Changeset d6bf5a in git
- Timestamp:
- Nov 11, 2019, 11:58:10 AM (4 years ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- 6051048d99eac13bf7a7d0247da45b4920172e17
- Parents:
- a9a6c71366db88517ac1a4fc14a310452c62802b
- Files:
-
- 7 edited
Legend:
- Unmodified
- Added
- Removed
-
Singular/LIB/finvar.lib
ra9a6c71 rd6bf5a 327 327 { int i=0; 328 328 while((n/root^i)<>1) 329 { i++; 330 } 329 { i++; } 331 330 return(i); 332 331 } … … 336 335 "USAGE: molien(G1,G2,...[,ringname,lcm,flags]); 337 336 G1,G2,...: nxn <matrices>, all elements of a finite matrix group, 338 ringname: a <string> giving a name for a new ring of characteristic 0339 for the Molienseries in case of prime characteristic, lcm: an <int>337 Finvar::newring: a new ring of characteristic 0 for the Molien 338 series in case of prime characteristic, lcm: an <int> 340 339 giving the lowest common multiple of the elements' orders in case of 341 340 prime characteristic, minpoly==0 and a non-cyclic group, flags: an … … 355 354 RETURN: in case of characteristic 0 a 1x2 <matrix> giving enumerator and 356 355 denominator of Molien series; in case of prime characteristic a ring 357 with the name `ringname`of characteristic 0 is created where the same356 with the name newring of characteristic 0 is created where the same 358 357 Molien series (named M) is stored 359 358 DISPLAY: information if the third component of flags does not equal 0 … … 386 385 { ERROR("In characteristic p>0 a <string> must be given for the name of a new ring where the Molien series can be stored"); } 387 386 else 388 { if (#[size(#)-2]=="") 389 { ERROR("<string> may not be empty"); } 390 string newring=#[size(#)-2]; 387 { 391 388 g=size(#)-3; 392 389 } … … 396 393 { ERROR("In characteristic p>0 a <string> must be given for the name of a new ring where the Molien series can be stored"); } 397 394 else 398 { if (#[size(#)-1]=="") 399 { ERROR("<string> may not be empty"); } 400 string newring=#[size(#)-1]; 395 { 401 396 g=size(#)-2; 402 397 int r=g; … … 417 412 if (typeof(#[size(#)-1])<>"string") 418 413 { ERROR("in characteristic p>0 a <string> must be given for the name of a new ring where the Molien series can be stored"); 419 return();420 414 } 421 415 else 422 { if (#[size(#)-1]=="") 423 { ERROR("<string> may not be empty"); } 424 string newring=#[size(#)-1]; 416 { 425 417 g=size(#)-2; 426 418 } … … 430 422 { ERROR("in characteristic p>0 a <string> must be given for the name of a new ring where the Molien series can be stored"); } 431 423 else 432 { if (#[size(#)]=="") 433 { ERROR("<string> may not be empty"); } 434 string newring=#[size(#)]; 424 { 435 425 g=size(#)-1; 436 426 int r=g; … … 564 554 // cyclotomic polynomial of Q, it is 565 555 // irreducible there 566 ring `newring`=(0,e),x,dp;556 ring newring=(0,e),x,dp; 567 557 map f=Q,ideal(e); 568 558 minpoly=number(f(minq)); // e is now a r-th primitive root of … … 612 602 // of unity - 613 603 k=exponent(number(F[j]),e); // F[j]==e^k 614 setring `newring`;604 setring newring; 615 605 p=p*(1-x*(e^k))^C[j]; // building the denominator of the new 616 606 setring bre; // term … … 622 612 // while (f3(p)==0) 623 613 // { p=p/(x-e^k); 624 // setring `newring`;614 // setring newring; 625 615 // p=p*(1-x*(e^k)); // building the denominator of the new 626 616 // setring bre; … … 632 622 // k=k+1; 633 623 // } 634 setring `newring`;624 setring newring; 635 625 M[1,1]=M[1,1]*p+M[1,2]; // expanding M[1,1]/M[1,2] + 1/p 636 626 M[1,2]=M[1,2]*p; … … 678 668 { ""; 679 669 } 680 setring `newring`;670 setring newring; 681 671 if (interval==0) // canceling common terms of denominator 682 672 { // and enumerator - … … 688 678 // M[1,2]=M[1,2]/p; 689 679 } 690 map slead= `newring`,ideal(0);680 map slead=newring,ideal(0); 691 681 s=slead(M); // forcing the constant term of numerator 692 682 M[1,1]=1/s[1,1]*M[1,1]; // and denominator to be 1 … … 697 687 } 698 688 else // if the group only contains an identity 699 { ring `newring`=0,x,dp; // element, it is very easy to calculate689 { ring newring=0,x,dp; // element, it is very easy to calculate 700 690 matrix M[1][2]=1,(1-x)^n; // the Molien series 701 691 } 702 export( `newring`); // we keep the ring where we computed the692 export(newring); // we keep the ring where we computed the 703 693 export M; // Molien series in such that we can 704 694 setring br; // keep it … … 724 714 if (minpoly==0) 725 715 { if (i>size(chst)) 726 { execute("ring "+newring+"=0,("+varstr(br)+"),("+ordstr(br)+")");716 { execute("ring newring=0,("+varstr(br)+"),("+ordstr(br)+")"); 727 717 } 728 718 else 729 719 { chst=chst[i..size(chst)]; 730 720 execute 731 ("ring "+newring+"=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")");721 ("ring newring=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")"); 732 722 } 733 723 } … … 736 726 minp=minp[2..size(minp)-1]; 737 727 chst=chst[i..size(chst)]; 738 execute("ring "+newring+"=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")");728 execute("ring newring=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")"); 739 729 execute("minpoly="+minp); 740 730 } … … 768 758 } 769 759 } 770 setring `newring`;760 setring newring; 771 761 execute("matrix G(i)["+string(n)+"]["+string(n)+"]="+stM(i)); 772 762 p=det(I-v1*G(i)); // denominator of new term - … … 797 787 // M[1,2]=M[1,2]/p; 798 788 } 799 map slead= `newring`,ideal(0);789 map slead=newring,ideal(0); 800 790 s=slead(M); 801 791 M[1,1]=1/s[1,1]*M[1,1]; // numerator and denominator have to have … … 807 797 } 808 798 kill G(1..g), s, slead, p, v1, I; 809 export `newring`; // we keep the ring where we computed the799 export newring; // we keep the ring where we computed the 810 800 export M; // the Molien series such that we can 811 801 setring br; // keep it … … 821 811 print(M); 822 812 ring S=3,(x,y,z),dp; 823 string newring="alksdfjlaskdjf";824 813 matrix A[3][3]=0,1,0,-1,0,0,0,0,-1; 825 814 list L=group_reynolds(A); 826 molien(L[2..size(L)], newring);827 setring Finvar:: alksdfjlaskdjf;815 molien(L[2..size(L)],""); 816 setring Finvar::newring; 828 817 print(M); 829 818 setring S; 830 kill Finvar:: alksdfjlaskdjf;819 kill Finvar::newring; 831 820 } 832 821 /////////////////////////////////////////////////////////////////////////////// … … 834 823 proc reynolds_molien (list #) 835 824 "USAGE: reynolds_molien(G1,G2,...[,ringname,flags]); 836 G1,G2,...: nxn <matrices> generating a finite matrix group, ringname:837 a <string> giving a name fora new ring of characteristic 0 for the825 G1,G2,...: nxn <matrices> generating a finite matrix group, 826 Finvar::newring: a new ring of characteristic 0 for the 838 827 Molien series in case of prime characteristic, flags: an optional 839 828 <intvec> with three components: if the first element is not equal to 0 … … 852 841 value and in case of characteristic 0 a 1x2 <matrix> giving enumerator 853 842 and denominator of Molien series is the second one; in case of prime 854 characteristic a ring with the name `ringname`of characteristic 0 is843 characteristic a ring with the name newring of characteristic 0 is 855 844 created where the same Molien series (named M) is stored 856 845 DISPLAY: information if the third component of flags does not equal 0 … … 887 876 if (ch<>0) 888 877 { if (typeof(#[size(#)-1])<>"string") 889 { ERROR("in characteristic p a <string> must be given for the name of a new ring where the Molien series can be stored"); }878 { ERROR("in characteristic p a <string> must be given"); } 890 879 else 891 { if (#[size(#)-1]=="") 892 { ERROR("<string> may not be empty"); } 880 { 893 881 string newring=#[size(#)-1]; 894 882 gen_num=size(#)-2; … … 905 893 if (ch<>0) 906 894 { if (typeof(#[size(#)])<>"string") 907 { ERROR("in characteristic p a <string> must be given for the name of a new ring where the Molien series can be stored"); }895 { ERROR("in characteristic p a <string> must be given"); } 908 896 else 909 { if (#[size(#)]=="") 910 { ERROR("<string> may not be empty"); } 911 string newring=#[size(#)]; 897 { 912 898 gen_num=size(#)-1; 913 899 } … … 948 934 } 949 935 if (typeof(L[2])=="int") 950 { molien(L[3..size(L)], newring,L[2],intvec(mol_flag,interval,v));936 { molien(L[3..size(L)],"",L[2],intvec(mol_flag,interval,v)); 951 937 } 952 938 else 953 { molien(L[2..size(L)], newring,intvec(mol_flag,interval,v));939 { molien(L[2..size(L)],"",intvec(mol_flag,interval,v)); 954 940 } 955 941 return(L[1]); … … 1126 1112 if (minpoly==0) 1127 1113 { if (i>size(chst)) 1128 { execute("ring "+newring+"=0,("+varstr(br)+"),("+ordstr(br)+")");1114 { execute("ring newring=0,("+varstr(br)+"),("+ordstr(br)+")"); 1129 1115 } 1130 1116 else 1131 1117 { chst=chst[i..size(chst)]; 1132 1118 execute 1133 ("ring "+newring+"=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")");1119 ("ring newring=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")"); 1134 1120 } 1135 1121 } … … 1138 1124 minp=minp[2..size(minp)-1]; 1139 1125 chst=chst[i..size(chst)]; 1140 execute("ring "+newring+"=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")");1126 execute("ring newring=(0"+chst+"),("+varstr(br)+"),("+ordstr(br)+")"); 1141 1127 execute("minpoly="+minp); 1142 1128 } … … 1158 1144 } 1159 1145 } 1160 setring `newring`;1146 setring newring; 1161 1147 execute("matrix G(1)["+string(n)+"]["+string(n)+"]="+stM(1)); 1162 1148 matrix A(2)[1][2]; // A(2) will contain the Molien series - … … 1191 1177 } 1192 1178 } 1193 setring `newring`;1179 setring newring; 1194 1180 execute("matrix G(i)["+string(n)+"]["+string(n)+"]="+stM(i)); 1195 1181 p=det(I-v1*G(i)); // denominator of new term - … … 1250 1236 } 1251 1237 } 1252 setring `newring`;1238 setring newring; 1253 1239 execute("matrix G(g)["+string(n)+"]["+string(n)+"]="+stM(g)); 1254 1240 p=det(I-v1*G(g)); // denominator of new term … … 1286 1272 // later on, we actually want 1xn 1287 1273 // matrices 1288 setring `newring`;1274 setring newring; 1289 1275 if (interval==0) // canceling common terms of denominator 1290 1276 { // and enumerator - … … 1307 1293 } 1308 1294 } 1309 map slead= `newring`,ideal(0);1295 map slead=newring,ideal(0); 1310 1296 s=slead(A(2)); 1311 1297 A(2)[1,1]=1/s[1,1]*A(2)[1,1]; // numerator and denominator have to have … … 1317 1303 matrix M=A(2); 1318 1304 kill G(1..g), s, slead, p, v1, I, A(2); 1319 export `newring`; // we keep the ring where we computed the1305 export newring; // we keep the ring where we computed the 1320 1306 export M; // the Molien series such that we can 1321 1307 setring br; // keep it … … 1332 1318 print(M); 1333 1319 ring S=3,(x,y,z),dp; 1334 string newring="Qadjoint";1335 1320 matrix A[3][3]=0,1,0,-1,0,0,0,0,-1; 1336 matrix REY=reynolds_molien(A, newring);1321 matrix REY=reynolds_molien(A,""); 1337 1322 print(REY); 1338 setring Finvar:: Qadjoint;1323 setring Finvar::newring; 1339 1324 print(M); 1340 1325 setring S; 1341 kill Finvar:: Qadjoint;1326 kill Finvar::newring; 1342 1327 } 1343 1328 /////////////////////////////////////////////////////////////////////////////// … … 2093 2078 proc primary_charp (matrix REY,string ring_name,list #) 2094 2079 "USAGE: primary_charp(REY,ringname[,v]); 2095 REY: a <matrix> representing the Reynolds operator, ringname: a2096 <string> giving the name of aring where the Molien series is stored,2080 REY: a <matrix> representing the Reynolds operator, 2081 Finvar::newring: the ring where the Molien series is stored, 2097 2082 v: an optional <int> 2098 2083 ASSUME: REY is the first return value of group_reynolds or reynolds_molien and … … 2130 2115 if (ncols(REY)<>n) 2131 2116 { ERROR("First parameter ought to be the Reynolds operator"): } 2132 if (typeof(`ring_name`)<>"ring")2133 { ERROR("Second parameter ought to be ring where the Molien series is stored"); }2134 2117 //---------------------------------------------------------------------------- 2135 2118 if (v && voice<>2) … … 2142 2125 //----------------------- initializing variables ----------------------------- 2143 2126 int dB; 2144 setring `ring_name`; // the Molien series is stores here -2127 setring newring; // the Molien series is stores here - 2145 2128 poly p(1..2); // p(1) will be used for single terms of 2146 2129 // the partial expansion, p(2) to store … … 2167 2150 while(1) // repeat until n primary invariants are 2168 2151 { // found 2169 setring `ring_name`;2152 setring newring; 2170 2153 p(1..2)=partial_molien(M,1,p(2)); // next term of the partial expansion - 2171 2154 d=deg(p(1)); // degree where we'll search - … … 2226 2209 matrix A[3][3]=0,1,0,-1,0,0,0,0,-1; 2227 2210 list L=group_reynolds(A); 2228 string newring="alskdfj"; 2229 molien(L[2..size(L)],newring); 2230 matrix P=primary_charp(L[1],newring); 2231 kill Finvar::`newring`; 2211 molien(L[2..size(L)],""); 2212 matrix P=primary_charp(L[1],""); 2213 kill Finvar::newring; 2232 2214 print(P); 2233 2215 } … … 3156 3138 proc primary_charp_random (matrix REY,string ring_name,int max,list #) 3157 3139 "USAGE: primary_charp_random(REY,ringname,r[,v]); 3158 REY: a <matrix> representing the Reynolds operator, ringname: a3159 <string> giving the name of aring where the Molien series is stored,3140 REY: a <matrix> representing the Reynolds operator, 3141 Finvar::newring: the ring where the Molien series is stored, 3160 3142 r: an <int> where -|r| to |r| is the range of coefficients of the 3161 3143 random combinations of bases elements, v: an optional <int> … … 3195 3177 if (ncols(REY)<>n) 3196 3178 { ERROR("First parameter ought to be the Reynolds operator"); } 3197 if (typeof(`ring_name`)<>"ring")3198 { EROOR("Second parameter ought to the name of a ring where the Molien is stored"); }3199 3179 //---------------------------------------------------------------------------- 3200 3180 if (v && voice<>2) … … 3207 3187 //----------------------- initializing variables ----------------------------- 3208 3188 int dB; 3209 setring `ring_name`; // the Molien series is stores here -3189 setring newring; // the Molien series is stores here - 3210 3190 poly p(1..2); // p(1) will be used for single terms of 3211 3191 // the partial expansion, p(2) to store … … 3231 3211 while(1) // repeat until n primary invariants are 3232 3212 { // found 3233 setring `ring_name`;3213 setring newring; 3234 3214 p(1..2)=partial_molien(M,1,p(2)); // next term of the partial expansion - 3235 3215 d=deg(p(1)); // degree where we'll search - … … 3289 3269 matrix A[3][3]=0,1,0,-1,0,0,0,0,-1; 3290 3270 list L=group_reynolds(A); 3291 string newring="alskdfj"; 3292 molien(L[2..size(L)],newring); 3293 matrix P=primary_charp_random(L[1],newring,1); 3294 kill Finvar::`newring`; 3271 molien(L[2..size(L)],""); 3272 matrix P=primary_charp_random(L[1],"",1); 3273 kill Finvar::newring; 3295 3274 print(P); 3296 3275 } … … 5105 5084 "USAGE: secondary_charp(P,REY,ringname[,v]); 5106 5085 P: a 1xn <matrix> with primary invariants, REY: a gxn <matrix> 5107 representing the Reynolds operator, ringname: a <string> giving the5108 name of aring of characteristic 0 where the Molien series is stored,5086 representing the Reynolds operator, Finvar::newring is 5087 the ring of characteristic 0 where the Molien series is stored, 5109 5088 v: an optional <int> 5110 5089 ASSUME: n is the number of variables of the basering, g the size of the group, 5111 5090 REY is the 1st return value of group_reynolds(), reynolds_molien() or 5112 the second one of primary_invariants(), `ringname` is aring of5091 the second one of primary_invariants(), Finvar::newring is the ring of 5113 5092 char 0 that has been created by molien() or reynolds_molien() or 5114 5093 primary_invariants() … … 5149 5128 if (ncols(REY)<>n) 5150 5129 { ERROR("The second parameter ought to be the Reynolds operator"); } 5151 if (typeof(`ring_name`)<>"ring")5152 { ERROR("The <string> should give the name of the ring where the Molien series is stored"); }5153 5130 if (v && voice==2) 5154 5131 { ""; … … 5160 5137 { deg_dim_vec[j]=deg(P[j]); 5161 5138 } 5162 setring `ring_name`;5139 setring newring; 5163 5140 poly p=1; 5164 5141 for (j=1;j<=n;j++) // calculating the denominator of the … … 5299 5276 ""; 5300 5277 } 5301 if (ring_name=="aksldfalkdsflkj")5302 { kill `ring_name`;5303 }5304 5278 return(matrix(S),matrix(IS)); 5305 5279 } … … 5309 5283 matrix A[3][3]=0,1,0,-1,0,0,0,0,-1; 5310 5284 list L=primary_invariants(A); 5311 matrix S,IS= secondary_charp(L[1..size(L)]);5285 matrix S,IS=old_secondary_charp(L[1..size(L)]); 5312 5286 print(S); 5313 5287 print(IS); … … 5322 5296 @* REY: a gxn <matrix> representing the Reynolds operator, where 5323 5297 g the size of the corresponding group; 5324 @* ringname: a <string> giving the name of aring of characteristic 05298 @* Finvar::newring is the ring of characteristic 0 5325 5299 containing a 1x2 <matrix> M giving numerator and denominator of the Molien 5326 5300 series; … … 5332 5306 REY is the 1st return value of group_reynolds(), reynolds_molien() or 5333 5307 the second one of primary_invariants(); 5334 @* `ringname` is the name of aring of characteristic 0 that has been created5308 @* Finvar::newring is the ring of characteristic 0 that has been created 5335 5309 by molien() or reynolds_molien() or primary_invariants() 5336 5310 RETURN: secondary invariants of the invariant ring (type <matrix>) and … … 5396 5370 if (ncols(REY)<>n) 5397 5371 { ERROR("The second parameter ought to be the Reynolds operator"); } 5398 if (typeof(`ring_name`)<>"ring")5399 { ERROR("The <string> should give the name of the ring where the Molien series is stored"); }5400 5372 if (v && voice==2) 5401 5373 { ""; … … 5407 5379 { deg_dim_vec[j]=deg(P[j]); 5408 5380 } 5409 setring `ring_name`;5381 setring newring; 5410 5382 poly p=1; 5411 5383 for (j=1;j<=n;j++) // calculating the denominator of the … … 5750 5722 } 5751 5723 } 5752 if (ring_name=="aksldfalkdsflkj")5753 { kill `ring_name`;5754 }5755 5724 option(set,saveopt); 5756 5725 return(matrix(S),matrix(compress(IS))); … … 7174 7143 /////////////////////////////////////////////////////////////////////////////// 7175 7144 7176 proc orbit_variety (matrix F,string newring)7145 proc orbit_variety (matrix F,string s) 7177 7146 "USAGE: orbit_variety(F,s); 7178 7147 F: a 1xm <matrix> defing an invariant ring, s: a <string> giving the 7179 7148 name for a new ring 7180 7149 RETURN: a Groebner basis (type <ideal>, named G) for the ideal defining the 7181 orbit variety (i.e. the syzygy ideal) in the new ring (named `s`)7150 orbit variety (i.e. the syzygy ideal) in the new ring (named newring) 7182 7151 THEORY: The ideal of algebraic relations of the invariant ring generators is 7183 7152 calculated, then the variables of the original ring are eliminated and … … 7185 7154 EXAMPLE: example orbit_variety; shows an example 7186 7155 " 7187 { if (newring=="") 7188 { ERROR("the second parameter may not be an empty <string>"); } 7156 { 7189 7157 if (nrows(F)==1) 7190 7158 { def br=basering; … … 7204 7172 { I[i]=I[i]-y(i); } 7205 7173 I=elim(I,1..n); 7206 execute("ring "+newring+"=("+charstr(br)+"),(y(1..m)),dp(m);");7174 execute("ring newring=("+charstr(br)+"),(y(1..m)),dp(m);"); 7207 7175 if (mp!="0") 7208 7176 { execute("minpoly=number("+mp+");"); } … … 7215 7183 ideal G=emb(I); 7216 7184 kill emb, vars, R; 7217 keepring `newring`;7185 keepring newring; 7218 7186 return(); 7219 7187 } … … 7225 7193 ring R=0,(x,y,z),dp; 7226 7194 matrix F[1][7]=x2+y2,z2,x4+y4,1,x2z-1y2z,xyz,x3y-1xy3; 7227 string newring="E"; 7228 orbit_variety(F,newring); 7195 orbit_variety(F,""); 7229 7196 print(G); 7230 7197 basering; … … 7391 7358 /////////////////////////////////////////////////////////////////////////////// 7392 7359 7393 proc relative_orbit_variety(ideal I,matrix F,string newring)7360 proc relative_orbit_variety(ideal I,matrix F,string s) 7394 7361 "USAGE: relative_orbit_variety(I,F,s); 7395 7362 I: an <ideal> invariant under the action of a group, 7396 7363 @* F: a 1xm <matrix> defining the invariant ring of this group, 7397 @* s: a <string> giving a name for anew ring7398 RETURN: The procedure ends with a new ring named s.7364 @* Finvar::newring: the new ring 7365 RETURN: The procedure ends with a new ring named newring. 7399 7366 It contains a Groebner basis 7400 7367 (type <ideal>, named G) for the ideal defining the … … 7411 7378 EXAMPLE: example relative_orbit_variety; shows an example 7412 7379 " 7413 { if (newring=="") 7414 { ERROR("the third parameter may not be empty a <string>"); } 7380 { 7415 7381 degBound=0; 7416 7382 if (nrows(F)==1) … … 7451 7417 } 7452 7418 G=compress(G); 7453 execute("ring "+newring+"=("+charstr(br)+"),(y(1..m)),lp;");7419 execute("ring newring=("+charstr(br)+"),(y(1..m)),lp;"); 7454 7420 if (mp!="0") 7455 7421 { execute("minpoly=number("+mp+");"); } … … 7462 7428 ideal G=emb(G); 7463 7429 kill vars, emb; 7464 keepring `newring`;7430 keepring newring; 7465 7431 return(); 7466 7432 } -
Tst/Manual/molien.res.gz.uu
ra9a6c71 rd6bf5a 1 begin 644 molien.res.gz 2 M'XL("$;2?50``VUO;&EE;BYR97,`G5);;X(P%'[G5YR0/4"XQ(*734,3EV6) 3 M">YA[,T8PZ1H%8NA=:O^^A5!T&0/<VW3R^EWSOG.)?IXF;P!`,(03IY!%URX 4 M&?W41Z!N"\JH,,R15IZ`,>SRC!+F,O+M<A$++:JUO5H[I>PK+BH#S:>/08?+ 5 M8+D@(-8$EC$GD*>P+^A.O=9Q$2\%*2@7=*F\:_=I-,ZZ&`K*5O`>=&Q#VD?[ 6 M9-K)OB734T'$HJ`2QC-_KI;"(;MC.^5630>U\#Z&3#F`,%@5^6&_*,B1Y5G" 7 MC;'9@@:-S6E09<@(9Y[K<GHB1FC.KZ"/N*3/A#%50NE;TG.DA6Q'#BS9MV3/ 8 MD5U+^DXE;K2>ZJ"BP/\M*-3!P,49H2I3GH$>9UN>I)LLYMMDD[;50.BN!"#O 9 M#PE`_J4S;N.V:S972%4>3BJJK^=>&0YOF;;0WG]2A?JM@ZBUI2I4MG/9LP=N 10 .('/TH/T`;FUP3OD"```` 1 begin 640 molien.res.gz 2 M'XL("-<ZR5T"`VUO;&EE;BYR97,`G5)=:\(P%'WW5US*'E*:%M/ZL2D-.,9` 3 MJ#ZL>Q.13J,&:BI)W**_?JG5UL$>YI*0CYMS;N[)O>G[RW@*`(1",GX&1RL= 4 MY/S#&8+=+;C@&KG#5KD"I;`K<LY$(-A7H'2F6^F%'5[8:RX^,UDYJ"\C"@Y< 5 MFR@T`[UEL,P4@V(->\EW]K3-9+;43'*E^=*2[R/4;W4H2"XV\!:W,3+XB$\N 6 M7NV;6+I60Z8E-S":17,[+([@-O;+J>H^:>`]"KE]`))X(XO#?B'9413Y2J&1 7 MVX#ZM<])7'T02F9A$"A^8BAQYS?01UJ&+S2:6*.)/!/ZQB/8-WW/]#S3]4W' 8 M,Y%?F6O6TT54&D>_B2+MNT01\@=1)+PF^Z<6[#@W()M9Q?0YMM=SY@<#6QKE 9 BN<%T_B.9=!O/:>/+IJ.LRK+T#@H1=_C0^@:F4/)`P`(````` 11 10 ` 12 11 end -
Tst/Manual/molien.stat
ra9a6c71 rd6bf5a 1 1 >> tst_memory_0 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:2682642 1 >> tst_memory_1 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:6933643 1 >> tst_memory_2 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:7595444 1 >> tst_timer_1 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:141 1 >> tst_memory_0 :: 1573468887:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:226464 2 1 >> tst_memory_1 :: 1573468887:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:2199552 3 1 >> tst_memory_2 :: 1573468887:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:2240976 4 1 >> tst_timer_1 :: 1573468887:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:8 -
Tst/Manual/molien.tst
ra9a6c71 rd6bf5a 8 8 print(M); 9 9 ring S=3,(x,y,z),dp; 10 string newring="alksdfjlaskdjf";11 10 matrix A[3][3]=0,1,0,-1,0,0,0,0,-1; 12 11 list L=group_reynolds(A); 13 molien(L[2..size(L)], newring);14 setring Finvar:: alksdfjlaskdjf;12 molien(L[2..size(L)],""); 13 setring Finvar::newring; 15 14 print(M); 16 15 setring S; -
Tst/Manual/reynolds_molien.res.gz.uu
ra9a6c71 rd6bf5a 1 1 begin 640 reynolds_molien.res.gz 2 M'XL(" `B/?%0``W)E>6YO;&1S7VUO;&EE;BYR97,`I5-=3\(P%'W?K[A9?-BR3 MEE#&A T*V!*,F)&(B\\480R84J8&.K%4+OYX[-E:COJ#KLM/=G?MU;I<\7(WN4 M `(#%<#NZ!%<KW5B)%W<`N)L**;3G#YP"(8XAYUN9K>9JNLY6@LN&Y)\-I5/M5 M )%685A5F(>1'FI>1ZH]A#"X<+YEI#GK)898J#MD"-KE8X]LRS=.9YKE06LRP6 M #.<TCSI9&ZL5\A4F49-XAFS)SB?SC2VF$\,ZU;DP,'P*G_%&'B--0HM'N2BS7 M ]&Y-GUP_DG'T30EOZ%MN+RY*D]I#*IJW!*@A=$><`K`0`@Z"03/:$)"P`ZC=8 M SX_N8W0V86!:U`2,4-,+3#<P'6K:@0EI::Z]+JI^DRC\K5_6C$'I`P.'5F#D9 M WJ?SMPP3V1$Q=I(JK/55E9^:D"J5U8:%_]*&X505+]NX.1RQ?O_8A<W1^8N`10 <K&M#)S86SK+X$8I#_JX\Y@_.G#U95IB+,P,`````2 M'XL("",[R5T"`W)E>6YO;&1S7VUO;&EE;BYR97,`I5)=3\(P%'W?K[A9?-BR 3 MEE#&A[*P!*,F).(#\\480^8HT@0ZLE8M_'IN^5B-^H*NRVY[=\[M.>W-'F]& 4 M#P#`4K@?78.OE6XLQ:N?`,ZF0@H=A(EG(Z0I5'PCR^5,35?E4G#9D/RSH72N 5 MO>Q8IG4L,Q?R(Z\.E>J?<0H^G!Y9:@YZP:'(%8=R#NM*K'"UR*N\T+P22HL" 6 MR><1ZKW:*%;(-Y@,FB0P9$.V(9FMG99."JM<5\+`\#E^P1=QC#0)M9_#H,S! 7 MNS5\<OM$QH-O!Q$,0X?MI5::U`%",;TA0`VA6^+9@$((>!@,IC&'`0%;@)I^ 8 M>:*/D6SBR+2HB1BAIA>9;F0ZU+0C$]-#NF9='?UF@_@WOZQYEE_&OOK]Z9;X 9 MOC/,6O\RS+`M%-=[]7?[MNGWL:_LVFW1_LNAL(ZKG+E:>)>VMVW?OJN`A<F% 10 *MP-?I*,W!@,````` 11 11 ` 12 12 end -
Tst/Manual/reynolds_molien.stat
ra9a6c71 rd6bf5a 1 1 >> tst_memory_0 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:2866122 1 >> tst_memory_1 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:7864323 1 >> tst_memory_2 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:8165404 1 >> tst_timer_1 :: 1 316104113:3132- exportiert :3-1-3:ix86-Linux:mamawutz:171 1 >> tst_memory_0 :: 1573468963:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:243008 2 1 >> tst_memory_1 :: 1573468963:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:2199552 3 1 >> tst_memory_2 :: 1573468963:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:2296352 4 1 >> tst_timer_1 :: 1573468963:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:8 -
Tst/Manual/reynolds_molien.tst
ra9a6c71 rd6bf5a 8 8 print(M); 9 9 ring S=3,(x,y,z),dp; 10 string newring="Qadjoint";11 10 matrix A[3][3]=0,1,0,-1,0,0,0,0,-1; 12 matrix REY=reynolds_molien(A, newring);11 matrix REY=reynolds_molien(A,""); 13 12 print(REY); 14 setring Finvar:: Qadjoint;13 setring Finvar::newring; 15 14 print(M); 16 15 setring S;
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