| | 1 | /* genus2reduction |
| | 2 | by Qing Liu <liu@math.u-bordeaux.fr> |
| | 3 | and Henri Cohen <cohen@math.u-bordeaux.fr> |
| | 4 | |
| | 5 | An algorithm 'à la Tate' for curves of genus 2 |
| | 6 | |
| | 7 | Current maintainer: William Stein (wstein@ucsd.edu) |
| | 8 | (as part of SAGE: Software for Algebra and Geometry Experimentation) |
| | 9 | */ |
| | 10 | |
| | 11 | /* Qing Liu: Last modified october 5th 1998 */ |
| | 12 | |
| | 13 | /* |
| | 14 | William Stein: Modified 2006-03-05. |
| | 15 | |
| | 16 | */ |
| | 17 | |
| | 18 | #include "pari.h" |
| | 19 | |
| | 20 | |
| | 21 | #ifdef LONG_IS_64BIT |
| | 22 | # define VERYBIGINT (9223372036854775807L) /* 2^63-1 */ |
| | 23 | # define EXP220 (1099511627776L) /* 2^40 */ |
| | 24 | # define BIGINT (2147483647) /* 2^31-1 */ |
| | 25 | #else |
| | 26 | # define VERYBIGINT (2147483647L) /* 2^31-1 */ |
| | 27 | # define EXP220 (1048576L) /* 2^20 */ |
| | 28 | # define BIGINT (32767) /* 2^15-1 */ |
| | 29 | #endif |
| | 30 | |
| | 31 | INLINE long |
| | 32 | min(long a, long b) |
| | 33 | { |
| | 34 | if (a < b) return a; |
| | 35 | return b; |
| | 36 | } |
| | 37 | |
| | 38 | INLINE long |
| | 39 | max(long a, long b) |
| | 40 | { |
| | 41 | if (a > b) return a; |
| | 42 | return b; |
| | 43 | } |
| | 44 | |
| | 45 | INLINE GEN |
| | 46 | mppgcd(GEN a, GEN b) |
| | 47 | { |
| | 48 | if (typ(a) != t_INT || typ(b) != t_INT) pari_err(arither1); |
| | 49 | return gcdii(a,b); |
| | 50 | } |
| | 51 | |
| | 52 | GEN |
| | 53 | caltheta(GEN pol, GEN p, long lambda); |
| | 54 | |
| | 55 | GEN |
| | 56 | calthetazi(GEN polh); |
| | 57 | |
| | 58 | GEN calthetazi2(GEN polh); |
| | 59 | |
| | 60 | GEN |
| | 61 | factmz(GEN polhp, GEN p); |
| | 62 | |
| | 63 | GEN |
| | 64 | polymini(GEN pol, GEN p); |
| | 65 | |
| | 66 | GEN |
| | 67 | polyminizi(GEN pol); |
| | 68 | |
| | 69 | GEN |
| | 70 | polyminizi2(GEN pol); |
| | 71 | |
| | 72 | GEN |
| | 73 | zi2mod(GEN u); |
| | 74 | |
| | 75 | long polval(GEN pol, GEN p); |
| | 76 | |
| | 77 | GEN factorpadicnonun(GEN pol, GEN p, long r); |
| | 78 | |
| | 79 | long |
| | 80 | discpart(GEN polh, GEN p, long ord); |
| | 81 | |
| | 82 | INLINE long |
| | 83 | myval(GEN x, GEN p) |
| | 84 | { |
| | 85 | return gequal0(x)?EXP220:ggval(x,p); |
| | 86 | } |
| | 87 | |
| | 88 | long |
| | 89 | myvalzi(GEN b); |
| | 90 | |
| | 91 | long |
| | 92 | myvalzi2(GEN b); |
| | 93 | |
| | 94 | int |
| | 95 | main() |
| | 96 | { |
| | 97 | char buf[1000]; |
| | 98 | GEN a0,a1,a2,a3,a4,a5,a6,jpol2,jpol4,jpol6,j2,j4,j6,j8,j10,i4,i12,j12,q,p,r,n,m; |
| | 99 | GEN p1,s,pro1,pro2,dk,d1k,d2k,dm,rk,polh,polh1,theta,theta1,polf,list,c1,c2,c3,c4,c5,c6,prod,facti,facto,factp,e0,b,polhp,unmodp; |
| | 100 | GEN apol2,apol3,apol4,apol5,bpol2,A2,A3,A4,A5,B2,e1,e2,e3,vl,vm,vn,polr,Ieps,sjinv,pjinv,cond,matmin; |
| | 101 | long eps,eps2,i,val[8],deg[8],va0,va2,va3,va4,va5,vb2,vb5,vb6,v12,flc; |
| | 102 | long tt,d,d1,d2,d3,f1,f2,g,h,v1,v2,j2m,r1,r2,r3,r4,dismin,alpha,lambda; |
| | 103 | long indice,vc6,mm,nb,dism,maxc,condp,R,alpha1,comp,beta,dd,pr,ip,j,temp; |
| | 104 | |
| | 105 | pari_init_opts(10000000, 500000, INIT_JMPm | INIT_DFTm); |
| | 106 | jpol2=readseq("a0;a1;a2;a3;a4;a5;a6;2^-2*(-120*a0*a6+20*a1*a5-8*a2*a4+3*a3^2)"); |
| | 107 | jpol4=readseq("a0;a1;a2;a3;a4;a5;a6;2^-7*(240*(a0*a3*a4*a5+a1*a2*a3*a6)-400*(a0*a2*a5^2+a1^2*a4*a6)-64*(a0*a4^3+a2^3*a6)+16*(a1*a3*a4^2+a2^2*a3*a5)-672*a0*a3^2*a6+240*a1^2*a5^2-112*a1*a2*a4*a5-8*a1*a3^2*a5+16*a2^2*a4^2-16*a2*a3^2*a4+3*a3^4+2640*a0^2*a6^2-880*a0*a1*a5*a6+1312*a0*a2*a4*a6)"); |
| | 108 | jpol6=readseq("a0;a1;a2;a3;a4;a5;a6;2^-10*(1600*(a0^2*a4^2*a5^2+a1^2*a2^2*a6^2)+1600*(a0*a1*a2*a5^3+a1^3*a4*a5*a6)+640*(a0*a1*a3*a4*a5^2+a1^2*a2*a3*a5*a6)-4000*(a0^2*a3*a5^3+a1^3*a3*a6^2)-384*(a0*a1*a4^3*a5+a1*a2^3*a5*a6)-640*(a0*a2^2*a4*a5^2+a1^2*a2*a4^2*a6)+80*(a0*a2*a3^2*a5^2+a1^2*a3^2*a4*a6)+192*(a0*a2*a3*a4^2*a5+a1*a2^2*a3*a4*a6)-48*(a0*a3^3*a4*a5+a1*a2*a3^3*a6)-224*(a1^2*a3*a4^2*a5+a1*a2^2*a3*a5^2)+64*(a1^2*a4^4+a2^4*a5^2)-64*(a1*a2*a3*a4^3+a2^3*a3*a4*a5)+16*(a1*a3^3*a4^2+a2^2*a3^3*a5)-4096*(a0^2*a4^3*a6+a0*a2^3*a6^2)+6400*(a0^2*a2*a5^2*a6+a0*a1^2*a4*a6^2)+10560*(a0^2*a3*a4*a5*a6+a0*a1*a2*a3*a6^2)+2624*(a0*a1*a3*a4^2*a6+a0*a2^2*a3*a5*a6)-4432*a0*a1*a3^2*a5*a6-8*a2*a3^4*a4+a3^6-320*a1^3*a5^3+64*a1^2*a2*a4*a5^2+176*a1^2*a3^2*a5^2+128*a1*a2^2*a4^2*a5+112*a1*a2*a3^2*a4*a5-28*a1*a3^4*a5+16*a2^2*a3^2*a4^2+5120*a0^3*a6^3-2544*a0^2*a3^2*a6^2+312*a0*a3^4*a6-14336*a0^2*a2*a4*a6^2+1024*a0*a2^2*a4^2*a6-2560*a0^2*a1*a5*a6^2-2240*a0*a1^2*a5^2*a6-6528*a0*a1*a2*a4*a5*a6-1568*a0*a2*a3^2*a4*a6)"); |
| | 109 | labinf: |
| | 110 | printf(" \n");fflush(stdout); |
| | 111 | printf("enter Q(x) : ");fflush(stdout);fflush(stdin); |
| | 112 | if (scanf("%s",buf) < 0) exit(0); /* Exit on end-of-file */ |
| | 113 | q=readseq(buf); |
| | 114 | printf("enter P(x) : ");fflush(stdout);fflush(stdin); |
| | 115 | if (scanf("%s",buf) < 0) exit(0); /* Exit on end-of-file */ |
| | 116 | p=readseq(buf); |
| | 117 | printf(" \n");fflush(stdout); |
| | 118 | polr=gadd(gmul(q,q),gmul2n(p,2)); |
| | 119 | if(gequal0(polr)) exit(0); |
| | 120 | if(lg(polr)>9||lg(polr)<8) |
| | 121 | { |
| | 122 | printf("It is not a curve of genus 2\n");fflush(stdout); |
| | 123 | goto labinf; |
| | 124 | } |
| | 125 | a0=truecoeff(polr,6); |
| | 126 | a1=truecoeff(polr,5); |
| | 127 | j10=gequal0(a0)?gmul2n(gmul(gmul(a1,a1),discsr(polr)),-12):gmul2n(discsr(polr),-12); |
| | 128 | if(gequal0(j10)) {printf("singular curve\n");fflush(stdout);exit(1);} |
| | 129 | facto=factor(gabs(j10, 0)); |
| | 130 | temp=timer(); |
| | 131 | printf("factorization CPU time = %ld\n",temp);fflush(stdout); |
| | 132 | factp=(GEN)facto[1]; |
| | 133 | pr=1; if(!cmpis((GEN)factp[1],2)) pr=2; |
| | 134 | matmin=cgetg(6,19); |
| | 135 | for(j=1;j<=5;j++) |
| | 136 | matmin[j]=(long)cgetg(lg(factp)-pr+1,18); |
| | 137 | for(i=pr;i<lg(factp);i++) |
| | 138 | { |
| | 139 | p=(GEN)factp[i]; |
| | 140 | polf=polymini(polr,p); |
| | 141 | coeff(matmin,i,1)=polf[1]; |
| | 142 | coeff(matmin,i,2)=polf[2]; |
| | 143 | coeff(matmin,i,3)=polf[3]; |
| | 144 | coeff(matmin,i,4)=polf[4]; |
| | 145 | coeff(matmin,i,5)=polf[5]; |
| | 146 | polr=gmul((GEN)polf[1],gpow(p,(GEN)polf[4],0)); |
| | 147 | } |
| | 148 | a0=truecoeff(polr,6); |
| | 149 | a1=truecoeff(polr,5); |
| | 150 | j10=gequal0(a0)?gmul2n(gmul(gmul(a1,a1),discsr(polr)),-12):gmul2n(discsr(polr),-12); |
| | 151 | for(i=1;i<lg(factp);i++) |
| | 152 | { |
| | 153 | gcoeff(facto,i,2)=stoi(myval(j10,(GEN)factp[i])); |
| | 154 | } |
| | 155 | dd=itos(gmul(gen_2,gdivent(stoi(polval(polr,gen_2)),gen_2))); |
| | 156 | printf("a minimal equation over Z[1/2] is : \n"); |
| | 157 | printf("y^2 = ");output(gdiv(polr,gpowgs(gen_2,dd))); |
| | 158 | printf(" \n");fflush(stdout); |
| | 159 | |
| | 160 | printf("factorization of the minimal (away from 2) discriminant : \n"); |
| | 161 | output(facto);printf(" \n");fflush(stdout); |
| | 162 | |
| | 163 | a2=truecoeff(polr,4);a3=truecoeff(polr,3); |
| | 164 | a4=truecoeff(polr,2);a5=truecoeff(polr,1); |
| | 165 | a6=truecoeff(polr,0); |
| | 166 | j2=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(jpol2,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 167 | j4=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(jpol4,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 168 | i4=gsub(gsqr(j2),gmulsg(24,j4)); |
| | 169 | j6=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(jpol6,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 170 | j8=gmul2n(gsub(gmul(j2,j6),gmul(j4,j4)),-2); |
| | 171 | i12=gmul2n(gsub(gadd(gsqr(gmul(j2,j4)),gmulsg(36,gmul(gmul(j2,j4),j6))),gadd(gadd(gmulsg(32,gmul(gsqr(j4),j4)),gmul(j6,gmul(gsqr(j2),j2))),gmulsg(108,gsqr(j6)))),-2); |
| | 172 | for(i=1;i<=2;i++) deg[i]=2*i; |
| | 173 | for(i=3;i<=7;i++) deg[i]=2*i-2; |
| | 174 | cond=gen_1; |
| | 175 | condp=0; |
| | 176 | ip=0; |
| | 177 | p=gen_1; |
| | 178 | |
| | 179 | recp: |
| | 180 | cond=gmul(cond,gpowgs(p,condp)); |
| | 181 | gcoeff(facto,ip,2)=stoi(condp); |
| | 182 | ip=ip+1; |
| | 183 | if(ip>=lg(factp)) |
| | 184 | { |
| | 185 | printf(" \n");fflush(stdout); |
| | 186 | dd=ggval(cond,gen_2); |
| | 187 | if(dd<4) |
| | 188 | { |
| | 189 | printf("the conductor is ");output(cond); |
| | 190 | printf("in factorized form : ");output(facto); |
| | 191 | temp+=timer(); |
| | 192 | printf("total CPU time = %ld\n",temp);fflush(stdout); |
| | 193 | goto labinf; |
| | 194 | } |
| | 195 | cond=gdiv(cond,gpowgs(gen_2,dd)); |
| | 196 | printf("the prime to 2 part of the conductor is ");output(cond); |
| | 197 | gcoeff(facto,1,2)=gen_0; |
| | 198 | printf("in factorized form : "); |
| | 199 | output(facto); |
| | 200 | temp+=timer(); |
| | 201 | printf("total CPU time = %ld\n",temp);fflush(stdout); |
| | 202 | goto labinf; |
| | 203 | } |
| | 204 | p=(GEN)factp[ip]; |
| | 205 | printf("p=");output(p); |
| | 206 | dismin=ggval(j10,p); |
| | 207 | val[1]=myval(j2,p);val[2]=myval(j4,p);val[3]=myval(i4,p); |
| | 208 | val[4]=myval(j6,p);val[5]=myval(j8,p);val[6]=dismin; |
| | 209 | val[7]=myval(i12,p); |
| | 210 | if(gcmp(p,stoi(5))>0) maxc=4; |
| | 211 | else |
| | 212 | { |
| | 213 | if(!cmpis(p,5)) maxc=9; |
| | 214 | else |
| | 215 | { |
| | 216 | if(!cmpis(p,3)) maxc=10; |
| | 217 | else maxc=20; |
| | 218 | } |
| | 219 | } |
| | 220 | /* maxc=maximum du conducteur */ |
| | 221 | unmodp=gmodulo(gen_1,p); |
| | 222 | |
| | 223 | printf("(potential) stable reduction : "); |
| | 224 | p1=cgetg(8,18); |
| | 225 | for(i=1;i<=7;i++) p1[i]=(long)gdiv(stoi(val[i]),stoi(deg[i])); |
| | 226 | s=(GEN)p1[1];for(i=2;i<=7;i++) if(gcmp((GEN)p1[i],s)<0) s=(GEN)p1[i]; |
| | 227 | if(gequal(s,(GEN)p1[6])) {tt=1;printf(" (I)\n");goto aff;} |
| | 228 | if(gequal(s,(GEN)p1[7])) |
| | 229 | { |
| | 230 | tt=2; |
| | 231 | printf(" (II), j=");fflush(stdout); |
| | 232 | output(lift(gmul(unmodp,gdiv(gpowgs(i4,3),i12)))); |
| | 233 | goto aff; |
| | 234 | } |
| | 235 | if(gequal(s,(GEN)p1[3])) |
| | 236 | { |
| | 237 | if((val[2]==val[3])||(2*val[4]==3*val[3])) |
| | 238 | {tt=3;printf(" (III)\n");goto aff;} |
| | 239 | else {tt=4;printf(" (IV)\n");goto aff;} |
| | 240 | } |
| | 241 | eps=1;if(gequal(p,gen_2)) eps=4;if(gequal(p,stoi(3))) eps=3; |
| | 242 | eps2=1;if(gequal(p,gen_2)) eps2=5;if(gequal(p,stoi(3))) eps2=4; |
| | 243 | Ieps=gdivgs(j2,12);if(gequal(p,gen_2)) Ieps=j8;if(gequal(p,stoi(3))) Ieps=j6; |
| | 244 | r1=3*eps*val[3]; |
| | 245 | r3=eps*val[6]+val[eps2]; |
| | 246 | r2=eps*val[7]; |
| | 247 | r4=r1;if(r2<r4) r4=r2;if(r3<r4) r4=r3; |
| | 248 | if(r3==r4) |
| | 249 | { |
| | 250 | tt=5; |
| | 251 | sjinv=lift(gmul(unmodp,gadd(stoi(1728),gdiv(gpowgs(i12,eps),gmul(gpowgs(j10,eps),Ieps))))); |
| | 252 | pjinv=lift(gmul(unmodp,gdiv(gpowgs(i4,3*eps),gmul(gpowgs(j10,eps),Ieps)))); |
| | 253 | printf(" (V), j1+j2=");fflush(stdout);brute(sjinv,'g',-1); |
| | 254 | printf(", j1*j2=");fflush(stdout);output(pjinv); |
| | 255 | goto aff; |
| | 256 | } |
| | 257 | if(r2==r4) |
| | 258 | { |
| | 259 | tt=6; |
| | 260 | printf(" (VI), j=");fflush(stdout); |
| | 261 | output(lift(gmul(unmodp,gdiv(gpowgs(i4,3),i12)))); |
| | 262 | goto aff; |
| | 263 | } |
| | 264 | if(r1==r4) {tt=7;printf(" (VII)\n");goto aff;} |
| | 265 | aff: |
| | 266 | if(!dismin) |
| | 267 | { |
| | 268 | printf("good reduction at p : [I{0-0-0}] page 155, (1), f=0\n"); |
| | 269 | condp=0;fflush(stdout);goto recp; |
| | 270 | } |
| | 271 | if(dismin==1) |
| | 272 | { |
| | 273 | condp=1; |
| | 274 | printf("reduction at p : [I{1-0-0}] page 170, (1), f=1\n"); |
| | 275 | fflush(stdout);goto recp; |
| | 276 | } |
| | 277 | if(dismin==2) |
| | 278 | { |
| | 279 | switch(tt) |
| | 280 | { |
| | 281 | case 2: |
| | 282 | { |
| | 283 | condp=1; |
| | 284 | printf("reduction at p : [I{2-0-0}] page 170, (2), f=1\n"); |
| | 285 | fflush(stdout);goto recp; |
| | 286 | } |
| | 287 | case 3: |
| | 288 | { |
| | 289 | condp=2; |
| | 290 | printf("reduction at p : [I{1-1-0}] page 179, (1), f=2\n"); |
| | 291 | fflush(stdout);goto recp; |
| | 292 | } |
| | 293 | case 5: |
| | 294 | { |
| | 295 | if(!cmpis(p,2)||!cmpis(p,3)) |
| | 296 | {printf("bug sur tt 1\n");fflush(stdout);exit(1);} |
| | 297 | condp=2; |
| | 298 | printf("reduction at p : [I{0}-II-0] page 159, (1), f=2\n"); |
| | 299 | fflush(stdout);goto recp; |
| | 300 | } |
| | 301 | default: {printf("bug sur tt 2\n");fflush(stdout);exit(1);} |
| | 302 | } |
| | 303 | } |
| | 304 | if(!cmpis(p,2)) {condp=4;goto recp;} |
| | 305 | printf("reduction at p : ");fflush(stdout); |
| | 306 | polh=gcoeff(matmin,ip,1); |
| | 307 | lambda=itos(gcoeff(matmin,ip,2)); |
| | 308 | theta=gcoeff(matmin,ip,3); |
| | 309 | alpha=itos(gcoeff(matmin,ip,4)); |
| | 310 | if(!gequal0(gcoeff(matmin,ip,5))) goto quadratic; |
| | 311 | if(gequal0(theta)&&lambda<=2) |
| | 312 | { |
| | 313 | if(tt>=5) {printf("bug sur tt 3\n");fflush(stdout);exit(1);} |
| | 314 | goto modere; |
| | 315 | } |
| | 316 | if(dismin==3) |
| | 317 | { |
| | 318 | switch(tt) |
| | 319 | { |
| | 320 | case 2: goto modere; |
| | 321 | case 3: condp=2;printf("[I{2-1-0}] page 179, (2), f=2\n");break; |
| | 322 | case 4: condp=2;printf("[I{1-1-1}] page 182, (3), f=2\n");break; |
| | 323 | case 5: |
| | 324 | { |
| | 325 | if(cmpis(p,3)||gequal(theta,ghalf)) |
| | 326 | { |
| | 327 | condp=2;printf("[I{0}-III-0] page 161, (2), f=2\n"); |
| | 328 | } |
| | 329 | else |
| | 330 | { |
| | 331 | goto labelm3; |
| | 332 | } |
| | 333 | } |
| | 334 | break; |
| | 335 | case 6: |
| | 336 | { |
| | 337 | if(!cmpis(p,3)) |
| | 338 | {printf("bug de conducteur\n");fflush(stdout);exit(1);} |
| | 339 | condp=3; |
| | 340 | printf("[I{1}-II-0] page 172, (1), f=3\n"); |
| | 341 | } |
| | 342 | break; |
| | 343 | default: printf("bug switch sur tt 4\n");fflush(stdout);exit(1); |
| | 344 | } |
| | 345 | fflush(stdout);goto recp; |
| | 346 | } |
| | 347 | switch(lambda) |
| | 348 | { |
| | 349 | case 0: |
| | 350 | { |
| | 351 | switch(itos(gmul(theta, stoi(60)))+alpha) |
| | 352 | { |
| | 353 | case 10: condp=dismin-1;printf("[V] page 156, (3), f=%ld\n",condp); |
| | 354 | fflush(stdout);break; |
| | 355 | case 11: condp=dismin-11;printf("[V*] page 156, (3), f=%ld\n",condp); |
| | 356 | fflush(stdout);break; |
| | 357 | case 12: condp=dismin-2;printf("[IX-2] page 157, (5), f=%ld\n",condp); |
| | 358 | fflush(stdout);break; |
| | 359 | case 13: condp=dismin-12;printf("[VIII-4] page 157, (1), f=%ld\n",condp); |
| | 360 | fflush(stdout);break; |
| | 361 | case 24: condp=dismin-8;printf("[IX-4] page 158, (5), f=%ld\n",condp); |
| | 362 | fflush(stdout);break; |
| | 363 | case 15: case 16: |
| | 364 | { |
| | 365 | if(tt>=5) {printf("bug sur tt 6\n");fflush(stdout);exit(1);} |
| | 366 | goto modere; |
| | 367 | } |
| | 368 | case 20: case 21: |
| | 369 | { |
| | 370 | vb5=myval(truecoeff(polh,1),p);vb6=myval(truecoeff(polh,0),p); |
| | 371 | if(vb6>=3) |
| | 372 | { |
| | 373 | if(vb5>=3) |
| | 374 | { |
| | 375 | condp=dismin-8; |
| | 376 | printf("[II*-IV-(-1)] page 164, (3), f=%ld\n",condp); |
| | 377 | fflush(stdout); |
| | 378 | } |
| | 379 | else |
| | 380 | { |
| | 381 | if(vb5<2) {printf("bug red1");fflush(stdout);exit(1);} |
| | 382 | condp=dismin-7; |
| | 383 | printf("[IV-III*-(-1)] page 167, (6), f=%ld\n",condp); |
| | 384 | fflush(stdout); |
| | 385 | } |
| | 386 | } |
| | 387 | else |
| | 388 | { |
| | 389 | b=cgetg(8,18); |
| | 390 | b[1]=(long)truecoeff(polh,6);b[2]=(long)truecoeff(polh,5); |
| | 391 | b[3]=(long)truecoeff(polh,4);b[4]=(long)truecoeff(polh,3); |
| | 392 | b[5]=(long)truecoeff(polh,2);b[6]=(long)truecoeff(polh,1); |
| | 393 | b[7]=(long)truecoeff(polh,0); |
| | 394 | if(gdvd((GEN)b[1],p)) |
| | 395 | {printf("bug sur b0");fflush(stdout);exit(1);} |
| | 396 | c1=gmul2n((GEN)b[2],-1); |
| | 397 | c2=gmul2n(gsub(gmul((GEN)b[1],(GEN)b[3]),gsqr(c1)),-1); |
| | 398 | c3=gmul2n(gsub(gmul(gsqr((GEN)b[1]),(GEN)b[4]),gmul2n(gmul(c1,c2),1)),-1); |
| | 399 | c4=gsub(gmul(gpowgs((GEN)b[1],3),(GEN)b[5]),gadd(gmul2n(gmul(c1,c3),1),gsqr(c2))); |
| | 400 | c5=gsub(gmul(gpowgs((GEN)b[1],4),(GEN)b[6]),gmul2n(gmul(c2,c3),1)); |
| | 401 | c6=gsub(gmul(gpowgs((GEN)b[1],5),(GEN)b[7]),gsqr(c3)); |
| | 402 | /* on a b0^5*H(x/b0)=(x^3+c1*x^2+c2*x+c3)^2+c4*x^2+c5*x+c6 */ |
| | 403 | vc6=myval(c6,p); |
| | 404 | if(vc6==2) |
| | 405 | { |
| | 406 | if(alpha) |
| | 407 | { |
| | 408 | condp=dismin-16; |
| | 409 | printf("[IV] page 155, (1), f=%ld\n",condp);fflush(stdout); |
| | 410 | } |
| | 411 | else |
| | 412 | { |
| | 413 | condp=dismin-6; |
| | 414 | printf("[III] page 155, (3)^2, f=%ld\n", condp);fflush(stdout); |
| | 415 | } |
| | 416 | } |
| | 417 | else |
| | 418 | { |
| | 419 | if(myval(c3,p)>1) |
| | 420 | {printf("bug c3");fflush(stdout);exit(1);} |
| | 421 | mm=min(min(3*myval(c4,p)-4,3*myval(c5,p)-5),3*vc6-6); |
| | 422 | if(alpha) |
| | 423 | { |
| | 424 | condp=dismin-mm-16; |
| | 425 | printf("[III*{%ld}] page 184, (1), f=%ld\n",mm,condp);fflush(stdout); |
| | 426 | } |
| | 427 | else |
| | 428 | { |
| | 429 | if(mm%3) |
| | 430 | { |
| | 431 | condp=dismin-mm-6; |
| | 432 | printf("[III{%ld}] page 184, (9), f=%ld\n",mm,condp);fflush(stdout); |
| | 433 | } |
| | 434 | else |
| | 435 | { |
| | 436 | condp=dismin-mm-6; |
| | 437 | printf("[III{%ld}] page 184, (3)^2, f=%ld\n",mm,condp);fflush(stdout); |
| | 438 | } |
| | 439 | } |
| | 440 | } |
| | 441 | } |
| | 442 | } |
| | 443 | break; |
| | 444 | case 30: |
| | 445 | { |
| | 446 | if(cmpis(p,3)) goto modere; |
| | 447 | else goto quartic; |
| | 448 | } |
| | 449 | break; |
| | 450 | default: printf("bug red2\n");fflush(stdout);exit(1); |
| | 451 | } |
| | 452 | } |
| | 453 | break; |
| | 454 | case 1: |
| | 455 | { |
| | 456 | switch(itos(gmul(theta, stoi(60)))+alpha) |
| | 457 | { |
| | 458 | case 12: |
| | 459 | condp=dismin; |
| | 460 | printf("[VIII-1] page 156, (1), f=%ld\n",condp);fflush(stdout);break; |
| | 461 | case 13: |
| | 462 | condp=dismin-10; |
| | 463 | printf("[IX-3] page 157, (5), f=%ld\n",condp);fflush(stdout);break; |
| | 464 | case 24: |
| | 465 | condp=dismin-4; |
| | 466 | printf("[IX-1] page 157, (5), f=%ld\n",condp);fflush(stdout);break; |
| | 467 | case 25: |
| | 468 | condp=dismin-14; |
| | 469 | printf("[VIII-3] page 157, (1), f=%ld\n",condp);fflush(stdout);break; |
| | 470 | case 36: |
| | 471 | condp=dismin-8; |
| | 472 | printf("[VIII-2] page 157, (1), f=%ld\n",condp);fflush(stdout);break; |
| | 473 | case 15: |
| | 474 | condp=dismin-1; |
| | 475 | printf("[VII] page 156, (2), f=%ld\n",condp);fflush(stdout);break; |
| | 476 | case 16: |
| | 477 | condp=dismin-11; |
| | 478 | printf("[VII*] page 156, (2), f=%ld\n",condp);fflush(stdout);break; |
| | 479 | case 20: |
| | 480 | { |
| | 481 | if(cmpis(p,3)) |
| | 482 | { |
| | 483 | d=6*val[6]-5*val[7]-2; |
| | 484 | if(d%6) |
| | 485 | { |
| | 486 | printf("bug dans le calcul d'un indice\n"); |
| | 487 | fflush(stdout);exit(1); |
| | 488 | } |
| | 489 | dism=(d/6); |
| | 490 | } |
| | 491 | else |
| | 492 | { |
| | 493 | list=factorpadicnonun(polh,p,dismin-5); |
| | 494 | nb=lg(list);prod=pol_1(varn(polh)); |
| | 495 | for(i=1;i<nb;i++) |
| | 496 | { |
| | 497 | facti=(GEN)list[i]; |
| | 498 | if(valp((GEN)facti[2])&&lg(facti)<=5) |
| | 499 | prod=gmul(prod,facti); |
| | 500 | } |
| | 501 | if(lg(prod)>5) |
| | 502 | { |
| | 503 | printf("bug factorpadicnonun");fflush(stdout);exit(1); |
| | 504 | } |
| | 505 | e0=truecoeff(prod,2);e1=truecoeff(prod,1); |
| | 506 | e2=truecoeff(prod,0); |
| | 507 | dism=valp(gsub(gsqr(e1),gmul2n(gmul(e0,e2),2)))-1; |
| | 508 | } |
| | 509 | condp=dismin-dism-3; |
| | 510 | printf("[II-II*{%ld}] page 176, H{%ld}, f=%ld\n",dism,dism+1,condp);fflush(stdout); |
| | 511 | } |
| | 512 | break; |
| | 513 | case 21: |
| | 514 | { |
| | 515 | vb6=myval(truecoeff(polh,0),p); |
| | 516 | if(vb6<2) {printf("bug red3\n");fflush(stdout);exit(1);} |
| | 517 | condp=dismin-14; |
| | 518 | printf("[IV*-II{0}] page 175, (1), f=%ld\n",condp);fflush(stdout); |
| | 519 | } |
| | 520 | break; |
| | 521 | case 30: |
| | 522 | { |
| | 523 | vb5=myval(truecoeff(polh,1),p); |
| | 524 | if(vb5==2) |
| | 525 | { |
| | 526 | if(tt>=5) {printf("bug sur tt 6\n");fflush(stdout);exit(1);} |
| | 527 | goto modere; |
| | 528 | } |
| | 529 | condp=dismin-7; |
| | 530 | printf("[II*-III-(-1)] page 167, (2), f=%ld\n",condp);fflush(stdout); |
| | 531 | } |
| | 532 | break; |
| | 533 | } |
| | 534 | } |
| | 535 | break; |
| | 536 | case 2: |
| | 537 | { |
| | 538 | if(!cmpis(denom(theta),4)) |
| | 539 | { |
| | 540 | if(tt>4) {printf("bug sur tt 5\n");fflush(stdout);exit(1);} |
| | 541 | goto modere; |
| | 542 | } |
| | 543 | if(cmpis(p,3)&&!cmpis(denom(theta),3)) goto modere; |
| | 544 | list=factorpadicnonun(polh,p,dismin-10*alpha); |
| | 545 | nb=lg(list);prod=pol_1(varn(polh)); |
| | 546 | for(i=1;i<nb;i++) |
| | 547 | { |
| | 548 | facti=(GEN)list[i]; |
| | 549 | if(!valp((GEN)facti[2])) |
| | 550 | prod=gmul(prod,facti); |
| | 551 | } |
| | 552 | if(lg(prod)>5) |
| | 553 | { |
| | 554 | printf("bug factorpadicnonun 2"); |
| | 555 | fflush(stdout);exit(1); |
| | 556 | } |
| | 557 | e0=truecoeff(prod,2);e1=truecoeff(prod,1);e2=truecoeff(prod,0); |
| | 558 | dism=valp(gsub(gsqr(e1),gmul2n(gmul(e0,e2),2))); |
| | 559 | switch(itos(gmulgs(theta,12))+alpha-4) |
| | 560 | { |
| | 561 | case 0: |
| | 562 | condp=dismin-dism-1; |
| | 563 | printf("[IV-II{%ld}] page 175, (%ld), f=%ld\n",dism,3*dism+2,condp); |
| | 564 | fflush(stdout);break; |
| | 565 | case 1: |
| | 566 | condp=dismin-dism-10; |
| | 567 | printf("[II*-II*{%ld}] page 175, H{%ld}, f=%ld\n",dism,dism+1,condp); |
| | 568 | fflush(stdout);break; |
| | 569 | case 2: case 3: |
| | 570 | { |
| | 571 | if(myval(truecoeff(polh,0),p)==2) |
| | 572 | { |
| | 573 | if(tt>4) {printf("bug sur tt 5\n");fflush(stdout);exit(1);} |
| | 574 | goto modere; |
| | 575 | } |
| | 576 | else |
| | 577 | { |
| | 578 | dism=dism+1; |
| | 579 | indice=val[6]-(5*val[3]/2)-dism; |
| | 580 | if((dism*indice)&1) |
| | 581 | { |
| | 582 | condp=dismin-dism-indice-2; |
| | 583 | printf("[II{%ld-%ld}] page 182, (2)x(%ld), f=%ld\n", |
| | 584 | dism,indice,2*dism,condp);fflush(stdout); |
| | 585 | } |
| | 586 | else |
| | 587 | { |
| | 588 | condp=dismin-dism-indice-2; |
| | 589 | printf("[II{%ld-%ld}] page 182, (%ld), f=%ld\n", |
| | 590 | dism,indice,4*dism,condp);fflush(stdout); |
| | 591 | } |
| | 592 | } |
| | 593 | } |
| | 594 | break; |
| | 595 | case 4: |
| | 596 | condp=dismin-dism-5; |
| | 597 | printf("[IV*-II{%ld}] page 175, (%ld), f=%ld\n",dism+1,3*dism+4,condp); |
| | 598 | fflush(stdout);break; |
| | 599 | } |
| | 600 | } |
| | 601 | break; |
| | 602 | case 3: |
| | 603 | { |
| | 604 | if(cmpis(p,3)||tt<=4) goto modere; |
| | 605 | goto labelm3; |
| | 606 | } |
| | 607 | break; |
| | 608 | default: printf("bug switch sur lambda\n");fflush(stdout);exit(1); |
| | 609 | } |
| | 610 | if(condp<2||condp>maxc) |
| | 611 | {printf("bug conducteur 3\n");fflush(stdout);exit(1);} |
| | 612 | goto recp; |
| | 613 | |
| | 614 | labelm3: |
| | 615 | polh1=gcopy(polh); |
| | 616 | theta1=gcopy(theta); |
| | 617 | alpha1=alpha; |
| | 618 | polh=gmul(gsubst(polh,0,ginv(pol_x(0))),gpowgs(pol_x(0),6)); |
| | 619 | polf=polymini(gmul(polh,gpowgs(p,alpha)),p); |
| | 620 | polh=(GEN)polf[1]; |
| | 621 | lambda=itos((GEN)polf[2]); |
| | 622 | theta=(GEN)polf[3]; |
| | 623 | alpha=itos((GEN)polf[4]); |
| | 624 | beta=itos((GEN)polf[6]); |
| | 625 | if(!lambda==3) |
| | 626 | {printf("bug lambda=3\n");fflush(stdout);exit(1);} |
| | 627 | R=beta-alpha1-alpha; |
| | 628 | if(R&1) |
| | 629 | { |
| | 630 | printf("bug R impair\n");fflush(stdout);exit(1); |
| | 631 | } |
| | 632 | R>>=1; |
| | 633 | if(R<=-2) |
| | 634 | { |
| | 635 | printf("bug R <=-2\n");fflush(stdout);exit(1); |
| | 636 | } |
| | 637 | if(val[eps2]%(2*eps)) |
| | 638 | { |
| | 639 | printf("bug sur val[eps2]\n");fflush(stdout);exit(1); |
| | 640 | } |
| | 641 | if(R>=0&&(alpha+alpha1)>=1) |
| | 642 | { |
| | 643 | printf("bug equation minimale\n");fflush(stdout);exit(1); |
| | 644 | } |
| | 645 | r1=itos(gmulgs(theta1,6))+6*alpha1; |
| | 646 | r2=itos(gmulgs(theta,6))+6*alpha; |
| | 647 | |
| | 648 | litredtp: |
| | 649 | if((r1==0||r1==6)&&(r2==0||r2==6)) |
| | 650 | { |
| | 651 | if(tt==5) |
| | 652 | { |
| | 653 | switch(2*r2+r1) |
| | 654 | { |
| | 655 | case 0: |
| | 656 | condp=0; |
| | 657 | printf("[I{0}-I{0}-%ld] page 158, (1), f=0\n",R); |
| | 658 | fflush(stdout);break; |
| | 659 | case 6: case 12: |
| | 660 | condp=2; |
| | 661 | printf("[I*{0}-I{0}-%ld] page 159, (2)^2, f=2\n",R); |
| | 662 | fflush(stdout);break; |
| | 663 | case 18: |
| | 664 | condp=4; |
| | 665 | printf("[I*{0}-I*{0}-%ld] page 158, (2)^4, f=4\n",R); |
| | 666 | fflush(stdout);break; |
| | 667 | } |
| | 668 | goto recp; |
| | 669 | } |
| | 670 | if(r1==r2) goto modere; |
| | 671 | if(tt==6) |
| | 672 | { |
| | 673 | d=val[6]-val[7]+(val[eps2]/eps); |
| | 674 | if(r1&&alpha1==0) |
| | 675 | { |
| | 676 | polh1=gdiv(gsubst(polh1,0,gmul(p,pol_x(0))),gpowgs(p,3)); |
| | 677 | } |
| | 678 | polhp=gmul(unmodp,polh1); |
| | 679 | if(!gequal0(discsr(polhp))) |
| | 680 | { |
| | 681 | indice=0; condp=3-r2/6; |
| | 682 | } |
| | 683 | else |
| | 684 | { |
| | 685 | indice=d; condp=3-r1/6; |
| | 686 | } |
| | 687 | } |
| | 688 | else /* donc tt==7 */ |
| | 689 | { |
| | 690 | if(gequal1(theta1)) |
| | 691 | { |
| | 692 | polh1=gdiv(gsubst(polh1,0,gmul(p,pol_x(0))),gpowgs(p,3)); |
| | 693 | } |
| | 694 | d=val[6]-3*val[3]+(val[eps2]/eps); |
| | 695 | d1=min(val[7]-3*val[3],d/2); |
| | 696 | if(d==2*d1) indice=d1; |
| | 697 | else |
| | 698 | { |
| | 699 | indice=discpart(polh1,p,d1+1); |
| | 700 | if(indice>=d1+1) indice=d-d1; |
| | 701 | else indice=d1; |
| | 702 | } |
| | 703 | condp=3; |
| | 704 | } |
| | 705 | if(r1) |
| | 706 | { |
| | 707 | if(tt==6) |
| | 708 | { |
| | 709 | printf("[I*{%ld}-I{%ld}-%ld] page 170, H{%ld}x(%ld), f=%ld\n", |
| | 710 | indice,d-indice,R,indice,d-indice,condp); |
| | 711 | fflush(stdout);goto recp; |
| | 712 | } |
| | 713 | else |
| | 714 | { |
| | 715 | printf("[I*{%ld}-I{%ld}-%ld] page 180, H{%ld}x(%ld), f=%ld\n", |
| | 716 | indice,d-indice,R,indice,d-indice,condp); |
| | 717 | fflush(stdout);goto recp; |
| | 718 | } |
| | 719 | } |
| | 720 | else |
| | 721 | { |
| | 722 | if(tt==6) |
| | 723 | { |
| | 724 | printf("[I{%ld}-I*{%ld}-%ld] page 170, (%ld)xH{%ld}, f=%ld\n", |
| | 725 | indice,d-indice,R,indice,d-indice,condp); |
| | 726 | fflush(stdout);goto recp; |
| | 727 | } |
| | 728 | printf("[I{%ld}-I*{%ld}-%ld] page 180, (%ld)xH{%ld}, f=%ld\n", |
| | 729 | indice,d-indice,R,indice,d-indice,condp); |
| | 730 | fflush(stdout);goto recp; |
| | 731 | } |
| | 732 | } |
| | 733 | if(tt==7) |
| | 734 | {printf("bug avant swith sur ri\n");fflush(stdout);exit(1);} |
| | 735 | switch(r1) |
| | 736 | { |
| | 737 | case 0: case 6: |
| | 738 | { |
| | 739 | if(r1&&alpha1==0) |
| | 740 | { |
| | 741 | polh1=gdiv(gsubst(polh1,0,gmul(p,pol_x(0))),gpowgs(p, 3)); |
| | 742 | } |
| | 743 | polhp=gmul(unmodp,polh1); |
| | 744 | if(!gequal0(discsr(polhp))) d=0; |
| | 745 | else d=val[6]-val[7]+(val[eps2]/eps); |
| | 746 | if(r1) |
| | 747 | {printf("[I*{%ld}-",d);comp=d+5;} |
| | 748 | else |
| | 749 | { |
| | 750 | printf("[I{%ld}-",d); |
| | 751 | if(d) comp=d; |
| | 752 | else comp=1; |
| | 753 | } |
| | 754 | } |
| | 755 | fflush(stdout);break; |
| | 756 | case 3: printf("[III-");fflush(stdout);comp=2;break; |
| | 757 | case 9: printf("[III*-");fflush(stdout);comp=8;break; |
| | 758 | case 2: printf("[II-");fflush(stdout);comp=1;break; |
| | 759 | case 8: printf("[IV*-");fflush(stdout);comp=7;break; |
| | 760 | case 4: printf("[IV-");fflush(stdout);comp=3;break; |
| | 761 | case 10: printf("[II*-");fflush(stdout);comp=9;break; |
| | 762 | default: printf("bug type1\n");fflush(stdout);exit(1); |
| | 763 | } |
| | 764 | switch(r2) |
| | 765 | { |
| | 766 | case 0: case 6: |
| | 767 | { |
| | 768 | if(r2&&alpha==0) |
| | 769 | { |
| | 770 | polh=gdiv(gsubst(polh,0,gmul(p,pol_x(0))),gpowgs(p,3)); |
| | 771 | } |
| | 772 | polhp=gmul(unmodp,polh); |
| | 773 | if(!gequal0(discsr(polhp))) indice=0; |
| | 774 | else indice=val[6]-val[7]+(val[eps2]/eps); |
| | 775 | if(r2) |
| | 776 | {printf("I*{%ld}-%ld] pages 159-177, ",indice,R);comp+=indice+5;} |
| | 777 | else |
| | 778 | { |
| | 779 | printf("I{%ld}-%ld] pages 159-177, ",indice,R); |
| | 780 | if(indice) comp+=indice; |
| | 781 | else comp+=1; |
| | 782 | } |
| | 783 | } |
| | 784 | break; |
| | 785 | case 3: printf("III-%ld] pages 161-177, ",R);comp+=2;break; |
| | 786 | case 9: printf("III*-%ld] pages 162-177, ",R);comp+=8;break; |
| | 787 | case 2: printf("II-%ld] pages 159-174, ",R);comp+=1;break; |
| | 788 | case 8: printf("IV*-%ld] pages 160-175, ",R);comp+=7;break; |
| | 789 | case 4: printf("IV-%ld] pages 160-174, ",R);comp+=3;break; |
| | 790 | case 10: printf("II*-%ld] pages 160-174, ",R);comp+=9;break; |
| | 791 | default: printf("bug type2\n");fflush(stdout);exit(1); |
| | 792 | } |
| | 793 | if(R>=0) condp=dismin-comp+2-12*R; |
| | 794 | else condp=dismin-comp+4; |
| | 795 | if(condp>maxc) |
| | 796 | {printf("bug conducteur\n");fflush(stdout);exit(1);} |
| | 797 | switch(r1) |
| | 798 | { |
| | 799 | case 0: |
| | 800 | if(indice) printf("(%ld)x",d); |
| | 801 | else printf("(1)x"); |
| | 802 | break; |
| | 803 | case 6: printf("H{%ld}x",d);break; |
| | 804 | case 3: printf("(2)x");break; |
| | 805 | case 9: printf("(2)x");break; |
| | 806 | case 2: printf("(1)x");break; |
| | 807 | case 8: printf("(3)x");break; |
| | 808 | case 4: printf("(3)x");break; |
| | 809 | case 10: printf("(1)x");break; |
| | 810 | default: printf("bug type3\n");fflush(stdout);exit(1); |
| | 811 | } |
| | 812 | switch(r2) |
| | 813 | { |
| | 814 | case 0: |
| | 815 | if(indice) |
| | 816 | {printf("(%ld), f=%ld\n",indice,condp);fflush(stdout);} |
| | 817 | else |
| | 818 | {printf("(1), f=%ld\n",condp);fflush(stdout);} |
| | 819 | break; |
| | 820 | case 6: printf("H{%ld}, f=%ld\n",indice,condp);fflush(stdout);break; |
| | 821 | case 3: printf("(2), f=%ld\n",condp);fflush(stdout);break; |
| | 822 | case 9: printf("(2), f=%ld\n",condp);fflush(stdout);break; |
| | 823 | case 2: printf("(1), f=%ld\n",condp);fflush(stdout);break; |
| | 824 | case 8: printf("(3), f=%ld\n",condp);fflush(stdout);break; |
| | 825 | case 4: printf("(3), f=%ld\n",condp);fflush(stdout);break; |
| | 826 | case 10: printf("(1), f=%ld\n",condp);fflush(stdout);break; |
| | 827 | default: printf("bug type4\n");fflush(stdout);exit(1); |
| | 828 | } |
| | 829 | goto recp; |
| | 830 | |
| | 831 | quadratic: |
| | 832 | if(cmpis(p,3)) goto modere; |
| | 833 | alpha1=alpha; |
| | 834 | polf=(GEN)polyminizi(gmul(polh,gpowgs(p,alpha))); |
| | 835 | theta=(GEN)polf[1]; |
| | 836 | alpha=itos((GEN)polf[2]); |
| | 837 | beta=itos((GEN)polf[3]); |
| | 838 | if(alpha&&beta>=1) |
| | 839 | {printf("bug, erreur d'appreciation\n");fflush(stdout);exit(1);} |
| | 840 | R=beta-alpha; |
| | 841 | if(R>=0&&alpha1) |
| | 842 | { |
| | 843 | dismin=dismin-10; |
| | 844 | printf("(care, the minimal discriminant over Z[i] is smaller than over Z) ");fflush(stdout); |
| | 845 | } |
| | 846 | r1=itos(gmulgs(theta,6))+6*alpha; |
| | 847 | r2=r1; |
| | 848 | alpha1=alpha; |
| | 849 | theta1=gcopy(theta); |
| | 850 | goto litredtp; |
| | 851 | |
| | 852 | quartic: |
| | 853 | polf=(GEN)polyminizi2(gmul(polh,gpowgs(p,alpha))); |
| | 854 | theta=(GEN)polf[1]; |
| | 855 | beta=itos((GEN)polf[2]); |
| | 856 | if(beta&1) |
| | 857 | { |
| | 858 | printf("bug, le type sur Z[i] doit etre [K-K-(2*m)]\n"); |
| | 859 | fflush(stdout);exit(1); |
| | 860 | } |
| | 861 | R=beta/2; |
| | 862 | r1=itos(gmulgs(theta,6)); |
| | 863 | switch(tt) |
| | 864 | { |
| | 865 | case 1: case 5: d=0;break; |
| | 866 | case 3: d=val[6]-5*val[3]/2;break; |
| | 867 | case 7: d=val[6]-3*val[3]+val[eps2]/eps;break; |
| | 868 | default: printf("bug choix de types\n");fflush(stdout);exit(1); |
| | 869 | } |
| | 870 | switch(r1) |
| | 871 | { |
| | 872 | case 0: |
| | 873 | { |
| | 874 | if(d) |
| | 875 | { |
| | 876 | condp=3;printf("[2I{%ld}-%ld] page 181, (%ld), f=3\n",d,R,d); |
| | 877 | } |
| | 878 | else |
| | 879 | { |
| | 880 | condp=2; |
| | 881 | if(R) |
| | 882 | { |
| | 883 | printf("[2I{0}-%ld] page 159, (1), f=2\n",R); |
| | 884 | } |
| | 885 | else |
| | 886 | { |
| | 887 | printf("[II] page 155, (1), f=2\n"); |
| | 888 | } |
| | 889 | } |
| | 890 | } |
| | 891 | break; |
| | 892 | case 6: |
| | 893 | { |
| | 894 | condp=4;printf("[2I*{%ld}-%ld] pages 159, 181, (2)^2, f=4\n",d,R); |
| | 895 | } |
| | 896 | break; |
| | 897 | case 3: |
| | 898 | condp=4;printf("[2III-%ld] page 168, (2), f=4\n",R);break; |
| | 899 | case 9: |
| | 900 | condp=4;printf("[2III*-%ld] page 168, (2), f=4\n",R);break; |
| | 901 | case 2: |
| | 902 | condp=dismin-12*R-13;printf("[2II-%ld] page 162, (1), f=%ld\n",R,condp);break; |
| | 903 | case 8: |
| | 904 | condp=dismin-12*R-19;printf("[2IV*-%ld] page 165, (3), f=%ld\n",R,condp);break; |
| | 905 | case 4: |
| | 906 | condp=dismin-12*R-15;printf("[2IV-%ld] page 165, (3), f=%ld\n",R,condp);break; |
| | 907 | case 10: |
| | 908 | condp=dismin-12*R-21;printf("[2II*-%ld] page 163, (1), f=%ld\n",R,condp);break; |
| | 909 | default: printf("bug type1\n");fflush(stdout);exit(1); |
| | 910 | } |
| | 911 | fflush(stdout); |
| | 912 | if(condp>maxc||condp<0) |
| | 913 | {printf("bug conducteur\n");fflush(stdout);exit(1);} |
| | 914 | goto recp; |
| | 915 | |
| | 916 | modere: |
| | 917 | /* printf("(moderee) ");fflush(stdout); */ |
| | 918 | apol2=readseq("a0;a1;a2;a3;a4;a5;a6;-5*a1^2+12*a0*a2"); |
| | 919 | apol3=readseq("a0;a1;a2;a3;a4;a5;a6;5*a1^3+9*a0*(-2*a1*a2+3*a0*a3)"); |
| | 920 | apol4=readseq("a0;a1;a2;a3;a4;a5;a6;-5*a1^4+24*a0*(a1^2*a2-3*a0*a1*a3+6*a0^2*a4)"); |
| | 921 | apol5=readseq("a0;a1;a2;a3;a4;a5;a6;a1^5+3*a0*(-2*a1^3*a2+9*a0*a1^2*a3-36*a0^2*a1*a4+108*a0^3*a5)"); |
| | 922 | bpol2=readseq("a0;a1;a2;a3;a4;a5;a6;2*a2^2-5*a1*a3+10*a0*a4"); |
| | 923 | A2=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(apol2,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 924 | A3=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(apol3,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 925 | A4=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(apol4,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 926 | A5=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(apol5,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 927 | B2=gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(gsubst(bpol2,1,a0),2,a1),3,a2),4,a3),5,a4),6,a5),7,a6); |
| | 928 | va0=myval(a0,p);va2=myval(A2,p);va3=myval(A3,p);va4=myval(A4,p); |
| | 929 | va5=myval(A5,p);vb2=myval(B2,p); |
| | 930 | |
| | 931 | switch(tt) |
| | 932 | { |
| | 933 | case 1: |
| | 934 | if((!gequal0(A5))&&(20*va0+val[6]>6*va5)) |
| | 935 | { |
| | 936 | n=glcm(denom(pro1=gdiv(stoi(val[6]-2*va5),stoi(20))),denom(pro2=gdiv(stoi(5*val[6]-6*va5),stoi(40)))); |
| | 937 | r=gmul(n,pro1);q=gmul(n,pro2); |
| | 938 | } |
| | 939 | else |
| | 940 | { |
| | 941 | n=glcm(denom(pro1=gdiv(stoi(10*va0-val[6]),stoi(30))),denom(pro2=gdiv(stoi(5*va0-val[6]),stoi(10)))); |
| | 942 | r=gmul(n,pro1);q=gmul(n,pro2); |
| | 943 | } |
| | 944 | r=gmod(r,n);q=gmod(q,n); |
| | 945 | switch(itos(n)) |
| | 946 | { |
| | 947 | case 1: condp=0; |
| | 948 | printf("[I{0-0-0}] page 155, (1)");fflush(stdout);break; |
| | 949 | case 2: |
| | 950 | switch(itos(r)) |
| | 951 | { |
| | 952 | case 0: condp=4; |
| | 953 | printf("[I*{0-0-0}] page 155, (2)^4");fflush(stdout);break; |
| | 954 | case 1: condp=2; |
| | 955 | printf("[II] page 155, (1)");fflush(stdout);break; |
| | 956 | default: printf("bug1\n");fflush(stdout);exit(1); |
| | 957 | } |
| | 958 | break; |
| | 959 | case 4: condp=4;printf("[VI] page 156, (2)^2");fflush(stdout);break; |
| | 960 | default: printf("bug8\n");fflush(stdout);exit(1); |
| | 961 | } |
| | 962 | break; |
| | 963 | case 2: case 3: case 4: |
| | 964 | switch(tt) |
| | 965 | { |
| | 966 | case 2: j12=i12;break; |
| | 967 | case 3: j12=gpowgs(i4,3);break; |
| | 968 | case 4: j12=gpowgs(j2,6);break; |
| | 969 | } |
| | 970 | v12=myval(j12,p); |
| | 971 | if((9*vb2>=(6*va0+v12))&&(36*va5>=(120*va0+5*v12))) |
| | 972 | { |
| | 973 | n=glcm(denom(pro1=gdiv(stoi(12*va0-v12),stoi(36))),denom(pro2=gdiv(stoi(6*va0-v12),stoi(12)))); |
| | 974 | r=gmul(n,pro1);q=gmul(n,pro2);flc=1; |
| | 975 | } |
| | 976 | else |
| | 977 | { |
| | 978 | if(((120*va0+5*v12)>36*va5)&&(60*vb2>=(12*va5+5*v12))) |
| | 979 | { |
| | 980 | n=denom(pro1=gdiv(stoi(36*va5-25*v12),stoi(240))); |
| | 981 | q=gmul(n,pro1);r=gmulsg(-2,q);flc=1; |
| | 982 | } |
| | 983 | else |
| | 984 | { |
| | 985 | if(((6*va0+v12)>9*vb2)&&((12*va5+5*v12)>60*vb2)) |
| | 986 | { |
| | 987 | n=glcm(denom(pro1=gdiv(stoi(v12-6*vb2),stoi(12))),denom(pro2=gdiv(stoi(v12-9*vb2),stoi(12)))); |
| | 988 | r=gmul(n,pro1);q=gmul(n,pro2);flc=2; |
| | 989 | } |
| | 990 | else {printf("bug9\n");fflush(stdout);exit(1);} |
| | 991 | } |
| | 992 | } |
| | 993 | r=gmod(r,n);q=gmod(q,n); |
| | 994 | switch(tt) |
| | 995 | { |
| | 996 | case 2: |
| | 997 | d=itos(gmul(n,gdivgs(stoi(6*val[6]-5*val[7]),6))); |
| | 998 | switch(itos(n)) |
| | 999 | { |
| | 1000 | case 1: condp=1; |
| | 1001 | printf("[I{%ld-0-0}] page 170, (%ld)",d,d);fflush(stdout);break; |
| | 1002 | case 2: |
| | 1003 | switch(itos(r)) |
| | 1004 | { |
| | 1005 | case 0: condp=4; |
| | 1006 | printf("[I*{%ld-0-0}] page 171, (2)^2xH{%ld}",d/2,d/2); |
| | 1007 | fflush(stdout);break; |
| | 1008 | case 1: |
| | 1009 | switch(itos(q)) |
| | 1010 | { |
| | 1011 | case 0: condp=2; |
| | 1012 | printf("[II*{%ld-0}] page 172, (1)",d/2); |
| | 1013 | fflush(stdout);break; |
| | 1014 | case 1: condp=3; |
| | 1015 | printf("[II{%ld-0}] page 171, (%ld)",d/2,2*d); |
| | 1016 | fflush(stdout);break; |
| | 1017 | default: {printf("bug10\n");fflush(stdout);exit(1);} |
| | 1018 | } |
| | 1019 | break; |
| | 1020 | default: {printf("bug11\n");fflush(stdout);exit(1);} |
| | 1021 | } |
| | 1022 | break; |
| | 1023 | case 3: |
| | 1024 | switch(itos(r)) |
| | 1025 | { |
| | 1026 | case 1: condp=3; |
| | 1027 | printf("[IV-II{%ld}] page 175, (%ld)",(d-2)/3,d); |
| | 1028 | fflush(stdout);break; |
| | 1029 | case 2: condp=3; |
| | 1030 | printf("[IV*-II{%ld}] page 175, (%ld)",(d-1)/3,d); |
| | 1031 | fflush(stdout);break; |
| | 1032 | default: {printf("bug12\n");fflush(stdout);exit(1);} |
| | 1033 | } |
| | 1034 | break; |
| | 1035 | case 4: |
| | 1036 | switch(itos(r)) |
| | 1037 | { |
| | 1038 | case 1: |
| | 1039 | switch(itos(q)) |
| | 1040 | { |
| | 1041 | case 1: condp=3; |
| | 1042 | printf("[III-II{%ld}] page 177, (%ld)",(d-2)/4,d/2); |
| | 1043 | fflush(stdout);break; |
| | 1044 | case 3: condp=4; |
| | 1045 | printf("[III*-II*{%ld}] page 178, (8)",(d-2)/4); |
| | 1046 | fflush(stdout);break; |
| | 1047 | default: {printf("bug13\n");fflush(stdout);exit(1);} |
| | 1048 | } |
| | 1049 | break; |
| | 1050 | case 3: |
| | 1051 | switch(itos(q)) |
| | 1052 | { |
| | 1053 | case 1: condp=4; |
| | 1054 | printf("[III-II*{%ld}] page 178, (8)",(d-2)/4); |
| | 1055 | fflush(stdout);break; |
| | 1056 | case 3: condp=3; |
| | 1057 | printf("[III*-II{%ld}] page 178, (%ld)",(d-2)/4,d/2); |
| | 1058 | fflush(stdout);break; |
| | 1059 | default: {printf("bug14\n");fflush(stdout);exit(1);} |
| | 1060 | } |
| | 1061 | break; |
| | 1062 | default: {printf("bug15\n");fflush(stdout);exit(1);} |
| | 1063 | } |
| | 1064 | break; |
| | 1065 | case 6: |
| | 1066 | switch(itos(r)) |
| | 1067 | { |
| | 1068 | case 2: condp=4; |
| | 1069 | printf("[II*-II*{%ld}] page 176, H{%ld}",(d-4)/6,(d+2)/6); |
| | 1070 | fflush(stdout);break; |
| | 1071 | case 4: condp=4; |
| | 1072 | printf("[II-II*{%ld}] page 176, H{%ld}",(d-2)/6,(d+4)/6); |
| | 1073 | fflush(stdout);break; |
| | 1074 | default: {printf("bug16\n");fflush(stdout);exit(1);} |
| | 1075 | } |
| | 1076 | break; |
| | 1077 | default: {printf("bug17\n");fflush(stdout);exit(1);} |
| | 1078 | } |
| | 1079 | break; |
| | 1080 | case 3: |
| | 1081 | va5=2*val[6]-5*val[3];e1=gmin(stoi(val[7]-3*val[3]),gmul2n(stoi(va5),-2)); |
| | 1082 | e2=gsub(gmul2n(stoi(va5),-1),e1); |
| | 1083 | d1=itos(gmul(n,e1));d2=itos(gmul(n,e2)); |
| | 1084 | switch(itos(n)) |
| | 1085 | { |
| | 1086 | case 1: condp=2; |
| | 1087 | printf("[I{%ld-%ld-0}] page 179, (%ld)x(%ld)",d1,d2,d1,d2); |
| | 1088 | fflush(stdout);break; |
| | 1089 | case 2: |
| | 1090 | switch(itos(r)) |
| | 1091 | { |
| | 1092 | case 0: condp=4; |
| | 1093 | printf("[I*{%ld-%ld-0}] page 180, H{%ld}xH{%ld}",d1/2,d2/2,d1/2,d2/2); |
| | 1094 | fflush(stdout);break; |
| | 1095 | case 1: |
| | 1096 | switch(flc) |
| | 1097 | { |
| | 1098 | case 1:condp=3; |
| | 1099 | printf("[2I{%ld}-0] page 181, (%ld)",d1,d1); |
| | 1100 | fflush(stdout);break; |
| | 1101 | case 2: condp=3; |
| | 1102 | printf("[II{%ld-%ld}] page 182, ",d1/2,d2/2); |
| | 1103 | if((d1*d2-4)&7) printf("(%ld)",2*d1); |
| | 1104 | else printf("(%ld)x(2)",d1); |
| | 1105 | printf("ou [II{%ld-%ld}] page 182, ",d2/2,d1/2); |
| | 1106 | if((d1*d2-4)&7) printf("(%ld)",2*d2); |
| | 1107 | else printf("(%ld)x(2)",d2); |
| | 1108 | fflush(stdout);break; |
| | 1109 | default: {printf("bug19\n");fflush(stdout);exit(1);} |
| | 1110 | } |
| | 1111 | break; |
| | 1112 | default: {printf("bug20\n");fflush(stdout);exit(1);} |
| | 1113 | } |
| | 1114 | break; |
| | 1115 | case 4: condp=4; |
| | 1116 | printf("[III{%ld}] page 182, H{%ld}",d1/2,d1/2); |
| | 1117 | fflush(stdout);break; |
| | 1118 | default: {printf("bug21\n");fflush(stdout);exit(1);} |
| | 1119 | } |
| | 1120 | break; |
| | 1121 | case 4: |
| | 1122 | vl=stoi(val[6]-5*val[1]);vn=stoi(val[7]-6*val[1]);vm=stoi(val[2]-2*val[1]); |
| | 1123 | e1=gmin(gmin(gdivgs(vl,3),gmul2n(vn,-1)),vm); |
| | 1124 | e2=gmin(gmul2n(gsub(vl,e1),-1),gsub(vn,e1)); |
| | 1125 | e3=gsub(vl,gadd(e1,e2)); |
| | 1126 | d1=itos(gmul(n,e1));d2=itos(gmul(n,e2));d3=itos(gmul(n,e3)); |
| | 1127 | g=d1*d2+d1*d3+d2*d3;h=itos(mppgcd(mppgcd(stoi(d1),stoi(d2)),stoi(d3))); |
| | 1128 | switch(itos(n)) |
| | 1129 | { |
| | 1130 | case 1: condp=2; |
| | 1131 | printf("[I{%ld-%ld-%ld}] page 182, (%ld)x(%ld)",d1,d2,d3,h,g/h); |
| | 1132 | fflush(stdout);break; |
| | 1133 | case 2: |
| | 1134 | switch(itos(r)) |
| | 1135 | { |
| | 1136 | case 0: condp=4; |
| | 1137 | printf("[I*{%ld-%ld-%ld}] page 183, H{%ld}xH{%ld}",d1/2,d2/2,d3/2,g/4,2-((h&2)>>1)); |
| | 1138 | fflush(stdout);break; |
| | 1139 | case 1: |
| | 1140 | if(d1==d2) f2=d1; |
| | 1141 | else |
| | 1142 | { |
| | 1143 | if(d1==d3) f2=d1; |
| | 1144 | else |
| | 1145 | { |
| | 1146 | if(d2==d3) f2=d2; |
| | 1147 | else {printf("bug23\n");fflush(stdout);exit(1);} |
| | 1148 | } |
| | 1149 | } |
| | 1150 | f1=d1+d2+d3-2*f2; |
| | 1151 | switch(itos(q)) |
| | 1152 | { |
| | 1153 | case 0: condp=3; |
| | 1154 | printf("[II*{%ld-%ld}] page 184, (%ld)",f1/2,f2,f2); |
| | 1155 | fflush(stdout);break; |
| | 1156 | case 1: condp=3; |
| | 1157 | printf("[II{%ld-%ld}] page 183, (%ld)",f1/2,f2,2*f1+f2); |
| | 1158 | fflush(stdout);break; |
| | 1159 | default: {printf("bug24\n");fflush(stdout);exit(1);} |
| | 1160 | } |
| | 1161 | break; |
| | 1162 | default: {printf("bug25\n");fflush(stdout);exit(1);} |
| | 1163 | } |
| | 1164 | break; |
| | 1165 | case 3: condp=4; |
| | 1166 | printf("[III{%ld}] page 184, ",d1); |
| | 1167 | if(d1%3) printf("(9)");else printf("(3)^2"); |
| | 1168 | fflush(stdout);break; |
| | 1169 | case 6: condp=4; |
| | 1170 | printf("[III*{%ld}] page 184, (1)",d1/2); |
| | 1171 | fflush(stdout);break; |
| | 1172 | default: {printf("bug26\n");fflush(stdout);exit(1);} |
| | 1173 | } |
| | 1174 | break; |
| | 1175 | } |
| | 1176 | break; |
| | 1177 | case 5: case 6: case 7: |
| | 1178 | switch(tt) |
| | 1179 | { |
| | 1180 | case 5: dk=gdivgs(stoi(eps*val[6]-5*val[eps2]),12*eps);break; |
| | 1181 | case 6: dk=gdivgs(stoi(eps*val[7]-6*val[eps2]),12*eps); |
| | 1182 | d1k=gdivgs(stoi(eps*val[6]+val[eps2]-eps*val[7]),eps);break; |
| | 1183 | case 7: dk=gdivgs(stoi(eps*val[3]-2*val[eps2]),4*eps); |
| | 1184 | pro1=gdivgs(stoi(eps*val[6]+val[eps2]-3*eps*val[3]),eps); |
| | 1185 | d1k=gmin(stoi(val[7]-3*val[3]),gmul2n(pro1,-1)); |
| | 1186 | d2k=gsub(pro1,d1k);break; |
| | 1187 | } |
| | 1188 | rk=gadd(gmul2n(stoi(va0),-1),gmin(gmul2n(dk,-1),gmin(gmul2n(stoi(2*va3-3*va2),-3),gdivgs(stoi(2*myval(gsub(gmul(A2,A3),gmulsg(3,A5)),p)-5*va2),12)))); |
| | 1189 | v1=2*va3-4*va0-val[1]; |
| | 1190 | v2=6*va5-20*va0-5*val[1]; |
| | 1191 | /* la definition de n est differente suivant val[1] mod 2, ici elle n'est pas |
| | 1192 | valable pour p=2 ou 3 */ |
| | 1193 | if(!(val[eps2]&1)) |
| | 1194 | { |
| | 1195 | if((3*vb2>=(2*va0+2*val[1]))&&(v1>=0)&&(v2>=0)&&((v1==0)||(v2==0))) |
| | 1196 | { |
| | 1197 | n=glcm(denom(dk),denom(pro1=gdivgs(stoi(va0+val[1]),6))); |
| | 1198 | r=gmul(n,pro1); |
| | 1199 | } |
| | 1200 | else |
| | 1201 | { |
| | 1202 | if(((20*va0+5*val[1])>6*va5)&&(10*vb2>=(2*va5+5*val[1]))) |
| | 1203 | { |
| | 1204 | n=glcm(denom(dk),denom(pro1=gdivgs(stoi(2*va5+val[1]),8))); |
| | 1205 | r=gmul(n,pro1); |
| | 1206 | } |
| | 1207 | else |
| | 1208 | { |
| | 1209 | if(((2*va0+2*val[1])>3*vb2)&&((2*va5+5*val[1])>10*vb2)) |
| | 1210 | { |
| | 1211 | n=glcm(denom(dk),denom(pro1=gmul2n(stoi(vb2),-2))); |
| | 1212 | r=gmul(n,pro1); |
| | 1213 | } |
| | 1214 | if((3*vb2>=(2*va0+2*val[1]))&&(2*va3>(4*va0+val[1]))&&(6*va5>(20*va0+5*val[1]))) |
| | 1215 | { |
| | 1216 | if(gequal0(A2)) {printf("bug27\n");fflush(stdout);exit(1);} |
| | 1217 | n=glcm(denom(dk),denom(rk));r=gmul(n,rk); |
| | 1218 | } |
| | 1219 | else |
| | 1220 | { |
| | 1221 | if(!cmpis(p,3)) /* following M. Stoll */ |
| | 1222 | { |
| | 1223 | printf("bug28\n");fflush(stdout);exit(1); |
| | 1224 | } |
| | 1225 | } |
| | 1226 | } |
| | 1227 | } |
| | 1228 | } |
| | 1229 | else |
| | 1230 | { |
| | 1231 | m=denom(dk);r=gmul(m,dk);n=gmul2n(m,1); |
| | 1232 | } |
| | 1233 | if(!cmpis(p,3)) n=stoi(1+r1/6); |
| | 1234 | d=itos(gmul(n,dk));dm=gmod(stoi(d),n);r=gmod(r,n); |
| | 1235 | if(!cmpis(p,3)) dm=gen_0; |
| | 1236 | switch(tt) |
| | 1237 | { |
| | 1238 | case 5: |
| | 1239 | if(!(val[eps2]&1)) |
| | 1240 | { |
| | 1241 | switch(itos(n)) |
| | 1242 | { |
| | 1243 | case 1: condp=0; |
| | 1244 | printf("[I{0}-I{0}-%ld] page 158, (1)",d); |
| | 1245 | fflush(stdout);break; |
| | 1246 | case 2: |
| | 1247 | switch(itos(dm)) |
| | 1248 | { |
| | 1249 | case 0: condp=4; |
| | 1250 | printf("[I*{0}-I*{0}-%ld] page 158, (2)^4",(d-2)/2); |
| | 1251 | fflush(stdout);break; |
| | 1252 | case 1: condp=2; |
| | 1253 | printf("[I{0}-I*{0}-%ld] page 159, (2)^2",(d-1)/2); |
| | 1254 | fflush(stdout);break; |
| | 1255 | } |
| | 1256 | break; |
| | 1257 | case 3: |
| | 1258 | switch(itos(dm)) |
| | 1259 | { |
| | 1260 | case 0: condp=4; |
| | 1261 | printf("[IV-IV*-%ld] page 165, (3)^2",(d-3)/3); |
| | 1262 | fflush(stdout);break; |
| | 1263 | case 1: |
| | 1264 | switch(itos(r)) |
| | 1265 | { |
| | 1266 | case 0: case 1: condp=2; |
| | 1267 | printf("[I{0}-IV-%ld] page 160, (3)",(d-1)/3); |
| | 1268 | fflush(stdout);break; |
| | 1269 | case 2: condp=4; |
| | 1270 | printf("[IV*-IV*-%ld] page 166, (3)^2",(d-4)/3); |
| | 1271 | fflush(stdout);break; |
| | 1272 | } |
| | 1273 | break; |
| | 1274 | case 2: |
| | 1275 | switch(itos(r)) |
| | 1276 | { |
| | 1277 | case 0: case 2: condp=2; |
| | 1278 | printf("[I{0}-IV*-%ld] page 160, (3)",(d-2)/3); |
| | 1279 | fflush(stdout);break; |
| | 1280 | case 1: condp=4; |
| | 1281 | printf("[IV-IV-%ld] page 165, (3)^2",(d-2)/3); |
| | 1282 | fflush(stdout);break; |
| | 1283 | } |
| | 1284 | break; |
| | 1285 | } |
| | 1286 | break; |
| | 1287 | case 4: |
| | 1288 | switch(itos(dm)) |
| | 1289 | { |
| | 1290 | case 0: condp=4; |
| | 1291 | printf("[III-III*-%ld] page 169, (2)^2",(d-4)/4); |
| | 1292 | fflush(stdout);break; |
| | 1293 | case 1: |
| | 1294 | switch(itos(r)) |
| | 1295 | { |
| | 1296 | case 0: case 1: condp=2; |
| | 1297 | printf("[I{0}-III-%ld] page 161, (2)",(d-1)/4); |
| | 1298 | fflush(stdout);break; |
| | 1299 | case 2: case 3: condp=4; |
| | 1300 | printf("[I*{0}-III*-%ld] page 162, (2)^3",(d-5)/4); |
| | 1301 | fflush(stdout);break; |
| | 1302 | } |
| | 1303 | break; |
| | 1304 | case 2: |
| | 1305 | switch(itos(r)) |
| | 1306 | { |
| | 1307 | case 1: condp=4; |
| | 1308 | printf("[III-III-%ld] page 169, (2)^2",(d-2)/4); |
| | 1309 | fflush(stdout);break; |
| | 1310 | case 3: condp=4; |
| | 1311 | printf("[III*-III*-%ld] page 169, (2)^2",(d-6)/4); |
| | 1312 | fflush(stdout);break; |
| | 1313 | default: {printf("bug29\n");fflush(stdout);exit(1);} |
| | 1314 | } |
| | 1315 | break; |
| | 1316 | case 3: |
| | 1317 | switch(itos(r)) |
| | 1318 | { |
| | 1319 | case 0: case 3: condp=2; |
| | 1320 | printf("[I{0}-III*-%ld] page 162, (2)",(d-3)/4); |
| | 1321 | fflush(stdout);break; |
| | 1322 | case 1: case 2: condp=4; |
| | 1323 | printf("[I*{0}-III-%ld] page 162, (2)^3",(d-3)/4); |
| | 1324 | fflush(stdout);break; |
| | 1325 | } |
| | 1326 | break; |
| | 1327 | } |
| | 1328 | break; |
| | 1329 | case 6: |
| | 1330 | switch(itos(dm)) |
| | 1331 | { |
| | 1332 | case 0: condp=4; |
| | 1333 | printf("[II-II*-%ld] page 163, (1)",(d-6)/6); |
| | 1334 | fflush(stdout);break; |
| | 1335 | case 1: |
| | 1336 | switch(itos(r)) |
| | 1337 | { |
| | 1338 | case 0: case 1: condp=2; |
| | 1339 | printf("[I{0}-II-%ld] page 159, (1)",(d-1)/6); |
| | 1340 | fflush(stdout);break; |
| | 1341 | case 2: case 5: condp=4; |
| | 1342 | printf("[II*-IV-%ld] page 164, (3)",(d-7)/6); |
| | 1343 | fflush(stdout);break; |
| | 1344 | case 3: case 4: condp=4; |
| | 1345 | printf("[I*{0}-IV*-%ld] page 161, (2)^2x(3)",(d-7)/6); |
| | 1346 | fflush(stdout);break; |
| | 1347 | } |
| | 1348 | break; |
| | 1349 | case 2: |
| | 1350 | switch(itos(r)) |
| | 1351 | { |
| | 1352 | case 1: condp=4; |
| | 1353 | printf("[II-II-%ld] page 163, (1)",(d-2)/6); |
| | 1354 | fflush(stdout);break; |
| | 1355 | case 3: case 5: condp=4; |
| | 1356 | printf("[I*{0}-II*-%ld] page 160-161, (2)^2",(d-8)/6); |
| | 1357 | fflush(stdout);break; |
| | 1358 | default: {printf("bug30\n");fflush(stdout);exit(1);} |
| | 1359 | } |
| | 1360 | break; |
| | 1361 | case 3: |
| | 1362 | switch(itos(r)) |
| | 1363 | { |
| | 1364 | case 1: case 2: condp=4; |
| | 1365 | printf("[II-IV-%ld] page 164, (3)",(d-3)/6); |
| | 1366 | fflush(stdout);break; |
| | 1367 | case 4: case 5: condp=4; |
| | 1368 | printf("[II*-IV*-%ld] page 164-165, (3)",(d-9)/6); |
| | 1369 | fflush(stdout);break; |
| | 1370 | default: {printf("bug31\n");fflush(stdout);exit(1);} |
| | 1371 | } |
| | 1372 | break; |
| | 1373 | case 4: |
| | 1374 | switch(itos(r)) |
| | 1375 | { |
| | 1376 | case 1: case 3: condp=4; |
| | 1377 | printf("[I*{0}-II-%ld] page 160, (2)^2",(d-4)/6); |
| | 1378 | fflush(stdout);break; |
| | 1379 | case 5: condp=4; |
| | 1380 | printf("[II*-II*-%ld] page 163, (1)",(d-10)/6); |
| | 1381 | fflush(stdout);break; |
| | 1382 | default: {printf("bug32\n");fflush(stdout);exit(1);} |
| | 1383 | } |
| | 1384 | break; |
| | 1385 | case 5: |
| | 1386 | switch(itos(r)) |
| | 1387 | { |
| | 1388 | case 0: case 5: condp=2; |
| | 1389 | printf("[I{0}-II*-%ld] page 160, (1)",(d-5)/6); |
| | 1390 | fflush(stdout);break; |
| | 1391 | case 1: case 4: condp=4; |
| | 1392 | printf("[II-IV*-%ld] page 164, (3)",(d-5)/6); |
| | 1393 | fflush(stdout);break; |
| | 1394 | case 2: case 3: condp=4; |
| | 1395 | printf("[I*{0}-IV-%ld] page 161, (2)^2x(3)",(d-5)/6); |
| | 1396 | fflush(stdout);break; |
| | 1397 | } |
| | 1398 | break; |
| | 1399 | default: {printf("bug33\n");fflush(stdout);exit(1);} |
| | 1400 | } |
| | 1401 | break; |
| | 1402 | case 12: |
| | 1403 | switch(itos(dm)) |
| | 1404 | { |
| | 1405 | case 1: |
| | 1406 | switch(itos(r)) |
| | 1407 | { |
| | 1408 | case 3: case 10: condp=4; |
| | 1409 | printf("[II*-III-%ld] page 166-167, (2)",(d-13)/12); |
| | 1410 | fflush(stdout);break; |
| | 1411 | case 4: case 9: condp=4; |
| | 1412 | printf("[IV-III*-%ld] page 167, (6)",(d-13)/12); |
| | 1413 | fflush(stdout);break; |
| | 1414 | default: {printf("bug34\n");fflush(stdout);exit(1);} |
| | 1415 | } |
| | 1416 | break; |
| | 1417 | case 5: |
| | 1418 | switch(itos(r)) |
| | 1419 | { |
| | 1420 | case 2: case 3: condp=4; |
| | 1421 | printf("[II-III-%ld] page 166, (2)",(d-5)/12); |
| | 1422 | fflush(stdout);break; |
| | 1423 | case 8: case 9: condp=4; |
| | 1424 | printf("[IV*-III*-%ld] page 168, (6)",(d-17)/12); |
| | 1425 | fflush(stdout);break; |
| | 1426 | default: {printf("bug35\n");fflush(stdout);exit(1);} |
| | 1427 | } |
| | 1428 | break; |
| | 1429 | case 7: |
| | 1430 | switch(itos(r)) |
| | 1431 | { |
| | 1432 | case 3: case 4: condp=4; |
| | 1433 | printf("[IV-III-%ld] page 167, (6)",(d-7)/12); |
| | 1434 | fflush(stdout);break; |
| | 1435 | case 9: case 10: condp=4; |
| | 1436 | printf("[II*-III*-%ld] page 167, (2)",(d-19)/12); |
| | 1437 | fflush(stdout);break; |
| | 1438 | default: {printf("bug36\n");fflush(stdout);exit(1);} |
| | 1439 | } |
| | 1440 | break; |
| | 1441 | case 11: |
| | 1442 | switch(itos(r)) |
| | 1443 | { |
| | 1444 | case 3: case 8: condp=4; |
| | 1445 | printf("[IV*-III-%ld] page 168, (6)",(d-11)/12); |
| | 1446 | fflush(stdout);break; |
| | 1447 | case 2: case 9: condp=4; |
| | 1448 | printf("[II-III*-%ld] page 166, (2)",(d-11)/12); |
| | 1449 | fflush(stdout);break; |
| | 1450 | default: {printf("bug37\n");fflush(stdout);exit(1);} |
| | 1451 | } |
| | 1452 | break; |
| | 1453 | default: {printf("bug38\n");fflush(stdout);exit(1);} |
| | 1454 | } |
| | 1455 | break; |
| | 1456 | default: {printf("bug39\n");fflush(stdout);exit(1);} |
| | 1457 | } |
| | 1458 | } |
| | 1459 | else |
| | 1460 | { |
| | 1461 | r=gmod(r,gmul2n(n,-1)); |
| | 1462 | switch(itos(n)) |
| | 1463 | { |
| | 1464 | case 2: condp=2; |
| | 1465 | printf("[2I{0}-%ld] page 159, (1)",(d/2)); |
| | 1466 | fflush(stdout);break; |
| | 1467 | case 4: condp=4; |
| | 1468 | printf("[2I*{0}-%ld] page 159, (2)^2",(d/2-1)/2); |
| | 1469 | fflush(stdout);break; |
| | 1470 | case 6: |
| | 1471 | switch(itos(r)) |
| | 1472 | { |
| | 1473 | case 1: condp=4; |
| | 1474 | printf("[2IV-%ld] page 165, (3)",(d/2-1)/3); |
| | 1475 | fflush(stdout);break; |
| | 1476 | case 2: condp=4; |
| | 1477 | printf("[2IV*-%ld] page 165, (3)",(d/2-2)/3); |
| | 1478 | fflush(stdout);break; |
| | 1479 | default: {printf("bug40\n");fflush(stdout);exit(1);} |
| | 1480 | } |
| | 1481 | break; |
| | 1482 | case 8: |
| | 1483 | switch(itos(r)) |
| | 1484 | { |
| | 1485 | case 1: condp=4; |
| | 1486 | printf("[2III-%ld] page 168, (2)",(d/2-1)/4); |
| | 1487 | fflush(stdout);break; |
| | 1488 | case 3: condp=4; |
| | 1489 | printf("[2III*-%ld] page 168, (2)",(d/2-3)/4); |
| | 1490 | fflush(stdout);break; |
| | 1491 | default: {printf("bug41\n");fflush(stdout);exit(1);} |
| | 1492 | } |
| | 1493 | break; |
| | 1494 | case 12: |
| | 1495 | switch(itos(r)) |
| | 1496 | { |
| | 1497 | case 1: condp=4; |
| | 1498 | printf("[2II-%ld] page 162, (1)",(d/2-1)/6); |
| | 1499 | fflush(stdout);break; |
| | 1500 | case 5: condp=4; |
| | 1501 | printf("[2II*-%ld] page 163, (1)",(d/2-5)/6); |
| | 1502 | fflush(stdout);break; |
| | 1503 | default: {printf("bug42\n");fflush(stdout);exit(1);} |
| | 1504 | } |
| | 1505 | break; |
| | 1506 | default: {printf("bug43\n");fflush(stdout);exit(1);} |
| | 1507 | } |
| | 1508 | } |
| | 1509 | break; |
| | 1510 | case 6: |
| | 1511 | d1=itos(gmul(n,d1k)); |
| | 1512 | switch(itos(n)) |
| | 1513 | { |
| | 1514 | case 1: condp=1; |
| | 1515 | printf("[I{%ld}-I{0}-%ld] page 170, (%ld)",d1,d,d1); |
| | 1516 | fflush(stdout);break; |
| | 1517 | case 2: |
| | 1518 | switch(itos(dm)) |
| | 1519 | { |
| | 1520 | case 0: condp=4; |
| | 1521 | printf("[I*{0}-I*{%ld}-%ld] page 171, (2)^2xH{%ld}", d1/2,(d-2)/2,d1/2); |
| | 1522 | fflush(stdout);break; |
| | 1523 | case 1: goto labelm3; |
| | 1524 | default: {printf("bug44\n");fflush(stdout);exit(1);} |
| | 1525 | } |
| | 1526 | break; |
| | 1527 | case 3: |
| | 1528 | switch(itos(dm)) |
| | 1529 | { |
| | 1530 | case 1: condp=3; |
| | 1531 | printf("[IV-I{%ld}-%ld] page 173, (3)x(%ld)",d1/3,(d-1)/3,d1/3); |
| | 1532 | fflush(stdout);break; |
| | 1533 | case 2: condp=3; |
| | 1534 | printf("[IV*-I{%ld}-%ld] page 173, (3)x(%ld)",d1/3,(d-2)/3,d1/3); |
| | 1535 | fflush(stdout);break; |
| | 1536 | default: {printf("bug45\n");fflush(stdout);exit(1);} |
| | 1537 | } |
| | 1538 | break; |
| | 1539 | case 4: |
| | 1540 | switch(itos(dm)) |
| | 1541 | { |
| | 1542 | case 1: |
| | 1543 | switch(itos(r)) |
| | 1544 | { |
| | 1545 | case 0: case 1: condp=3; |
| | 1546 | printf("[III-I{%ld}-%ld] page 176, (2)x(%ld)",d1/4,(d-1)/4,d1/4); |
| | 1547 | fflush(stdout);break; |
| | 1548 | case 2: case 3: condp=4; |
| | 1549 | printf("[III*-I*{%ld}-%ld] page 177, (2)xH{%ld}",d1/4,(d-5)/4,d1/4); |
| | 1550 | fflush(stdout);break; |
| | 1551 | default: {printf("bug46\n");fflush(stdout);exit(1);} |
| | 1552 | } |
| | 1553 | break; |
| | 1554 | case 3: |
| | 1555 | switch(itos(r)) |
| | 1556 | { |
| | 1557 | case 0: case 3: condp=3; |
| | 1558 | printf("[III*-I{%ld}-%ld] page 176, (2)x(%ld)",d1/4,(d-3)/4,d1/4); |
| | 1559 | fflush(stdout);break; |
| | 1560 | case 1: case 2: condp=4; |
| | 1561 | printf("[III-I*{%ld}-%ld] page 177, (2)xH{%ld}",d1/4,(d-3)/4,d1/4); |
| | 1562 | fflush(stdout);break; |
| | 1563 | default: {printf("bug47\n");fflush(stdout);exit(1);} |
| | 1564 | } |
| | 1565 | break; |
| | 1566 | default: {printf("bug48\n");fflush(stdout);exit(1);} |
| | 1567 | } |
| | 1568 | break; |
| | 1569 | case 6: |
| | 1570 | switch(itos(dm)) |
| | 1571 | { |
| | 1572 | case 1: |
| | 1573 | switch(itos(r)) |
| | 1574 | { |
| | 1575 | case 0: case 1: condp=3; |
| | 1576 | printf("[II-I{%ld}-%ld] page 172, (%ld)",d1/6,(d-1)/6,d1/6); |
| | 1577 | fflush(stdout);break; |
| | 1578 | case 3: case 4: condp=4; |
| | 1579 | printf("[IV*-I*{%ld}-%ld] page 174-175, (3)xH{%ld}",d1/6,(d-7)/6,d1/6); |
| | 1580 | fflush(stdout);break; |
| | 1581 | default: {printf("bug49\n");fflush(stdout);exit(1);} |
| | 1582 | } |
| | 1583 | break; |
| | 1584 | case 2: condp=4; |
| | 1585 | printf("[II*-I*{%ld}-%ld] page 174, H{%ld}",d1/6,(d-8)/6,d1/6); |
| | 1586 | fflush(stdout);break; |
| | 1587 | case 4: condp=4; |
| | 1588 | printf("[II-I*{%ld}-%ld] page 173, H{%ld}",d1/6,(d-4)/6,d1/6); |
| | 1589 | fflush(stdout);break; |
| | 1590 | case 5: |
| | 1591 | switch(itos(r)) |
| | 1592 | { |
| | 1593 | case 0: case 5: condp=3; |
| | 1594 | printf("[II*-I{%ld}-%ld] page 172, (%ld)",d1/6,(d-5)/6,d1/6); |
| | 1595 | fflush(stdout);break; |
| | 1596 | case 2: case 3: condp=4; |
| | 1597 | printf("[IV-I*{%ld}-%ld] page 174, (3)xH{%ld}",d1/6,(d-5)/6,d1/6); |
| | 1598 | fflush(stdout);break; |
| | 1599 | default: {printf("bug50\n");fflush(stdout);exit(1);} |
| | 1600 | } |
| | 1601 | break; |
| | 1602 | default: {printf("bug51\n");fflush(stdout);exit(1);} |
| | 1603 | } |
| | 1604 | break; |
| | 1605 | default: {printf("bug52\n");fflush(stdout);exit(1);} |
| | 1606 | } |
| | 1607 | break; |
| | 1608 | case 7: |
| | 1609 | j2m=val[eps2]&1;d1=itos(gmul(n,d1k));d2=itos(gmul(n,d2k)); |
| | 1610 | switch(itos(n)) |
| | 1611 | { |
| | 1612 | case 1: condp=2; |
| | 1613 | printf("[I{%ld}-I{%ld}-%ld] page 179, (%ld)x(%ld)",d1,d2,d,d1,d2); |
| | 1614 | fflush(stdout);break; |
| | 1615 | case 2: |
| | 1616 | if(j2m) |
| | 1617 | { |
| | 1618 | condp=3;printf("[2I{%ld}-%ld] page 181, (%ld)",d1,d/2,d1); |
| | 1619 | fflush(stdout); |
| | 1620 | } |
| | 1621 | else |
| | 1622 | { |
| | 1623 | if(itos(dm)==0) |
| | 1624 | { |
| | 1625 | condp=4; |
| | 1626 | printf("[I*{%ld}-I*{%ld}-%ld] page 180, H{%ld}xH{%ld}", |
| | 1627 | d1/2,d2/2,(d-2)/2, d1/2, d2/2); |
| | 1628 | fflush(stdout); |
| | 1629 | } |
| | 1630 | else |
| | 1631 | { |
| | 1632 | if(d1==d2) |
| | 1633 | { |
| | 1634 | condp=3; |
| | 1635 | printf("[I{%ld}-I*{%ld}-%ld] page 180, (%ld)xH{%ld}", |
| | 1636 | d1/2,d1/2,(d-1)/2,d1/2,d1/2); |
| | 1637 | fflush(stdout); |
| | 1638 | } |
| | 1639 | else goto labelm3; |
| | 1640 | } |
| | 1641 | } |
| | 1642 | break; |
| | 1643 | case 4: condp=4; |
| | 1644 | printf("[2I*{%ld}-%ld] page 181, H{%ld}",d1/2,(d-2)/4,d1/2); |
| | 1645 | fflush(stdout);break; |
| | 1646 | default: {printf("bug55\n");fflush(stdout);exit(1);} |
| | 1647 | } |
| | 1648 | break; |
| | 1649 | default: {printf("bug56\n");fflush(stdout);exit(1);} |
| | 1650 | } |
| | 1651 | break; |
| | 1652 | default: {printf("bug57\n");fflush(stdout);exit(1);} |
| | 1653 | } |
| | 1654 | printf(", f=%ld\n",condp);fflush(stdout); |
| | 1655 | goto recp; |
| | 1656 | } |
| | 1657 | |
| | 1658 | long |
| | 1659 | polval(GEN pol, GEN p) /* la plus grande puissance de p divisant pol */ |
| | 1660 | { |
| | 1661 | long lx,v,i; |
| | 1662 | |
| | 1663 | lx=lg(pol); |
| | 1664 | if(!signe(pol)) return EXP220; |
| | 1665 | else |
| | 1666 | { |
| | 1667 | v=myval((GEN)pol[2],p); |
| | 1668 | for(i=3;i<lx;i++) v=min(myval((GEN)pol[i],p),v); |
| | 1669 | } |
| | 1670 | return v; |
| | 1671 | } |
| | 1672 | |
| | 1673 | /* Factorisation p-adique (sur Q_p) a l'ordre r d'un polynome pol, de |
| | 1674 | contenu non divisible par p et sans racine multiple. Le resultat est |
| | 1675 | un vecteur. */ |
| | 1676 | |
| | 1677 | GEN |
| | 1678 | factorpadicnonun(GEN pol, GEN p, long r) |
| | 1679 | { |
| | 1680 | long lx=lg(pol),vx=varn(pol),i,contpol,nb; |
| | 1681 | GEN td,list,ep,fact,upol; |
| | 1682 | |
| | 1683 | if(gequal1(td=(GEN)pol[lx-1])) |
| | 1684 | { |
| | 1685 | list=(GEN)factorpadic(pol,p,r)[1]; |
| | 1686 | return list; |
| | 1687 | } |
| | 1688 | else |
| | 1689 | { |
| | 1690 | contpol=polval(pol,p); |
| | 1691 | if(contpol) {printf("contenu non trivial, erreur\n");fflush(stdout);exit(1);} |
| | 1692 | pol=gdiv(pol,gpowgs(p,contpol)); |
| | 1693 | r=(lx-4)*ggval(td,p)+r; |
| | 1694 | upol=gsubst(gmul(pol,gpowgs(td,lx-4)),vx,gdiv(pol_x(vx),td)); |
| | 1695 | fact=gsubst(factorpadic(upol,p,r),vx,gmul(pol_x(vx),td)); |
| | 1696 | list=(GEN)fact[1];ep=(GEN)fact[2];nb=lg(list)-1; |
| | 1697 | for(i=1;i<=nb;i++) |
| | 1698 | if(!gequal1((GEN)ep[i])) |
| | 1699 | { |
| | 1700 | printf("erreur, racine multiple\n");fflush(stdout);exit(1); |
| | 1701 | } |
| | 1702 | for(i=1;i<=nb;i++) |
| | 1703 | /* (GEN)list[i] = gdiv((GEN)list[i],gpowgs(p,polval((GEN)list[i],p))); */ |
| | 1704 | list[i] = (long) gdiv((GEN)list[i],gpowgs(p,polval((GEN)list[i],p))); |
| | 1705 | } |
| | 1706 | return list; |
| | 1707 | } |
| | 1708 | |
| | 1709 | GEN |
| | 1710 | polymini(GEN pol, GEN p) /* polynome minimal dans Z_p, p\ne 2 */ |
| | 1711 | { |
| | 1712 | GEN polh,polhp,fac,rac,ent,pent,theta,polf,pro; |
| | 1713 | long alpha,i,lambda,maxord,beta; |
| | 1714 | |
| | 1715 | polf=cgetg(7,18); |
| | 1716 | rec1: |
| | 1717 | alpha=polval(pol,p);polh=gdiv(pol,gpowgs(p,alpha)); |
| | 1718 | if(gdvd(truecoeff(polh,6),p)&&gdvd(truecoeff(polh,5),p)&&gdvd(truecoeff(polh,4),p)&&gdvd(truecoeff(polh,3),p)) |
| | 1719 | {polh=gmul(gpowgs(pol_x(0),6),gsubst(polh,0,ginv(pol_x(0))));} |
| | 1720 | alpha=alpha&1; |
| | 1721 | beta=0; |
| | 1722 | lambda=0; |
| | 1723 | for(i=1;i<=3;i++) |
| | 1724 | { |
| | 1725 | if(!gdvd(truecoeff(polh,6-i),p)) lambda=i; |
| | 1726 | } |
| | 1727 | |
| | 1728 | labelm6: |
| | 1729 | theta=caltheta(polh,p,lambda); |
| | 1730 | polf[5]=(long)gen_0; /* 1 si racine d'ordre 3 non dans F_p, 0 sinon */ |
| | 1731 | if(gcmp(theta,gen_1)>=0) |
| | 1732 | { |
| | 1733 | ent=gfloor(theta);pent=gpow(p,ent,0); |
| | 1734 | polh=gdiv(gsubst(polh,0,gmul(pent,pol_x(0))),gpowgs(pent,6-lambda)); |
| | 1735 | alpha=(alpha+lambda*itos(ent))&1; |
| | 1736 | beta=beta+itos(ent); |
| | 1737 | theta=gsub(theta,ent); |
| | 1738 | } |
| | 1739 | polhp=gmul(gmodulo(gen_1,p),polh); |
| | 1740 | if(gequal0(theta)) |
| | 1741 | { |
| | 1742 | fac=factmz(polhp,p); |
| | 1743 | maxord=itos((GEN)fac[1]); |
| | 1744 | if(maxord>=3) |
| | 1745 | { |
| | 1746 | rac=(GEN)fac[2]; |
| | 1747 | if(lg(rac)==5) |
| | 1748 | { |
| | 1749 | polf[5]=(long)gen_1; |
| | 1750 | goto sortie; |
| | 1751 | } |
| | 1752 | rac=lift(gdiv(gneg(truecoeff(rac,0)),truecoeff(rac,1))); |
| | 1753 | polh=gsubst(polh,0,gadd(pol_x(0),rac)); |
| | 1754 | lambda=6-maxord; goto labelm6; |
| | 1755 | } |
| | 1756 | if(maxord<=2&&lg(polhp)>=7) goto sortie; |
| | 1757 | } |
| | 1758 | if(lambda<=2) |
| | 1759 | { |
| | 1760 | if((myval(truecoeff(polh,2),p)>1-alpha)&&(myval(truecoeff(polh,1),p)>2-alpha)&&(myval(truecoeff(polh,0),p)>3-alpha)) |
| | 1761 | { |
| | 1762 | pol=gsubst(polh,0,gmul(p,pol_x(0))); |
| | 1763 | if(alpha) pol=gmul(p,pol); |
| | 1764 | goto rec1; |
| | 1765 | } |
| | 1766 | goto sortie; |
| | 1767 | } |
| | 1768 | if(lambda==3&&alpha==1) |
| | 1769 | { |
| | 1770 | if(lg(polhp)==6) |
| | 1771 | { |
| | 1772 | if(myval(truecoeff(polh,6),p)>=3&&myval(truecoeff(polh,5),p)>=2) |
| | 1773 | { |
| | 1774 | polh=gmul(gsubst(polh,0,gdiv(pol_x(0),p)),gpowgs(p,3)); |
| | 1775 | theta=gadd(theta,gen_1); |
| | 1776 | alpha=0; |
| | 1777 | beta=beta-1; |
| | 1778 | goto sortie; |
| | 1779 | } |
| | 1780 | } |
| | 1781 | if(lg(polhp)==9&&!gequal0(theta)) |
| | 1782 | { |
| | 1783 | pro=gdiv(polhp,gpowgs(pol_x(0),3)); |
| | 1784 | fac=factmz(pro,p); |
| | 1785 | if(!cmpis((GEN)fac[1],3)) |
| | 1786 | { |
| | 1787 | rac=(GEN)fac[2]; |
| | 1788 | rac=lift(gdiv(gneg(truecoeff(rac,0)),truecoeff(rac,1))); |
| | 1789 | pro=gsubst(polh,0,gadd(rac,gmul(p,pol_x(0)))); |
| | 1790 | if(polval(pro,p)>=3) |
| | 1791 | { |
| | 1792 | polh=gdiv(pro,gpowgs(p,3)); |
| | 1793 | alpha=0; |
| | 1794 | beta=beta-1; |
| | 1795 | theta=caltheta(polh,p,3); |
| | 1796 | } |
| | 1797 | } |
| | 1798 | } |
| | 1799 | } |
| | 1800 | sortie: |
| | 1801 | polf[1]=(long)polh; |
| | 1802 | polf[2]=(long)stoi(lambda); |
| | 1803 | polf[3]=(long)theta; |
| | 1804 | polf[4]=(long)stoi(alpha); |
| | 1805 | polf[6]=(long)stoi(beta); |
| | 1806 | return polf; |
| | 1807 | } |
| | 1808 | |
| | 1809 | GEN |
| | 1810 | caltheta(GEN pol, GEN p, long lambda) |
| | 1811 | { |
| | 1812 | GEN theta,b; |
| | 1813 | long i; |
| | 1814 | b=cgetg(8,17); |
| | 1815 | b[1]=(long)truecoeff(pol,6);b[2]=(long)truecoeff(pol,5); |
| | 1816 | b[3]=(long)truecoeff(pol,4);b[4]=(long)truecoeff(pol,3); |
| | 1817 | b[5]=(long)truecoeff(pol,2);b[6]=(long)truecoeff(pol,1); |
| | 1818 | b[7]=(long)truecoeff(pol,0); |
| | 1819 | theta=stoi(myval((GEN)b[2+lambda],p)); |
| | 1820 | for(i=2+lambda;i<=6;i++) |
| | 1821 | theta=gmin(theta,gdivgs(stoi(myval((GEN)b[i+1],p)),i-lambda)); |
| | 1822 | return theta; |
| | 1823 | } |
| | 1824 | |
| | 1825 | long |
| | 1826 | discpart(GEN polh, GEN p, long ord) |
| | 1827 | /* discriminant d'un facteur p-adic de degre 3 */ |
| | 1828 | { |
| | 1829 | GEN polhp,list,facti,prod,dis; |
| | 1830 | long i,j,fl; |
| | 1831 | |
| | 1832 | polhp=gmul(gmodulo(gen_1,p),polh); |
| | 1833 | if(lg(polhp)!=6) |
| | 1834 | {printf("bug, on ne doit pas arriver dans discpart");fflush(stdout);exit(1);} |
| | 1835 | list=factorpadicnonun(polh,p,ord); |
| | 1836 | prod=pol_1(varn(polh)); |
| | 1837 | for(i=1;i<lg(list);i++) |
| | 1838 | { |
| | 1839 | facti=(GEN)list[i]; |
| | 1840 | fl=0; |
| | 1841 | for(j=2;j<lg(facti);j++) |
| | 1842 | { |
| | 1843 | if(!valp(facti[j])&&j>=3) fl=1; |
| | 1844 | } |
| | 1845 | if(fl) |
| | 1846 | {prod=gmul(prod,facti);} |
| | 1847 | } |
| | 1848 | if(lg(prod)!=6) |
| | 1849 | {printf("bug, degre de prod");fflush(stdout);exit(1);} |
| | 1850 | dis=discsr(prod); |
| | 1851 | if(gequal0(dis)) return ord+1; |
| | 1852 | else return valp(dis); |
| | 1853 | } |
| | 1854 | |
| | 1855 | long |
| | 1856 | myvalzi(GEN b) /* valuation par rapport a 3 dans Z[i] */ |
| | 1857 | { |
| | 1858 | return min(myval(greal(b),stoi(3)),myval(gimag(b),stoi(3))); |
| | 1859 | } |
| | 1860 | |
| | 1861 | GEN |
| | 1862 | polyminizi(GEN pol) /* polynome minimal dans Z[i] */ |
| | 1863 | { |
| | 1864 | GEN p,polh,ent,pent,unmodp,rac,theta,polf; |
| | 1865 | long alpha,beta; |
| | 1866 | |
| | 1867 | polf=cgetg(4,18); |
| | 1868 | p=stoi(3); |
| | 1869 | unmodp=gmodulo(gen_1,p); |
| | 1870 | alpha=polval(pol,p)&1; |
| | 1871 | polh=pol; |
| | 1872 | if(alpha) polh=gdiv(pol,p); |
| | 1873 | beta=0; |
| | 1874 | rac=gadd(lift(gdiv(gmul(unmodp,truecoeff(polh,3)),gmul(unmodp,truecoeff(polh,6)))),gen_I()); |
| | 1875 | |
| | 1876 | labelm6: |
| | 1877 | polh=gsubst(polh,0,gadd(pol_x(0),rac)); |
| | 1878 | theta=calthetazi(polh); |
| | 1879 | if(gcmp(theta,gen_1)>=0) |
| | 1880 | { |
| | 1881 | ent=gfloor(theta);pent=gpow(p,ent,0); |
| | 1882 | polh=gdiv(gsubst(polh,0,gmul(pent,pol_x(0))),gpowgs(pent,3)); |
| | 1883 | alpha=(alpha+itos(ent))&1; |
| | 1884 | beta=beta+itos(ent); |
| | 1885 | theta=gsub(theta,ent); |
| | 1886 | } |
| | 1887 | if(gequal0(theta)) |
| | 1888 | { |
| | 1889 | if(myvalzi(truecoeff(polh,2))&&myvalzi(truecoeff(polh,1))) |
| | 1890 | { |
| | 1891 | rac=gdiv(gmul(unmodp,truecoeff(polh,0)),gmul(unmodp,truecoeff(polh,3))); |
| | 1892 | rac=lift(gneg(gmul(gmul(rac,rac),rac))); |
| | 1893 | goto labelm6; |
| | 1894 | } |
| | 1895 | } |
| | 1896 | if(alpha) |
| | 1897 | { |
| | 1898 | if(myvalzi(truecoeff(polh,6))>=3&&myvalzi(truecoeff(polh,5))>=2&&myvalzi(truecoeff(polh,4))>=1) |
| | 1899 | { |
| | 1900 | polh=gmul(gsubst(polh,0,gdiv(pol_x(0),p)),gpowgs(p,3)); |
| | 1901 | theta=gadd(theta,gen_1); |
| | 1902 | beta=beta-1; |
| | 1903 | alpha=0; |
| | 1904 | } |
| | 1905 | } |
| | 1906 | polf[1]=(long)theta; |
| | 1907 | polf[2]=(long)stoi(alpha); |
| | 1908 | polf[3]=(long)stoi(beta); |
| | 1909 | return polf; |
| | 1910 | } |
| | 1911 | |
| | 1912 | GEN |
| | 1913 | calthetazi(GEN polh) |
| | 1914 | /* on calcule theta (avec lambda=3) pour un polh a coefficients dans Z[i] */ |
| | 1915 | { |
| | 1916 | GEN theta; |
| | 1917 | |
| | 1918 | theta=gmin(stoi(myvalzi(truecoeff(polh,2))),gmul2n(stoi(myvalzi(truecoeff(polh,1))),-1)); |
| | 1919 | theta=gmin(theta,gdivgs(stoi(myvalzi(truecoeff(polh,0))),3)); |
| | 1920 | return theta; |
| | 1921 | } |
| | 1922 | |
| | 1923 | long |
| | 1924 | myvalzi2(GEN b) |
| | 1925 | /* on calcule la valuation de b dans Z[i, Y]/(Y^2-3) */ |
| | 1926 | { |
| | 1927 | b=lift(b); |
| | 1928 | return min(2*myvalzi(truecoeff(b,0)),2*myvalzi(truecoeff(b,1))+1); |
| | 1929 | } |
| | 1930 | |
| | 1931 | GEN |
| | 1932 | calthetazi2(GEN polh) |
| | 1933 | /* on calcule theta (avec lambda=3) d'un polh a coefficients |
| | 1934 | dans Z[i, Y]/(Y^2-3) */ |
| | 1935 | { |
| | 1936 | GEN theta; |
| | 1937 | |
| | 1938 | theta=gmin(stoi(myvalzi2(truecoeff(polh,2))),gmul2n(stoi(myvalzi2(truecoeff(polh,1))),-1)); |
| | 1939 | theta=gmin(theta,gdivgs(stoi(myvalzi2(truecoeff(polh,0))),3)); |
| | 1940 | return theta; |
| | 1941 | } |
| | 1942 | |
| | 1943 | GEN |
| | 1944 | polyminizi2(GEN pol) /* polynome minimal dans Z_3[i,Y]/(Y^2-3) */ |
| | 1945 | { |
| | 1946 | GEN p,polh,ent,pent,rac,theta,polf,y,b3,b6; |
| | 1947 | long alpha,beta; |
| | 1948 | |
| | 1949 | p=stoi(3); |
| | 1950 | polf=cgetg(3,18); |
| | 1951 | y=readseq("Mod(y,y^2-3)"); |
| | 1952 | if(polval(pol,p)) |
| | 1953 | {printf("bug, le polynome n'est pas minimal\n");fflush(stdout);exit(1);} |
| | 1954 | polh=pol;alpha=0; |
| | 1955 | beta=0; |
| | 1956 | polh=gdivgs(gsubst(polh,0,gmul(pol_x(0),y)),27); |
| | 1957 | if(myvalzi2(truecoeff(polh,4))>0&&myvalzi2(truecoeff(polh,2))>0) |
| | 1958 | { |
| | 1959 | if(myvalzi2(gsub(truecoeff(polh,6),truecoeff(polh,0)))>0) rac=gen_I(); |
| | 1960 | else rac=gen_1; |
| | 1961 | } |
| | 1962 | else |
| | 1963 | { |
| | 1964 | theta=gen_0; |
| | 1965 | goto sortie; |
| | 1966 | } |
| | 1967 | |
| | 1968 | labelm6: |
| | 1969 | polh=gsubst(polh,0,gadd(pol_x(0),rac)); |
| | 1970 | theta=calthetazi2(polh); |
| | 1971 | if(gcmp(theta,gen_1)>=0) |
| | 1972 | { |
| | 1973 | ent=gfloor(theta);pent=gpow(y,ent,0); |
| | 1974 | polh=gdiv(gsubst(polh,0,gmul(pent,pol_x(0))),gpowgs(pent,3)); |
| | 1975 | alpha=(alpha+itos(ent))&1; |
| | 1976 | beta=beta+itos(ent); |
| | 1977 | theta=gsub(theta,ent); |
| | 1978 | } |
| | 1979 | if(gequal0(theta)) |
| | 1980 | { |
| | 1981 | if(myvalzi2(truecoeff(polh,2))&&myvalzi2(truecoeff(polh,1))) |
| | 1982 | { |
| | 1983 | b3=zi2mod(truecoeff(polh,3)); |
| | 1984 | b6=zi2mod(truecoeff(polh,0)); |
| | 1985 | rac=gdiv(b6,gneg(b3)); |
| | 1986 | rac=lift(gmul(gmul(rac,rac),rac)); |
| | 1987 | goto labelm6; |
| | 1988 | } |
| | 1989 | } |
| | 1990 | if(alpha) |
| | 1991 | { |
| | 1992 | if(myvalzi2(truecoeff(polh,6))>=3&&myvalzi2(truecoeff(polh,5))>=2&&myvalzi2(truecoeff(polh,5))>=1) |
| | 1993 | { |
| | 1994 | theta=gadd(theta,gen_1); |
| | 1995 | beta=beta-1; |
| | 1996 | alpha=0; |
| | 1997 | } |
| | 1998 | else |
| | 1999 | { |
| | 2000 | printf("bug dans polyminizi2\n");fflush(stdout);exit(1); |
| | 2001 | } |
| | 2002 | } |
| | 2003 | sortie: |
| | 2004 | polf[1]=(long)theta; |
| | 2005 | polf[2]=(long)stoi(beta); |
| | 2006 | return polf; |
| | 2007 | } |
| | 2008 | |
| | 2009 | GEN |
| | 2010 | zi2mod(GEN u) /* u est un element de Z[i,Y]/(Y^2-3), on calcule u modulo y */ |
| | 2011 | { |
| | 2012 | GEN a,b,unmodp; |
| | 2013 | |
| | 2014 | unmodp=gmodulo(gen_1,stoi(3)); |
| | 2015 | u=truecoeff(lift(u),0); |
| | 2016 | a=gmul(unmodp,greal(u)); |
| | 2017 | b=gmul(unmodp,gimag(u)); |
| | 2018 | u=gadd(a,gmul(b,gen_I())); |
| | 2019 | return u; |
| | 2020 | } |
| | 2021 | |
| | 2022 | GEN |
| | 2023 | factmz(GEN polhp, GEN p) |
| | 2024 | /* donne un facteur de multiplicite maximale d'un polynome |
| | 2025 | dans F_p de degre <7 */ |
| | 2026 | { |
| | 2027 | GEN dh,z,b,fac; |
| | 2028 | long m,i,vx,l; |
| | 2029 | |
| | 2030 | b=cgetg(3,18); |
| | 2031 | m=0; |
| | 2032 | z=polhp; |
| | 2033 | if(gcmp(p,stoi(5))<=0) |
| | 2034 | { |
| | 2035 | if(!gequal0(discsr(polhp))) m=1; |
| | 2036 | else |
| | 2037 | { |
| | 2038 | fac=(GEN)factmod(polhp,p); |
| | 2039 | for(i=1;i<lg((GEN)fac[2]);i++) |
| | 2040 | m=max(m,itos(gcoeff(fac,i,2))); |
| | 2041 | for(i=1;i<lg((GEN)fac[1]);i++) |
| | 2042 | if(!cmpis(gcoeff(fac,i,2),m)) l=i; |
| | 2043 | z=gcoeff(fac,l,1); |
| | 2044 | } |
| | 2045 | b[1]=(long)stoi(m); |
| | 2046 | b[2]=(long)z; |
| | 2047 | return b; |
| | 2048 | } |
| | 2049 | dh=polhp; |
| | 2050 | vx=varn(polhp); |
| | 2051 | lab: |
| | 2052 | m=m+1; |
| | 2053 | dh=deriv(dh,vx); |
| | 2054 | if(lg(ggcd(z,dh))<=3) goto sort1; |
| | 2055 | z=ggcd(z,dh); |
| | 2056 | goto lab; |
| | 2057 | sort1: |
| | 2058 | if(m>=3 && lg(z)==5) |
| | 2059 | { |
| | 2060 | fac=(GEN)factmod(z,p); |
| | 2061 | z=gcoeff(fac,1,1); |
| | 2062 | } |
| | 2063 | sort: |
| | 2064 | b[1]=(long)stoi(m); |
| | 2065 | b[2]=(long)z; |
| | 2066 | return b; |
| | 2067 | } |
