1]=sagbiNF(G[1],ideal(G[2]),12); 981 //arrange the first element to be t4 982 while(size(G[1])>1) 983 { 984 G=subst(G,t,t1/5*(G[1]lead(G[1]))/t^4); 985 G=jet(G,12); 986 } 987 } 988 G[2]=sagbiNF(G[2],ideal(G[1]),12); 989 //arrange the coefficient of t9 to become 1 990 number m=leadcoef(G[2]lead(G[2])); 991 G[2]=m^8*subst(G[2],t,1/m*t); 992 J=G; 993 } 994 995 if(K[4]==intvec(4,7,16)) 996 { 997 G=reducedSagbiAlg(G,14); 998 if(ord(G[2][2])==11) 999 { 1000 //kill the term t11 by some transformation 1001 G=subst(G,t,tleadcoef(G[2][2])/8*t^4); 1002 G=jet(G,14); 1003 G[1]=sagbiNF(G[1],ideal(G[2]),14); 1004 //arrange the first element to be t4 1005 while(size(G[1])>1) 1006 { 1007 G=subst(G,t,t1/5*(G[1]lead(G[1]))/t^4); 1008 G=jet(G,14); 1009 } 1010 } 1011 G[2]=sagbiNF(G[2],ideal(G[1]),14); 1012 //arrange the coefficient of t12 to become 1 1013 number m=leadcoef(G[2]lead(G[2])); 1014 number l=leadcoef(G[2][3]); 1015 //lambda^2=l^2/m^3 1016 J=G; 1017 1018 } 1019 if(K[4]==intvec(4,7,18)) 1020 { 1021 G=reducedSagbiAlg(G,17); 1022 if(ord(G[2][2])==11) 1023 { 1024 //kill the term t11 by some transformation 1025 G=subst(G,t,tleadcoef(G[2][2])/8*t^4); 1026 G=jet(G,17); 1027 G[1]=sagbiNF(G[1],ideal(G[2]),17); 1028 //arrange the first element to be t4 1029 while(size(G[1])>1) 1030 { 1031 G=subst(G,t,t1/5*(G[1]lead(G[1]))/t^4); 1032 G=jet(G,17); 1033 } 1034 } 1035 G[2]=sagbiNF(G[2],ideal(G[1]),17); 1036 //arrange the coefficient of t12 to become 1 1037 number m=leadcoef(G[2]lead(G[2])); 1038 number l=leadcoef(G[2][3]); 1039 //lambda^2=l^2/m^3 1040 J=G; 1041 } 1042 } 1043 setring R; 1044 ideal J=fetch(@S,J); 1045 if(size(J)==0) 1046 { 1047 return("not in the unimodal list"); 1048 } 1049 return(J); 1050 } 1051 example 1052 { 1053 "EXAMPLE:"; echo=2; 1054 ring R=0,t,ds; 1055 ideal I=t4,9t9+18t10+38t11216t12+144t13288t14; 1056 classifyAEQunimodal(I); 1057 I=t4,9t9+18t10+40t11216t12+144t13288t14; 1058 classifyAEQunimodal(I); 1059 I=t4,t11+t12+3t14+2t15+7t16+7t17; 1060 classifyAEQunimodal(I); 1061 I=t4,t11+t14+25/22t17+3t18+4t21; 1062 classifyAEQunimodal(I); 1063 I=t5,t6+2t7+t8+3t9; 1064 classifyAEQunimodal(I); 1065 I=t5,t7+3t8+3t9+5t10; 1066 classifyAEQunimodal(I); 1067 I=t5,t7+3t11+3t12+5t13; 1068 classifyAEQunimodal(I); 1069 I=t5,t8+3t9+5t10+2t11+3t12+5t13; 1070 classifyAEQunimodal(I); 1071 I=t5,t8+5t11+3t12+7t13+5t14; 1072 classifyAEQunimodal(I); 1073 I=t5,t8+5t11+7t13+5t14+7t15+2t16+8t17; 1074 classifyAEQunimodal(I); 1075 I=subst(I,t,t+t2); 1076 classifyAEQunimodal(I); 1077 I=t4+2t5+3t6+5t7+t8,9t9+18t10+40t11216t12+144t13288t14; 1078 classifyAEQunimodal(I); 1079 } 1080 //////////////////////////////////////////////////////////////////////////////// NEU 1081 proc computeModulus(poly p) 1082 "USAGE": computeModulus(p); p monic poly with 3 or 4 monomials 1083 RETURN: A polynomial with first and second coefficient 1 1084 EXAMPLE: computeModulus; shows an example 1085 ASSUME: the basering has one vearable and one parameter 1086 " 1087 { 1088 def R=basering; 1089 int a1=ord(p); 1090 int a2=ord(plead(p)); 1091 number m=leadcoef(plead(p)); 1092 1093 poly q=par(1)^(a2a1)1/m; 1094 ring S=(0,a),t,ds; 1095 number m=fetch(R,m); 1096 minpoly=par(1)^(a2a1)1/m; 1097 poly p=fetch(R,p); 1098 p=1/par(1)^a1*subst(p,var(1),par(1)*var(1)); 1099 setring R; 1100 p=imap(S,p); 1101 return(list(p,q)); 1102 } 1103 example 1104 { 1105 "EXAMPLE:"; echo=2; 1106 ring R=(0,a),t,ds; 1107 poly p=t8395/16t14+4931/32t17; 1108 computeModulus(p); 1109 p=t8+3t12395/16t14; 1110 computeModulus(p); 1111 p=t8395/16t14+4931/32t17; 1112 computeModulus(p); 1113 1114 } 1115 1116 //////////////////////////////////////////////////////////////////////////////// NEU 1117 static proc n_thRoot(poly p,int n, int b) 1118 { 1119 //computes the nth root of 1+p up to order b 1120 //assumes that p(0)=0 1121 poly s=1; 1122 poly q=jet(p,b); 1123 if(q==0){return(s);} 1124 int i; 1125 for(i=1;i<=b;i++) 1126 { 1127 s=s+bino(n,i)*q; 1128 q=jet(q*p,b); 1129 } 1130 return(jet(s,b)); 1131 } 1132 //////////////////////////////////////////////////////////////////////////////// NEU 1133 static proc bino(number n, int i) 1134 { 1135 //computes the ith binomial coefficient of 1/n 1136 if(i==0){return(1);} 1137 return(bino(n,i1)*(1/ni+1)/i); 1138 } 712 1139 //////////////////////////////////////////////////////////////////////////////// 713 1140 proc sagbiMod(ideal I,ideal G) … … 1283 1710 execute 1284 1711 ("ring T=("+charstr(br)+",x(1),z(1..n)),(x(2),y(1..m)),dp;"); 1285 execute 1286 ("ring R=("+charstr(br)+"),(x(1..2),y(1..m),z(1..n)),(lp(m+2),dp(n));"); 1712 execute 1713 ("ring R=("+charstr(br)+"),(x(1..2),y(1..m),z(1..n)),(lp(2),dp(m),dp(n));"); 1714 1287 1715 map phi = br,x(1); 1288 1716 ideal P = phi(G1); … … 1305 1733 M[size(M)+1]=checkx(2); 1306 1734 check=check*keep; 1735 1307 1736 option(redSB); 1308 1737 M=std(M); 1309 1738 int j,s; 1739 1310 1740 for(i=1;i<=size(M);i++) 1311 1741 { … … 1342 1772 f=sagbiNFMODO(f,G,I,b); 1343 1773 } 1344 return( f+sagbiNFMOD(plead(p),G,I,b));1774 return(lead(f)+sagbiNFMOD(plead(p),G,I,b)); 1345 1775 } 1346 1776 ////////////////////////////////////////////////////////////////////////////////
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