Changeset 4869982 in git
 Timestamp:
 Apr 8, 2009, 7:13:02 PM (14 years ago)
 Branches:
 (u'jengelhdatetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
 Children:
 06984ae84863612ab64e2e3f8903aa78ef9e0d44
 Parents:
 9df212d331f045aa0b28d25854ee5041cdbc55f1
 File:

 1 edited
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Singular/LIB/nctools.lib
r9df212 r4869982 1 1 /////////////////////////////////////////////////////////////////////////////// 2 version="$Id: nctools.lib,v 1.4 3 20090330 18:11:40motsak Exp $";2 version="$Id: nctools.lib,v 1.44 20090408 17:13:02 motsak Exp $"; 3 3 category="Noncommutative"; 4 4 info=" … … 22 22 Exterior(); return qring, the exterior algebra of a basering, 23 23 findimAlgebra(M,[r]); create finite dimensional algebra structure from the basering and the multiplication matrix M, 24 SuperCommutative([b,e,Q]); return qring, the supercommutative algebra over a basering,24 superCommutative([b,e,Q]); return qring, the supercommutative algebra over a basering, 25 25 rightStd(I); compute a right Groebner basis of an ideal, 26 26 … … 720 720 721 721 /////////////////////////////////////////////////////////////////////////////// 722 proc SuperCommutative(list #)723 "USAGE: SuperCommutative([b,[e, [Q, [flag]]]]);722 proc superCommutative(list #) 723 "USAGE: superCommutative([b,[e, [Q, [flag]]]]); 724 724 RETURN: qring 725 725 PURPOSE: create the supercommutative algebra (as a GRalgebra) 'over' a basering, … … 728 728 THEORY: given a basering, this procedure introduces the anticommutative relations x(j)x(i)=x(i)x(j) for all e>=j>i>=b, 729 729 @* moreover, creates a factor algebra modulo the twosided ideal, generated by x(b)^2, ..., x(e)^2[ + Q] 730 EXAMPLE: example SuperCommutative; shows examples 731 " 732 { 733 734 // NOTE: as a side effect the basering will be changed (if not in a commutative case) to bo the ground Galgebra (without factor). 735 int fprot = (find(option(),"prot") != 0); 730 DISPLAY: If @code{printlevel} > 1, warning debug messages will be printed 731 EXAMPLE: example superCommutative; shows examples 732 " 733 { 734 int fprot = (printlevel > 1); // (find(option(),"prot") != 0); 736 735 737 736 string rname=nameof(basering); … … 739 738 if ( rname == "basering") // i.e. no ring has been set yet 740 739 { 741 ERROR("You have to call the procedure from thering");740 ERROR("You have to call the procedure from a ring"); 742 741 return(); 743 742 } … … 893 892 { 894 893 print("Warning: Since the current ordering is not global there might be problems computing twostd(Q)!"); 895 print("Q:", @Q); 894 "Q:"; 895 @Q; 896 896 } 897 897 … … 909 909 "EXAMPLE:";echo=2; 910 910 ring R = 0,(x(1..4)),dp; // global! 911 def ER = SuperCommutative(); // the same as Exterior (b = 1, e = N)911 def ER = superCommutative(); // the same as Exterior (b = 1, e = N) 912 912 setring ER; ER; 913 913 "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; 914 914 kill R; kill ER; 915 915 ring R = 0,(x(1..4)),(lp(1), dp(3)); // global! 916 def ER = SuperCommutative(2); // b = 2, e = N916 def ER = superCommutative(2); // b = 2, e = N 917 917 setring ER; ER; 918 918 "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; 919 919 kill R; kill ER; 920 920 ring R = 0,(x(1..6)),(ls(2), dp(2), lp(2)); // local! 921 def ER = SuperCommutative(3,4); // b = 3, e = 4921 def ER = superCommutative(3,4); // b = 3, e = 4 922 922 setring ER; ER; 923 923 "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; … … 1092 1092 "EXAMPLE:";echo=2; 1093 1093 ring R = 0,(x(1..4)),dp; // global! 1094 def ER = SuperCommutative(2); // (b = 2, e = N)1094 def ER = superCommutative(2); // (b = 2, e = N) 1095 1095 setring ER; ER; 1096 1096 "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; … … 1120 1120 "EXAMPLE:";echo=2; 1121 1121 ring R = 0,(x(1..4)),dp; // global! 1122 def ER = SuperCommutative(2); // (b = 2, e = N)1122 def ER = superCommutative(2); // (b = 2, e = N) 1123 1123 setring ER; ER; 1124 1124 "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; … … 1129 1129 "USAGE: IsSCA(); 1130 1130 RETURN: int 1131 PURPOSE: returns 1 if basering is a super commutative algebra and 0 otherwise.1131 PURPOSE: returns 1 if basering is a supercommutative algebra and 0 otherwise. 1132 1132 NOTE: shows hint message for nonSCA algebras if the 'prot' option is on. 1133 1133 EXAMPLE: example IsSCA; shows examples … … 1156 1156 { "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; } 1157 1157 else 1158 { "Not a super commutative algebra!!!"; }1158 { "Not a supercommutative algebra!!!"; } 1159 1159 kill R; 1160 1160 ///////////////////////////////////////////////////////////////////// … … 1164 1164 { "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; } 1165 1165 else 1166 { "Not a super commutative algebra!!!"; }1166 { "Not a supercommutative algebra!!!"; } 1167 1167 kill R, S; 1168 1168 ///////////////////////////////////////////////////////////////////// … … 1189 1189 { "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; } 1190 1190 else 1191 { "Not a super commutative algebra!!!"; }1191 { "Not a supercommutative algebra!!!"; } 1192 1192 kill R, ER, S; 1193 1193 ///////////////////////////////////////////////////////////////////// 1194 1194 ring R = 0,(x(1..4)),dp; 1195 def ER = SuperCommutative(2); // (b = 2, e = N)1195 def ER = superCommutative(2); // (b = 2, e = N) 1196 1196 setring ER; ER; 1197 1197 if(IsSCA()) 1198 1198 { "This is a SCA! Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; } 1199 1199 else 1200 { "Not a super commutative algebra!!!"; }1200 { "Not a supercommutative algebra!!!"; } 1201 1201 kill R, ER; 1202 1202 }
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