Changeset 0a2f7d in git
- Timestamp:
- Sep 30, 2010, 9:58:57 PM (13 years ago)
- Branches:
- (u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')
- Children:
- f4490f5c61db9f9a1ab08da7fe11fb449e09f040
- Parents:
- 3576f6fb6a525ec1407b464179ffc8ad1f2c0ea7
- Location:
- Singular/LIB
- Files:
-
- 5 edited
-
dmod.lib (modified) (5 diffs)
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dmodapp.lib (modified) (5 diffs)
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fpadim.lib (modified) (3 diffs)
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freegb.lib (modified) (5 diffs)
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ncfactor.lib (modified) (11 diffs)
Legend:
- Unmodified
- Added
- Removed
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Singular/LIB/dmod.lib
r3576f6 r0a2f7d 7 7 Jorge Martin Morales, jorge@unizar.es 8 8 9 THEORY: Let K be a field of characteristic 0. Given a polynomial ring 9 OVERVIEW: 10 Theory: Let K be a field of characteristic 0. Given a polynomial ring 10 11 R = K[x_1,...,x_n] and a polynomial F in R, 11 12 one is interested in the R[1/F]-module of rank one, generated by … … 28 29 PS*F^(s+1) = bs*F^s holds in K[x_1,...,x_n,1/F]*F^s. 29 30 30 R EFERENCES:31 References: 31 32 We provide the following implementations of algorithms: 32 33 @*(OT) the classical Ann F^s algorithm from Oaku and Takayama (Journal of … … 41 42 42 43 43 G UIDE:44 Guide: 44 45 @*- Ann F^s = I(F^s) = LD in D(R)[s] can be computed by Sannfs [BM, OT, LOT] 45 46 @*- Ann^(1) F^s in D(R)[s] can be computed by Sannfslog … … 58 59 59 60 PROCEDURES: 60 61 61 annfs(F[,S,eng]); compute Ann F^s0 in D and Bernstein polynomial for a poly F 62 62 annfspecial(I, F, m, n); compute Ann F^n from Ann F^s for a polynomial F and a number n 63 63 Sannfs(F[,S,eng]); compute Ann F^s in D[s] for a polynomial F 64 64 Sannfslog(F[,eng]); compute Ann^(1) F^s in D[s] for a polynomial F 65 bernsteinBM(F[,eng]); compute global Bernstein polynomial for a polynomial F (algorithmof Briancon-Maisonobe)66 bernsteinLift(I,F [,eng]); compute a possible multiple of Bernsteinpolynomial via lift-like procedure67 operatorBM(F[,eng]); compute Ann F^s, Ann F^s0, BS and PS for a poly nomialF (algorithm of Briancon-Maisonobe)65 bernsteinBM(F[,eng]); compute global Bernstein-Sato polynomial of a poly F (alg of Briancon-Maisonobe) 66 bernsteinLift(I,F [,eng]); compute a multiple of Bernstein-Sato polynomial via lift-like procedure 67 operatorBM(F[,eng]); compute Ann F^s, Ann F^s0, BS and PS for a poly F (algorithm of Briancon-Maisonobe) 68 68 operatorModulo(F, I, b); compute PS via the modulo approach 69 69 annfsParamBM(F[,eng]); compute the generic Ann F^s (algorithm by Briancon and Maisonobe) and exceptional parametric constellations for a polynomial F with parametric coefficients … … 75 75 annfsRB(I,F [,eng]); compute Ann F^s0 in D and Bernstein polynomial from the known Ann F^s in D[s] by using Jacobian ideal 76 76 checkFactor(I,F,q[,eng]); check whether a polynomial q in K[s] is a factor of the global Bernstein polynomial of F from the known Ann F^s in D[s] 77 77 78 78 79 arrange(p); create a poly, describing a full hyperplane arrangement -
Singular/LIB/dmodapp.lib
r3576f6 r0a2f7d 7 7 @* Daniel Andres, daniel.andres@math.rwth-aachen.de 8 8 9 S UPPORT: DFG Graduiertenkolleg 1632 'Experimentelle und konstruktive Algebra'10 11 GUIDE: Let K be a field of characteristic 0, R = K[x1,...,xN] and9 Support: DFG Graduiertenkolleg 1632 'Experimentelle und konstruktive Algebra' 10 11 OVERVIEW: Let K be a field of characteristic 0, R = K[x1,...,xN] and 12 12 @* D be the Weyl algebra in variables x1,...,xN,d1,...,dN. 13 13 @* In this library there are the following procedures for algebraic D-modules: … … 42 42 43 43 44 R EFERENCES:44 References: 45 45 @* (SST) Saito, Sturmfels, Takayama 'Groebner Deformations of Hypergeometric 46 46 @* Differential Equations', Springer, 2000 … … 49 49 50 50 51 MAINPROCEDURES:51 PROCEDURES: 52 52 53 53 annPoly(f); annihilator of a polynomial f in the corr. Weyl algebra … … 74 74 75 75 76 AUXILIARY PROCEDURES:77 76 78 77 appelF1(); create an ideal annihilating Appel F1 function … … 103 102 D-module; D-integration; integration of D-module; characteristic variety; 104 103 Appel function; Appel hypergeometric function 105 106 104 "; 107 105 -
Singular/LIB/fpadim.lib
r3576f6 r0a2f7d 6 6 AUTHORS: Grischa Studzinski, grischa.studzinski@rwth-aachen.de 7 7 8 S UPPORT: Projects LE 2697/2-1; KR 1907/3-1 of the Priority Programme SPP 1489:8 Support: Projects LE 2697/2-1; KR 1907/3-1 of the Priority Programme SPP 1489: 9 9 @* 'Algorithmische und Experimentelle Methoden in Algebra, Geometrie und Zahlentheorie' 10 10 @* of the German DFG … … 41 41 @* 42 42 43 R EFERENCES:43 References: 44 44 45 45 @* [ufna] Ufnarovskij: Combinatorical and asymptotic methods in algebra, 1990 … … 49 49 associative algebras, Diploma thesis, RWTH Aachen, 2010 50 50 51 A SSUMPTIONS:51 Assumptions: 52 52 @* - basering is always a Letterplace ring 53 53 @* - all intvecs correspond to Letterplace monomials -
Singular/LIB/freegb.lib
r3576f6 r0a2f7d 6 6 AUTHOR: Viktor Levandovskyy, levandov@math.rwth-aachen.de 7 7 8 THEORY: See chapter 'LETTERPLACE' in the @sc{Singular} Manual.8 OVERVIEW: For the theory, see chapter 'Letterplace' in the @sc{Singular} Manual. 9 9 10 10 PROCEDURES: … … 13 13 setLetterplaceAttributes(R,d,b); supplies ring R with the letterplace structure 14 14 15 AUXILIARY PROCEDURES:16 15 17 16 lpMult(f,g); letterplace multiplication of letterplace polynomials … … 28 27 ademRelations(i,j); compute the ideal of Adem relations for i<2j in char 0 29 28 30 SEE ALSO: LETTERPLACE31 " 29 SEE ALSO: fpadim_lib, Letterplace 30 "; 32 31 33 32 // this library computes two-sided GB of an ideal … … 907 906 RETURN: ring 908 907 PURPOSE: creates a ring with the ordering, used in letterplace computations 909 NOTE: if h is given an nonzero, the pure homogeneous letterplace block ordering will be used.908 NOTE: if h is given and nonzero, the pure homogeneous letterplace block ordering will be used. 910 909 EXAMPLE: example makeLetterplaceRing; shows examples 911 910 " … … 1136 1135 attrib(A,"lV"); // number of variables in the main block 1137 1136 } 1137 1138 1139 proc makeLetterplaceRing3(int d) 1140 "USAGE: makeLetterplaceRing1(d); d an integer 1141 RETURN: ring 1142 PURPOSE: creates a ring with a special ordering, representing 1143 @* the original P[s,sigma] (adds d blocks of shifted s) 1144 ASSUME: basering is a letterplace ring as well 1145 NOTE: experimental status 1146 EXAMPLE: example makeLetterplaceRing1; shows examples 1147 " 1148 { 1149 // d = up to degree, will be shifted to d+1 1150 if (d<1) {"bad d"; return(0);} 1151 1152 int uptodeg = d; int lV = nvars(basering); 1153 1154 int ppl = printlevel-voice+2; 1155 string err = ""; 1156 1157 int i,j,s; 1158 def save = basering; 1159 int D = d-1; 1160 list LR = ringlist(save); 1161 list L, tmp; 1162 L[1] = LR[1]; // ground field 1163 L[4] = LR[4]; // quotient ideal 1164 tmp = LR[2]; // varnames 1165 tmp[size(tmp)+1] = "s"; 1166 // add s's 1167 // string newSname = "@s"; 1168 s = size(LR[2]); 1169 for (i=1; i<=D; i++) 1170 { 1171 for (j=1; j<=s; j++) 1172 { 1173 tmp[i*s+j] = string(tmp[j])+"("+string(i+1)+")"; 1174 } 1175 } 1176 // the final index is D*s+s = (D+1)*s = degBound*s 1177 for (i=1; i<=d; i++) 1178 { 1179 tmp[FIndex + i] = string(newSname)+"("+string(i)+")"; 1180 } 1181 L[2] = tmp; 1182 list OrigNames = LR[2]; 1183 // ordering: d blocks of the MODIFIED ord on r 1184 // try to get whether the ord on r is blockord itself 1185 // TODO: make L(2) ordering! exponent is maximally 2 1186 s = size(LR[3]); 1187 1188 // assume: basering was a letterplace, so get its block 1189 tmp = LR[3][1]; // ASSUME: it's a nice block 1190 // modify it 1191 // add (0,..,0,1) ... as antiblock part 1192 intvec iv; list ttmp, tmp1; 1193 for (i=1; i<=d; i++) 1194 { 1195 // the position to hold 1: 1196 iv = intvec( gen( i*(lV+1)-1 ) ); 1197 ttmp[1] = "a"; 1198 ttmp[2] = iv; 1199 tmp1[i] = ttmp; 1200 } 1201 // finished: antiblock part //TOCONTINUE 1202 1203 if (s==2) 1204 { 1205 // not a blockord, 1 block + module ord 1206 tmp = LR[3][s]; // module ord 1207 for (i=1; i<=D; i++) 1208 { 1209 LR[3][s-1+i] = LR[3][1]; 1210 } 1211 LR[3][s+D] = tmp; 1212 } 1213 if (s>2) 1214 { 1215 // there are s-1 blocks 1216 int nb = s-1; 1217 tmp = LR[3][s]; // module ord 1218 for (i=1; i<=D; i++) 1219 { 1220 for (j=1; j<=nb; j++) 1221 { 1222 LR[3][i*nb+j] = LR[3][j]; 1223 } 1224 } 1225 // size(LR[3]); 1226 LR[3][nb*(D+1)+1] = tmp; 1227 } 1228 L[3] = LR[3]; 1229 def @R = ring(L); 1230 // setring @R; 1231 // int uptodeg = d; int lV = nvars(basering); // were defined before 1232 def @@R = setLetterplaceAttributes(@R,uptodeg,lV); 1233 return (@@R); 1234 } 1235 example 1236 { 1237 "EXAMPLE:"; echo = 2; 1238 ring r = 0,(x,y,z),(dp(1),dp(2)); 1239 def A = makeLetterplaceRing3(2); 1240 setring A; 1241 A; 1242 attrib(A,"isLetterplaceRing"); 1243 attrib(A,"uptodeg"); // degree bound 1244 attrib(A,"lV"); // number of variables in the main block 1245 } 1246 1247 1138 1248 1139 1249 /* EXAMPLES: -
Singular/LIB/ncfactor.lib
r3576f6 r0a2f7d 1 //////////////////////////////////////////////////////////// ////////////////////////////////////////1 //////////////////////////////////////////////////////////// 2 2 version = "$Id: ncfactor.lib, v 1.00 2010/02/15 10:06 heinle Exp $"; 3 3 category="Noncommutative"; … … 6 6 AUTHORS: Albert Heinle, albert.heinle@rwth-aachen.de 7 7 8 MAIN PROCEDURES: 9 homogfac(h); computes one factorization of a homogeneous polynomial h 10 homogfac_all(h); computes all factorizations of a homogeneous polynomial h 11 facwa(h); computes all factorizations of an inhomogeneous polynomial h 12 8 PROCEDURES: 9 facfirstwa(h); factorization in the first Weyl algebra 10 "; 11 12 LIB "general.lib"; 13 LIB "nctools.lib"; 14 LIB "involut.lib"; 15 16 //static homogfac(h); computes one factorization of a homogeneous polynomial h 17 //static homogfac_all(h); computes all factorizations of a homogeneous polynomial h 18 //static facwa(h); computes all factorizations of an inhomogeneous polynomial h 13 19 /* ring R = 0,(x,y),Ws(-1,1); */ 14 20 /* def r = nc_algebra(1,1); */ 15 21 /* setring(r); */ 16 ";17 LIB "general.lib";18 LIB "nctools.lib";19 LIB "involut.lib";20 22 21 23 //////////////////////////////////////////////////////////////////////////////////////////////////// … … 428 430 //one factorization of a homogeneous polynomial 429 431 //in the first Weyl Algebra 430 proc homogfac(poly h)432 static proc homogfac(poly h) 431 433 "USAGE: homogfac(h); h is a homogeneous polynomial in the first Weyl algebra with respect to the weight vector [-1,1] 432 434 RETURN: list … … 436 438 SEE ALSO: homogfac_all 437 439 "{//proc homogfac 438 if (!isWeyl())439 {//Our basering is not the Weyl algebra440 return(list());441 }//Our basering is not the Weyl algebra442 if(nvars(basering)!=2)443 {//Our basering is the Weyl algebra, but not the first444 return(list());445 }//Our basering is the Weyl algebra, but not the first446 440 def r = basering; 447 441 poly hath; … … 530 524 return(result); 531 525 }//proc homogfac 532 example 533 { 534 "EXAMPLE:";echo=2; 535 ring R = 0,(x,y),Ws(-1,1); 536 def r = nc_algebra(1,1); 537 setring(r); 538 poly h = (x^2*y^2+1)*(x^4); 539 homogfac(h); 540 } 526 /* example */ 527 /* { */ 528 /* "EXAMPLE:";echo=2; */ 529 /* ring R = 0,(x,y),Ws(-1,1); */ 530 /* def r = nc_algebra(1,1); */ 531 /* setring(r); */ 532 /* poly h = (x^2*y^2+1)*(x^4); */ 533 /* homogfac(h); */ 534 /* } */ 541 535 542 536 //================================================== 543 537 //Computes all possible homogeneous factorizations 544 proc homogfac_all(poly h)538 static proc homogfac_all(poly h) 545 539 "USAGE: homogfac_all(h); h is a homogeneous polynomial in the first Weyl algebra with respect to the weight vector [-1,1] 546 540 RETURN: list … … 554 548 return(list(list(h))); 555 549 }//h is a constant 556 if (!isWeyl())557 {//Our basering is not the Weyl algebra558 return(list());559 }//Our basering is not the Weyl algebra560 if(nvars(basering)!=2)561 {//Our basering is the Weyl algebra, but not the first562 return(list());563 }//Our basering is the Weyl algebra, but not the first564 550 def r = basering; 565 551 list one_hom_fac; //stands for one homogeneous factorization … … 800 786 return(result); 801 787 }//proc HomogFacAll 802 example 803 { 804 "EXAMPLE:";echo=2; 805 ring R = 0,(x,y),Ws(-1,1); 806 def r = nc_algebra(1,1); 807 setring(r); 808 poly h = (x^2*y^2+1)*(x^4); 809 homogfac_all(h); 810 } 788 /* example */ 789 /* { */ 790 /* "EXAMPLE:";echo=2; */ 791 /* ring R = 0,(x,y),Ws(-1,1); */ 792 /* def r = nc_algebra(1,1); */ 793 /* setring(r); */ 794 /* poly h = (x^2*y^2+1)*(x^4); */ 795 /* homogfac_all(h); */ 796 /* } */ 811 797 812 798 //==================================================* … … 887 873 //================================================== 888 874 //factorization of the first Weyl Algebra 889 proc facwa(poly h) 875 876 //The following procedure just serves the purpose to 877 //transform the input into an appropriate input for 878 //the procedure sfacwa, where the ring must contain the 879 //variables in a certain order. 880 proc facfirstwa(poly h) 881 {//proc facfirstwa 882 //Redefine the ring in my standard form 883 if (!isWeyl()) 884 {//Our basering is not the Weyl algebra 885 return(list()); 886 }//Our basering is not the Weyl algebra 887 if(nvars(basering)!=2) 888 {//Our basering is the Weyl algebra, but not the first 889 return(list()); 890 }//Our basering is the Weyl algebra, but not the first 891 if (ringlist(basering)[6][1,2] == -1) //manual of ringlist will tell you why 892 { 893 def r = basering; 894 ring tempRing = ringlist(r)[1][1],(x,y),Ws(-1,1); 895 def tempRingnc = nc_algebra(1,1); 896 setring(tempRingnc); 897 map transf = r, var(2), var(1); 898 list result = sfacwa(transf(h)); 899 setring(r); 900 map transfback = tempRingnc, var(2),var(1); 901 return(transfback(result)); 902 } 903 else { return(sfacwa(h));} 904 }//proc facfirstwa 905 example 906 { 907 "EXAMPLE:";echo=2; 908 ring R = 0,(x,y),dp; 909 def r = nc_algebra(1,1); 910 setring(r); 911 poly h = (x^2*y^2+x)*(y-1); 912 facfirstwa(h); 913 } 914 915 //This is the main program 916 static proc sfacwa(poly h) 890 917 "USAGE: facwa(h); h is a polynomial in the first Weyl algebra 891 918 RETURN: list … … 894 921 EXAMPLE: example facwa; shows examples 895 922 SEE ALSO: homogfac_all, homogfac 896 "{//proc facwa923 "{//proc sfacwa 897 924 if(homogwithorder(h,intvec(-1,1))) 898 925 { 899 926 return(homogfac_all(h)); 900 927 } 901 //Redefine the ring in my standard form902 if (!isWeyl())903 {//Our basering is not the Weyl algebra904 return(list());905 }//Our basering is not the Weyl algebra906 if(nvars(basering)!=2)907 {//Our basering is the Weyl algebra, but not the first908 return(list());909 }//Our basering is the Weyl algebra, but not the first910 928 def r = basering; 911 929 map invo = basering,-var(1),var(2); … … 1058 1076 result = delete_dublicates_noteval(result); 1059 1077 return(result); 1060 }//proc facwa 1061 example 1062 { 1063 "EXAMPLE:";echo=2; 1064 ring R = 0,(x,y),Ws(-1,1); 1065 def r = nc_algebra(1,1); 1066 setring(r); 1067 poly h = (x^2*y^2+x)*x; 1068 facwa(h); 1069 } 1078 }//proc sfacwa 1079 1070 1080 1071 1081 //================================================== … … 1090 1100 return(1); 1091 1101 }//proc homogwithorder 1102 1103 //================================================== 1104 //Testfac: Given a list with different factorizations of 1105 // one polynomial, the following procedure checks 1106 // whether they all refer to the same polynomial. 1107 // If they do, the output will be a list, that contains 1108 // the product of each factorization. If not, the empty 1109 // list will be returned. 1110 // If the optional argument # is given (i.e. the polynomial 1111 // which is factorized by the elements of the given list), 1112 // then we look, if the entries are factorizations of p 1113 // and if not, a list with the products subtracted by p 1114 // will be returned 1115 proc testfac(list l, list #) 1116 "USAGE: - testfac(l); l is a list, that contains lists with entries in the first Weyl algebra or 1117 @*- testfac(l,p); l is a list, that contains lists with entries in the first Weyl algebra and p is a polynomial in the first Weyl algebra 1118 RETURN: list@* 1119 PURPOSE: Checks whether a list of factorizations contains factorizations of the same element in the first Weyl algebra@* 1120 THEORY: @code{testfac} multiplies out each factorization and checks whether each factorization was a factorization of the same element. 1121 @* - if there is only a list given, the output will be the empty list, if it does not contain factorizations of the same element. Otherwise it will multiply out all the factorizations and return a list of the length if the given one, in which each entry is the factorized polynomial 1122 @* - if there is a polynomial in the second argument, then the procedure checks whether the given list contains factorizations of this polynomial. If it does, then the output will be a list with the length of the given one and each entry contains this polynomial. If it does not, then the procedure returns a list, in which each entry is the given polynomial subtracted by the multiplied candidate for its factorization. 1123 EXAMPLE: example testfac; shows examples 1124 SEE ALSO: homogfac_all, homogfac, facwa 1125 "{//proc testfac 1126 if (size(l)==0) 1127 {//The empty list is given 1128 return(list()); 1129 }//The empty list is given 1130 if (size(#)>1) 1131 {//We want max. one optional argument 1132 return(list()); 1133 }//We want max. one optional argument 1134 list result; 1135 int i; int j; 1136 if (size(#)==0) 1137 {//No optional argument is given 1138 int valid = 1; 1139 for (i = size(l);i>=1;i--) 1140 {//iterate over the elements of the given list 1141 if (size(result)>0) 1142 { 1143 if (product(l[i])!=result[size(l)-i]) 1144 { 1145 valid = 0; 1146 break; 1147 } 1148 } 1149 result = insert(result, product(l[i])); 1150 }//iterate over the elements of the given list 1151 if (valid) 1152 { 1153 return(result); 1154 } 1155 return(list()); 1156 }//No optional argument is given 1157 else 1158 { 1159 int valid = 1; 1160 for (i = size(l);i>=1;i--) 1161 {//iterate over the elements of the given list 1162 if (product(l[i])!=#[1]) 1163 { 1164 valid = 0; 1165 } 1166 result = insert(result, product(l[i])); 1167 }//iterate over the elements of the given list 1168 if (valid) 1169 { 1170 return(result); 1171 } 1172 for (i = 1 ; i<= size(result);i++) 1173 {//subtract p from every entry in result 1174 result[i] = result[i] - #[1]; 1175 }//subtract p from every entry in result 1176 return(result); 1177 } 1178 }//proc testfac 1179 example 1180 { 1181 "EXAMPLE:";echo=2; 1182 ring R = 0,(x,y),Ws(-1,1); 1183 def r = nc_algebra(1,1); 1184 setring(r); 1185 poly h = (x^2*y^2+1)*(x^4); 1186 def t1 = facfirstwa(h); 1187 //fist a correct list 1188 testfac(t1); 1189 //now a correct list with the factorized polynomial 1190 testfac(t1,h); 1191 //now we put in an incorrect list without a polynomial 1192 t1[5][3] = y; 1193 testfac(t1); 1194 //and last but not least we take h as additional input 1195 testfac(t1,h); 1196 } 1197 //================================================== 1198 //Procedure facsubwa: 1199 //This procedure serves the purpose to compute a 1200 //factorization of a given polynomial in a ring, whose subring 1201 //is the first Weyl algebra. The polynomial must only contain 1202 //the two arguments, which are also given by the user. 1203 proc facsubwa(poly h, X, D) 1204 "USAGE: facsubwa(h,x,y) - h is a polynomial in the first Weyl algebra, X and D are the variables in h, which have the commutation rule DX = XD + 1@* 1205 RETURN: list@* 1206 PURPOSE: Given a polynomial in a Ring, which contains the first Weyl algebra as a subring. Furthermore let this polynomial be in the first Weyl algebra with the variables X and D with DX = XD +1.@* 1207 THEORY: @code{facsubwa} computes some factorizations of the given polynomial, which is a polynomial in the variables X and D@* 1208 EXAMPLE: example facsubwa; shows examples 1209 SEE ALSO: facfirstwa 1210 "{//proc facsubwa 1211 if(!isWeyl()) 1212 { 1213 return(list()); 1214 } 1215 def r = basering; 1216 //We begin to check the input 1217 if (size(X)>1) 1218 { 1219 return(list()); 1220 } 1221 if (size(D)>1) 1222 { 1223 return(list()); 1224 } 1225 intvec lexpofX = leadexp(X); 1226 intvec lexpofD = leadexp(D); 1227 if (sum(lexpofX)!=1) 1228 { 1229 return(list()); 1230 } 1231 if (sum(lexpofD)!=1) 1232 { 1233 return(list()); 1234 } 1235 int varnumX=1; 1236 int varnumD=1; 1237 while(lexpofX[varnumX] != 1) 1238 { 1239 varnumX++; 1240 } 1241 while(lexpofD[varnumD] != 1) 1242 { 1243 varnumD++; 1244 } 1245 lexpofX = lexpofX +1; 1246 lexpofX[varnumX] = 0; 1247 lexpofX[varnumD] = 0; 1248 if (deg(h,lexpofX)!=0) 1249 { 1250 return(list()); 1251 } 1252 //Input successfully checked 1253 ring firstweyl = 0,(var(varnumX),var(varnumD)),dp; 1254 def Firstweyl = nc_algebra(1,1); 1255 setring Firstweyl; 1256 poly h = imap(r,h); 1257 list result = facfirstwa(h); 1258 setring r; 1259 list result = imap(Firstweyl,result); 1260 return(result); 1261 }//proc facsubwa 1262 example 1263 { 1264 "EXAMPLE:";echo=2; 1265 ring R = 0,(x,y),Ws(-1,1); 1266 def r = nc_algebra(1,1); 1267 setring(r); 1268 poly h = (x^2*y^2+x)*x; 1269 facsubwa(h,x,y); 1270 } 1271 //================================================== 1092 1272 /* 1093 1273 Example polynomials where one can find factorizations
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