Annotation of OpenXM_contrib/pari/src/basemath/base5.c, Revision 1.1.1.1
1.1 maekawa 1: /*******************************************************************/
2: /* */
3: /* BASIC NF OPERATIONS */
4: /* (continued 2) */
5: /* */
6: /*******************************************************************/
7: /* $Id: base5.c,v 1.1.1.1 1999/09/16 13:47:22 karim Exp $ */
8: #include "pari.h"
9: GEN mat_to_vecpol(GEN x, long v);
10:
11: GEN
12: matbasistoalg(GEN nf,GEN x)
13: {
14: long i,j,lx,li;
15: GEN p1,z;
16:
17: if (typ(x)!=t_MAT)
18: err(talker,"argument must be a matrix in matbasistoalg");
19: lx=lg(x); z=cgetg(lx,t_MAT); if (lx==1) return z;
20:
21: li=lg(x[1]);
22: for (j=1; j<lx; j++)
23: {
24: p1=cgetg(li,t_COL); z[j]=(long)p1;
25: for (i=1; i<li; i++) p1[i]=(long)basistoalg(nf,gcoeff(x,i,j));
26: }
27: return z;
28: }
29:
30: GEN
31: matalgtobasis(GEN nf,GEN x)
32: {
33: long i,j,lx,li;
34: GEN p1,z;
35:
36: if (typ(x)!=t_MAT)
37: err(talker,"argument must be a matrix in matalgtobasis");
38: lx=lg(x); z=cgetg(lx,t_MAT); if (lx==1) return z;
39:
40: li=lg(x[1]);
41: for (j=1; j<lx; j++)
42: {
43: p1=cgetg(li,t_COL); z[j]=(long)p1;
44: for (i=1; i<li; i++) p1[i]=(long)algtobasis(nf,gcoeff(x,i,j));
45: }
46: return z;
47: }
48:
49: static GEN
50: rnfmakematrices(GEN rnf)
51: {
52: long i,j,k,n,r1,r2,ru,ruk,r1rel,r2rel;
53: GEN nf,pol,rac,base,base1,r1r2,racnf,sig,vecmat,vecM,vecMC,vecT2,rack;
54: GEN M,p2,p3,MC,sigk,T2,T,p1,MD,TI,MDI;
55:
56: nf=(GEN)rnf[10]; racnf=(GEN)nf[6]; pol=(GEN)rnf[1];
57: n=lgef(pol)-3;
58: base=(GEN)rnf[7]; base1=(GEN)base[1]; rac=(GEN)rnf[6]; sig=(GEN)rnf[2];
59: r1r2=(GEN)nf[2]; r1=itos((GEN)r1r2[1]); r2=itos((GEN)r1r2[2]); ru=r1+r2;
60: vecmat=cgetg(8,t_VEC);
61: vecM=cgetg(ru+1,t_VEC); vecmat[1]=(long)vecM;
62: vecMC=cgetg(ru+1,t_VEC); vecmat[2]=(long)vecMC;
63: vecT2=cgetg(ru+1,t_VEC); vecmat[3]=(long)vecT2;
64: for (k=1; k<=ru; k++)
65: {
66: rack=(GEN)rac[k]; ruk=lg(rack)-1;
67: M=cgetg(n+1,t_MAT); vecM[k]=(long)M;
68: for (j=1; j<=n; j++)
69: {
70: p2=cgetg(ruk+1,t_COL); M[j]=(long)p2; p3=lift((GEN)base1[j]);
71: p3=gsubst(p3,varn(nf[1]),(GEN)racnf[k]);
72: for (i=1; i<=ruk; i++) p2[i]=lsubst(p3,varn(rnf[1]),(GEN)rack[i]);
73: }
74: MC=gconj(gtrans(M)); vecMC[k]=(long)MC;
75: if (k<=r1)
76: {
77: sigk=(GEN)sig[k]; r1rel=itos((GEN)sigk[1]); r2rel=itos((GEN)sigk[2]);
78: if (r1rel+r2rel != lg(MC)-1) err(talker,"bug in rnfmakematrices");
79: for (j=r1rel+1; j<=r1rel+r2rel; j++) MC[j]=lmul2n((GEN)MC[j],1);
80: }
81: T2=gmul(MC,M); vecT2[k]=(long)T2;
82: }
83: T=cgetg(n+1,t_MAT); vecmat[4]=(long)T;
84: for (j=1; j<=n; j++)
85: {
86: p1=cgetg(n+1,t_COL); T[j]=(long)p1;
87: for (i=1; i<=n; i++)
88: p1[i]=ltrace(gmodulcp(gmul((GEN)base1[i],(GEN)base1[j]),pol));
89: }
90: MD=cgetg(1,t_MAT); vecmat[5]=(long)MD; /* matrice de la differente */
91: TI=cgetg(1,t_MAT); vecmat[6]=(long)TI; /* matrice .... ? */
92: MDI=cgetg(1,t_MAT); vecmat[7]=(long)MDI; /* matrice .... ? */
93: return vecmat;
94: }
95:
96: GEN
97: rnfinitalg(GEN nf,GEN pol,long prec)
98: {
99: long av=avma,tetpil,m,n,r1,r2,vnf,i,j,k,vpol,v1,r1j,r2j,lfac,degabs;
100: GEN RES,sig,r1r2,rac,p1,p2,liftpol,delta,RAC,ro,p3,bas;
101: GEN f,f2,fac,fac1,fac2,id,p4,p5;
102:
103: if (typ(pol)!=t_POL) err(notpoler,"rnfinitalg");
104: nf=checknf(nf); n=lgef(pol)-3; vpol=varn(pol);
105: vnf=0;
106: for (i=0; i<=n; i++)
107: {
108: long tp1;
109:
110: p1=(GEN)pol[i+2];
111: tp1=typ(p1);
112: if (! is_const_t(tp1))
113: {
114: if (tp1!=t_POLMOD) err(typeer,"rnfinitalg");
115: if (!gegal((GEN)p1[1],(GEN)nf[1]))
116: err(talker,"incompatible number fields in rnfinitalg");
117: p1=(GEN)p1[2];
118: if (! is_const_t(typ(p1)))
119: {
120: v1=varn(p1);
121: if (vnf && vnf!=v1) err(talker,"different variables in rnfinitalg");
122: if (!vnf) vnf=v1;
123: }
124: }
125: }
126: if (!vnf) vnf=varn(nf[1]);
127: if (vpol>=vnf)
128: err(talker,"main variable must be of higher priority in rnfinitalg");
129: RES=cgetg(12,t_VEC);
130: RES[1]=(long)pol;
131: m=lgef(nf[1])-3; degabs=n*m;
132: r1r2=(GEN)nf[2]; r1=itos((GEN)r1r2[1]); r2=itos((GEN)r1r2[2]);
133: sig=cgetg(r1+r2+1,t_VEC); RES[2]=(long)sig;
134: rac=(GEN)nf[6]; liftpol=lift(pol);
135: RAC=cgetg(r1+r2+1,t_VEC); RES[6]=(long)RAC;
136: for (j=1; j<=r1; j++)
137: {
138: p1=gsubst(liftpol,vnf,(GEN)rac[j]);
139: ro=roots(p1,prec);
140: r1j=0;
141: while (r1j<n && gcmp0(gimag((GEN)ro[r1j+1]))) r1j++;
142: p2=cgetg(3,t_VEC); p2[1]=lstoi(r1j); p2[2]=lstoi(r2j=((n-r1j)>>1));
143: sig[j]=(long)p2;
144: p3=cgetg(r1j+r2j+1,t_VEC);
145: for (i=1; i<=r1j; i++) p3[i]=lreal((GEN)ro[i]);
146: for (; i<=r1j+r2j; i++) p3[i]=(long)ro[(i<<1)-r1j];
147: RAC[j]=(long)p3;
148: }
149: for (; j<=r1+r2; j++)
150: {
151: p2=cgetg(3,t_VEC); p2[1]=zero; p2[2]=lstoi(n); sig[j]=(long)p2;
152: p1=gsubst(liftpol,vnf,(GEN)rac[j]);
153: RAC[j]=(long)roots(p1,prec);
154: }
155: p1 = rnfpseudobasis(nf,pol);
156:
157: delta = cgetg(3,t_VEC);
158: delta[1]=p1[3];
159: delta[2]=p1[4];
160: RES[3]=(long)delta;
161: p2 = matbasistoalg(nf,(GEN)p1[1]);
162: bas = cgetg(3,t_VEC);
163: bas[1]=(long)mat_to_vecpol(p2,vpol);
164: bas[2]=(long)p1[2];
165: RES[7]=(long)bas;
166: RES[8]=linvmat(p2);
167:
168: f2=idealdiv(nf,discsr(pol),(GEN)p1[3]);
169: fac=idealfactor(nf,f2);
170: fac1=(GEN)fac[1]; fac2=(GEN)fac[2]; lfac=lg(fac1)-1;
171: f=idmat(m);
172: for (i=1; i<=lfac; i++)
173: {
174: if (mpodd((GEN)fac2[i])) err(bugparier,"rnfinitalg (odd exponent)");
175: f=idealmul(nf,f,idealpow(nf,(GEN)fac1[i],gmul2n((GEN)fac2[i],-1)));
176: }
177: RES[4]=(long)f;
178: RES[10]=(long)nf;
179: RES[5]=(long)rnfmakematrices(RES);
180: if (DEBUGLEVEL>1) msgtimer("matrices");
181: RES[9]=lgetg(1,t_VEC); /* table de multiplication */
182: p2=cgetg(6,t_VEC); RES[11]=(long)p2;
183: p1=rnfequation2(nf,pol); for (i=1; i<=3; i++) p2[i]=p1[i];
184: p4=cgetg(degabs+1,t_MAT);
185: for (i=1; i<=n; i++)
186: { /* removing denominators speeds up multiplication */
187: GEN cop3,com, om = rnfelementreltoabs(RES,gmael(bas,1,i));
188:
189: if (DEBUGLEVEL>1) msgtimer("i = %ld",i);
190: com = content(om); om = gdiv(om,com);
191: id=gmael(bas,2,i);
192: for (j=1; j<=m; j++)
193: {
194: p5=cgetg(degabs+1,t_COL); p4[(i-1)*m+j]=(long)p5;
195: p1=gmul((GEN)nf[7],(GEN)id[j]);
196: p3 = gsubst(p1,varn(nf[1]), (GEN)p2[2]);
197: cop3 = content(p3); p3 = gdiv(p3,cop3);
198: p3 = gmul(gmul(com,cop3), lift_intern(gmul(om,p3)));
199:
200: for (k=1; k<lgef(p3)-1; k++) p5[k]=p3[k+1];
201: for ( ; k<=degabs; k++) p5[k]=zero;
202: }
203: }
204: if (DEBUGLEVEL>1) msgtimer("p4");
205: p3=denom(p4); if (gcmp1(p3)) p3=NULL; else p4=gmul(p3,p4);
206: p4=hnfmod(p4,detint(p4));
207: if (DEBUGLEVEL>1) msgtimer("hnfmod");
208: for (j=degabs-1; j>0; j--)
209: if (cmpis(gcoeff(p4,j,j),2) > 0)
210: {
211: p1=shifti(gcoeff(p4,j,j),-1);
212: for (k=j+1; k<=degabs; k++)
213: if (cmpii(gcoeff(p4,j,k),p1) > 0)
214: for (i=1; i<=j; i++)
215: coeff(p4,i,k)=lsubii(gcoeff(p4,i,k),gcoeff(p4,i,j));
216: }
217: if (p3) p4=gdiv(p4,p3);
218: p2[4]=(long)mat_to_vecpol(p4,vpol);
219: p2[5]=linvmat(p4);
220: tetpil=avma; return gerepile(av,tetpil,gcopy(RES));
221: }
222:
223: GEN
224: rnfbasistoalg(GEN rnf,GEN x)
225: {
226: long tx=typ(x),lx=lg(x),av=avma,tetpil,i,n;
227: GEN p1,z,nf;
228:
229: checkrnf(rnf); nf=(GEN)rnf[10];
230: switch(tx)
231: {
232: case t_VEC:
233: x=gtrans(x); /* fall through */
234: case t_COL:
235: n=lg(x)-1; p1=cgetg(n+1,t_COL);
236: for (i=1; i<=n; i++)
237: {
238: if (typ(x[i])==t_COL) p1[i]=(long)basistoalg(nf,(GEN)x[i]);
239: else p1[i]=x[i];
240: }
241: p1=gmul(gmael(rnf,7,1),p1); tetpil=avma;
242: return gerepile(av,tetpil,gmodulcp(p1,(GEN)rnf[1]));
243:
244: case t_MAT:
245: z=cgetg(lx,tx);
246: for (i=1; i<lx; i++) z[i]=(long)rnfbasistoalg(rnf,(GEN)x[i]);
247: return z;
248:
249: case t_POLMOD:
250: return gcopy(x);
251:
252: default:
253: z=cgetg(3,t_POLMOD); z[1]=lcopy((GEN)rnf[1]);
254: z[2]=lmul(x,polun[varn(rnf[1])]); return z;
255: }
256: }
257:
258: long polegal_spec(GEN x, GEN y);
259:
260: /* assuem x is a t_POLMOD */
261: GEN
262: lift_to_pol(GEN x)
263: {
264: GEN y = (GEN)x[2];
265: return (typ(y) != t_POL)? gtopoly(y,varn(x[1])): y;
266: }
267:
268: GEN
269: rnfalgtobasis(GEN rnf,GEN x)
270: {
271: long av=avma,tetpil,tx=typ(x),lx=lg(x),i,N;
272: GEN z;
273:
274: checkrnf(rnf);
275: switch(tx)
276: {
277: case t_VEC: case t_COL: case t_MAT:
278: z=cgetg(lx,tx);
279: for (i=1; i<lx; i++) z[i]=(long)rnfalgtobasis(rnf,(GEN)x[i]);
280: return z;
281:
282: case t_POLMOD:
283: if (!polegal_spec((GEN)rnf[1],(GEN)x[1]))
284: err(talker,"not the same number field in rnfalgtobasis");
285: x=lift_to_pol(x); /* fall through */
286: case t_POL:
287: N=lgef(rnf[1])-3;
288: if (tx==t_POL && lgef(x)-3 >= N) x=gmod(x,(GEN)rnf[1]);
289: z=cgetg(N+1,t_COL); for (i=1; i<=N; i++) z[i]=(long)truecoeff(x,i-1);
290: tetpil=avma; return gerepile(av,tetpil,gmul((GEN)rnf[8],z));
291: }
292: return gscalcol(x, lgef(rnf[1])-3);
293: }
294:
295: /* x doit etre un polymod ou un polynome ou un vecteur de tels objets... */
296: GEN
297: rnfelementreltoabs(GEN rnf,GEN x)
298: {
299: long av=avma,tx,i,lx,va,tp3;
300: GEN z,p1,p2,p3,polabs,teta,alpha,s,k;
301:
302: checkrnf(rnf); tx=typ(x); lx=lg(x); va=varn((GEN)rnf[1]);
303: switch(tx)
304: {
305: case t_VEC: case t_COL: case t_MAT:
306: z=cgetg(lx,tx);
307: for (i=1; i<lx; i++) z[i]=(long)rnfelementreltoabs(rnf,(GEN)x[i]);
308: return z;
309:
310: case t_POLMOD:
311: x=lift_to_pol(x); /* fall through */
312: case t_POL:
313: if (gvar(x) > va)
314: {
315: if (gcmp0(x)) {x=cgetg(2,t_POL); x[1]=evalvarn(va) | evallgef(2);}
316: else
317: {
318: p1=cgetg(3,t_POL); p1[1]=evalvarn(va) | evallgef(3) | evalsigne(1);
319: p1[2]=(long)x; x=p1;
320: }
321: }
322: p1=(GEN)rnf[11]; polabs=(GEN)p1[1]; alpha=(GEN)p1[2]; k=(GEN)p1[3];
323: teta=gmodulcp(gsub(polx[va],gmul(k,(GEN)alpha[2])),polabs);
324: s=gzero;
325: for (i=lgef(x)-1; i>1; i--)
326: {
327: p3=(GEN)x[i]; tp3=typ(p3);
328: if (is_const_t(tp3)) p2 = p3;
329: else
330: switch(tp3)
331: {
332: case t_POLMOD:
333: p3 = (GEN)p3[2]; /* fall through */
334: case t_POL:
335: p2 = poleval(p3,alpha);
336: }
337: s=gadd(p2,gmul(teta,s));
338: }
339: return gerepileupto(av,s);
340:
341: default: return gcopy(x);
342: }
343: }
344:
345: GEN
346: rnfelementabstorel(GEN rnf,GEN x)
347: {
348: long av=avma,tx,i,lx;
349: GEN z,p1,s,tetap,k,nf;
350:
351: checkrnf(rnf); tx=typ(x); lx=lg(x);
352: switch(tx)
353: {
354: case t_VEC: case t_COL: case t_MAT:
355: z=cgetg(lx,tx);
356: for (i=1; i<lx; i++) z[i]=(long)rnfelementabstorel(rnf,(GEN)x[i]);
357: return z;
358:
359: case t_POLMOD:
360: x=lift_to_pol(x); /* fall through */
361: case t_POL:
362: p1=(GEN)rnf[11]; k=(GEN)p1[3]; nf=(GEN)rnf[10];
363: tetap=gmodulcp(gadd(polx[varn(rnf[1])],
364: gmul(k,gmodulcp(polx[varn(nf[1])],(GEN)nf[1]))),(GEN)rnf[1]);
365: s=gzero;
366: for (i=lgef(x)-1; i>1; i--) s=gadd((GEN)x[i],gmul(tetap,s));
367: return gerepileupto(av,s);
368:
369: default: return gcopy(x);
370: }
371: }
372:
373: /* x doit etre un polymod ou un polynome ou un vecteur de tels objets... */
374: GEN
375: rnfelementup(GEN rnf,GEN x)
376: {
377: long i,lx,tx;
378: GEN z;
379:
380: checkrnf(rnf); tx=typ(x); lx=lg(x);
381: switch(tx)
382: {
383: case t_VEC: case t_COL: case t_MAT:
384: z=cgetg(lx,tx);
385: for (i=1; i<lx; i++) z[i]=(long)rnfelementup(rnf,(GEN)x[i]);
386: return z;
387:
388: case t_POLMOD:
389: x=(GEN)x[2]; /* fall through */
390: case t_POL:
391: return poleval(x,gmael(rnf,11,2));
392:
393: default: return gcopy(x);
394: }
395: }
396:
397: /* x doit etre un polymod ou un polynome ou un vecteur de tels objets..*/
398: GEN
399: rnfelementdown(GEN rnf,GEN x)
400: {
401: long av=avma,tetpil,i,lx,tx;
402: GEN p1,z;
403:
404: checkrnf(rnf); tx=typ(x); lx=lg(x);
405: switch(tx)
406: {
407: case t_VEC: case t_COL: case t_MAT:
408: z=cgetg(lx,tx);
409: for (i=1; i<lx; i++) z[i]=(long)rnfelementdown(rnf,(GEN)x[i]);
410: return z;
411:
412: case t_POLMOD:
413: x=(GEN)x[2]; /* fall through */
414: case t_POL:
415: if (gcmp0(x)) return gzero;
416:
417: p1=rnfelementabstorel(rnf,x);
418: if (typ(p1)==t_POLMOD && varn(p1[1])==varn(rnf[1])) p1=(GEN)p1[2];
419: if (gvar(p1)>varn(rnf[1]))
420: {
421: tetpil=avma;
422: return gerepile(av,tetpil,gcopy(p1));
423: }
424: if (lgef(p1)==3)
425: {
426: tetpil=avma;
427: return gerepile(av,tetpil,gcopy((GEN)p1[2]));
428: }
429: err(talker,"element is not in the base field in rnfelementdown");
430:
431: default: return gcopy(x);
432: }
433: }
434:
435: /* x est exprime sur la base relative */
436: static GEN
437: rnfprincipaltohermite(GEN rnf,GEN x)
438: {
439: long av=avma,tetpil;
440: GEN nf,bas,bas1,p1,z;
441:
442: x=rnfbasistoalg(rnf,x); nf=(GEN)rnf[10];
443: bas=(GEN)rnf[7]; bas1=(GEN)bas[1];
444: p1=rnfalgtobasis(rnf,gmul(x,gmodulcp(bas1,(GEN)rnf[1])));
445: z=cgetg(3,t_VEC); z[2]=bas[2];
446: settyp(p1,t_MAT); z[1]=(long)matalgtobasis(nf,p1);
447:
448: tetpil=avma;
449: return gerepile(av,tetpil,nfhermite(nf,z));
450: }
451:
452: GEN
453: rnfidealhermite(GEN rnf,GEN x)
454: {
455: long tx=typ(x),lx=lg(x),av=avma,tetpil,i,j,n,m;
456: GEN z,p1,p2,x1,x2,x1j,nf,bas,unnf,zeronf;
457:
458: checkrnf(rnf);
459: n=lgef(rnf[1])-3; nf=(GEN)rnf[10]; bas=(GEN)rnf[7];
460:
461: switch(tx)
462: {
463: case t_INT: case t_FRAC: case t_FRACN: z=cgetg(3,t_VEC);
464: m=lgef(nf[1])-3; zeronf=gscalcol_i(gzero,m); unnf=gscalcol_i(gun,m);
465: p1=cgetg(n+1,t_MAT); z[1]=(long)p1;
466: for (j=1; j<=n; j++)
467: {
468: p2=cgetg(n+1,t_COL); p1[j]=(long)p2;
469: for (i=1; i<=n; i++) p2[i]=(i==j)?(long)unnf:(long)zeronf;
470: }
471: z[2]=lmul(x,(GEN)bas[2]); return z;
472:
473: case t_POLMOD: case t_POL:
474: p1=rnfalgtobasis(rnf,x); tetpil=avma;
475: return gerepile(av,tetpil,rnfprincipaltohermite(rnf,p1));
476:
477: case t_VEC:
478: switch(lx)
479: {
480: case 3:
481: x1=(GEN)x[1];
482: if (typ(x1)!=t_MAT || lg(x1) < n+1 || lg(x1[1]) != n+1)
483: err(talker,"incorrect type in rnfidealhermite");
484: p1=cgetg(n+1,t_MAT);
485: for (j=1; j<=n; j++)
486: {
487: p2=cgetg(n+1,t_COL); p1[j]=(long)p2; x1j=(GEN)x1[j];
488: for (i=1; i<=n; i++)
489: {
490: tx = typ(x1j[i]);
491: if (is_const_t(tx)) p2[i] = x1j[i];
492: else
493: switch(tx)
494: {
495: case t_POLMOD: case t_POL:
496: p2[i]=(long)algtobasis(nf,(GEN)x1j[i]); break;
497: case t_COL:
498: p2[i]=x1j[i]; break;
499: default: err(talker,"incorrect type in rnfidealhermite");
500: }
501: }
502: }
503: x2=(GEN)x[2];
504: if (typ(x2)!=t_VEC || lg(x2)!=lg(x1))
505: err(talker,"incorrect type in rnfidealhermite");
506: tetpil=avma; z=cgetg(3,t_VEC); z[1]=lcopy(p1); z[2]=lcopy(x2);
507: z=gerepile(av,tetpil,nfhermite(nf,z));
508: if (lg(z[1]) != n+1)
509: err(talker,"not an ideal in rnfidealhermite");
510: return z;
511:
512: case 6:
513: err(impl,"rnfidealhermite for prime ideals");
514: default:
515: err(typeer,"rnfidealhermite");
516: }
517:
518: case t_COL:
519: if (lx!=(n+1)) err(typeer,"rnfidealhermite");
520: return rnfprincipaltohermite(rnf,x);
521:
522: case t_MAT:
523: return rnfidealabstorel(rnf,x);
524: }
525: err(typeer,"rnfidealhermite");
526: return NULL; /* not reached */
527: }
528:
529: GEN
530: rnfidealnormrel(GEN rnf,GEN id)
531: {
532: long av=avma,i,n;
533: GEN z,id2,nf;
534:
535: checkrnf(rnf);
536: id=rnfidealhermite(rnf,id); id2=(GEN)id[2];
537: n=lgef(rnf[1])-3; nf=(GEN)rnf[10];
538: if (n==1) { avma=av; return idmat(lgef(nf[1]-3)); }
539: z=(GEN)id2[1]; for (i=2; i<=n; i++) z=idealmul(nf,z,(GEN)id2[i]);
540: return gerepileupto(av,z);
541: }
542:
543: GEN
544: rnfidealnormabs(GEN rnf,GEN id)
545: {
546: long av=avma,i,n;
547: GEN z,id2;
548:
549: checkrnf(rnf);
550: id=rnfidealhermite(rnf,id); id2=(GEN)id[2];
551: n=lgef(rnf[1])-3;
552: z=gun; for (i=1; i<=n; i++) z=gmul(z,dethnf((GEN)id2[i]));
553: return gerepileupto(av,z);
554: }
555:
556: GEN
557: rnfidealreltoabs(GEN rnf,GEN x)
558: {
559: long av=avma,tetpil,i,j,k,n,m;
560: GEN nf,basinv,om,id,p1,p2,p3,p4,p5;
561:
562: checkrnf(rnf);
563: x=rnfidealhermite(rnf,x);
564: n=lgef(rnf[1])-3; nf=(GEN)rnf[10]; m=lgef(nf[1])-3;
565: basinv=(GEN)((GEN)rnf[11])[5];
566: p3=cgetg(n*m+1,t_MAT); p2=gmael(rnf,11,2);
567: for (i=1; i<=n; i++)
568: {
569: om=rnfbasistoalg(rnf,gmael(x,1,i)); id=gmael(x,2,i);
570: om=rnfelementreltoabs(rnf,om);
571: for (j=1; j<=m; j++)
572: {
573: p1=gmul((GEN)nf[7],(GEN)id[j]);
574: p4=lift_intern(gmul(om,gsubst(p1,varn(nf[1]),p2)));
575: p5=cgetg(n*m+1,t_COL);
576: for (k=0; k<n*m; k++) p5[k+1]=(long)truecoeff(p4,k);
577: p3[(i-1)*m+j]=(long)p5;
578: }
579: }
580: p1=gmul(basinv,p3); p2=detint(p1);
581: tetpil=avma; return gerepile(av,tetpil,hnfmod(p1,p2));
582: }
583:
584: GEN
585: rnfidealabstorel(GEN rnf,GEN x)
586: {
587: long av=avma,tetpil,n,m,j,k;
588: GEN nf,basabs,ma,xj,p1,p2,id;
589:
590: checkrnf(rnf); n=lgef(rnf[1])-3; nf=(GEN)rnf[10]; m=lgef(nf[1])-3;
591: if (typ(x)!=t_MAT || lg(x)!=(n*m+1) || lg(x[1])!=(n*m+1))
592: err(impl,"rnfidealabstorel for an ideal not in HNF");
593: basabs=gmael(rnf,11,4); ma=cgetg(n*m+1,t_MAT);
594: for (j=1; j<=n*m; j++)
595: {
596: p2=cgetg(n+1,t_COL); ma[j]=(long)p2;
597: xj=gmul(basabs,(GEN)x[j]);
598: xj=lift_intern(rnfelementabstorel(rnf,xj));
599: for (k=0; k<n; k++)
600: p2[k+1]=(long)truecoeff(xj,k);
601: }
602: ma=gmul((GEN)rnf[8],ma);
603: ma=matalgtobasis(nf,ma);
604: p1=cgetg(n*m+1,t_VEC); id=idmat(m);
605: for (j=1; j<=n*m; j++) p1[j]=(long)id;
606: p2=cgetg(3,t_VEC); p2[1]=(long)ma; p2[2]=(long)p1;
607: tetpil=avma; return gerepile(av,tetpil,nfhermite(nf,p2));
608: }
609:
610: GEN
611: rnfidealdown(GEN rnf,GEN x)
612: {
613: long av=avma,tetpil;
614:
615: checkrnf(rnf); x=rnfidealhermite(rnf,x);
616: tetpil=avma; return gerepile(av,tetpil,gcopy(gmael(x,2,1)));
617: }
618:
619: /* lift ideal x to the relative extension, returns a Z-basis */
620: GEN
621: rnfidealup(GEN rnf,GEN x)
622: {
623: long av=avma,tetpil,i,n,m;
624: GEN nf,bas,bas2,p1,p2,zeronf,unnf;
625:
626: checkrnf(rnf);
627: bas=(GEN)rnf[7]; bas2=(GEN)bas[2];
628: n=lg(bas2)-1; nf=(GEN)rnf[10]; m=lgef((GEN)nf[1])-3;
629: zeronf=zerocol(m); unnf=gscalcol_i(gun,m);
630: p2=cgetg(3,t_VEC); p1=cgetg(n+1,t_VEC);
631: p2[1]=(long)idmat_intern(n,unnf,zeronf);
632: p2[2]=(long)p1;
633: for (i=1; i<=n; i++) p1[i]=(long)idealmul(nf,x,(GEN)bas2[i]);
634: tetpil=avma; return gerepile(av,tetpil,rnfidealreltoabs(rnf,p2));
635: }
636:
637: /* x a relative HNF ---> vector of 2 generators (relative polymods) */
638: GEN
639: rnfidealtwoelement(GEN rnf,GEN x)
640: {
641: long av=avma,tetpil,j;
642: GEN p1,p2,p3,res,polabs,nfabs,z;
643:
644: res=(GEN)rnf[11]; polabs=(GEN)res[1];
645: nfabs=cgetg(10,t_VEC); nfabs[1]=(long)polabs;
646: for (j=2; j<=9; j++) nfabs[j]=zero;
647: nfabs[7]=(long)lift((GEN)res[4]); nfabs[8]=res[5];
648: p1=rnfidealreltoabs(rnf,x);
649: p2=ideal_two_elt(nfabs,p1);
650: p3=rnfelementabstorel(rnf,gmul((GEN)res[4],(GEN)p2[2]));
651: tetpil=avma; z=cgetg(3,t_VEC); z[1]=lcopy((GEN)p2[1]);
652: z[2]=(long)rnfalgtobasis(rnf,p3);
653: return gerepile(av,tetpil,z);
654: }
655:
656: GEN
657: rnfidealmul(GEN rnf,GEN x,GEN y) /* x et y sous HNF relative uniquement */
658: {
659: long av=avma,tetpil,i,j,n;
660: GEN z,nf,x1,x2,p1,p2,p3,p4,p5,res;
661:
662: z=rnfidealtwoelement(rnf,y);
663: nf=(GEN)rnf[10]; n=lgef(rnf[1])-3;
664: x=rnfidealhermite(rnf,x);
665: x1=gmodulcp(gmul(gmael(rnf,7,1),matbasistoalg(nf,(GEN)x[1])),(GEN) rnf[1]);
666: x2=(GEN)x[2]; p1=gmul((GEN)z[1],(GEN)x[1]);
667: p2=lift_intern(gmul(rnfbasistoalg(rnf,(GEN)z[2]),x1));
668: p3=cgetg(n+1,t_MAT);
669: for (j=1; j<=n; j++)
670: {
671: p4=cgetg(n+1,t_COL); p3[j]=(long)p4; p5=(GEN)p2[j];
672: for (i=1; i<=n; i++)
673: p4[i]=(long)algtobasis(nf,truecoeff((GEN)p5,i-1));
674: }
675: res=cgetg(3,t_VEC);
676: res[1]=(long)concatsp(p1,p3);
677: res[2]=(long)concatsp(x2,x2);
678: tetpil=avma; return gerepile(av,tetpil,nfhermite(nf,res));
679: }
680:
681: /*********************************************************************/
682: /** **/
683: /** LIBRARY FOR POLYNOMIALS WITH COEFFS. IN Z_K/P **/
684: /** An element in Z_K/P is a t_COL with degree(nf[1]) components. **/
685: /** These are integers modulo the prime p under prime ideal P **/
686: /** (only f(P/p) elements are non zero). These components are **/
687: /** given on the integer basis of K. **/
688: /** **/
689: /*********************************************************************/
690:
691: /* K.B: What follows is not meant to work (yet?) */
692:
693: GEN
694: polnfmulscal(GEN nf,GEN s,GEN x)
695: {
696: long i,lx=lgef(x);
697: GEN z;
698:
699: if (lx<3) return gcopy(x);
700: if (gcmp0(s))
701: {
702: z=cgetg(2,t_POL); z[1]=evallgef(2) | evalvarn(varn(x));
703: return z;
704: }
705: z=cgetg(lx,t_POL); z[1]=x[1];
706: for (i=2; i<lx; i++) z[i]=(long)element_mul(nf,s,(GEN)x[i]);
707: return z;
708: }
709:
710: GEN
711: polnfmul(GEN nf, GEN x, GEN y)
712: {
713: long av,tetpil,m,i,d,imin,imax,lx,ly,lz;
714: GEN p1,z,zeronf;
715:
716: if (gcmp0(x)||gcmp0(y))
717: {
718: z=cgetg(2,t_POL); z[1]=evallgef(2) | evalvarn(varn(x));
719: return z;
720: }
721: m=lgef(nf[1])-3; av=avma;
722: lx=lgef(x)-3; ly=lgef(y)-3; lz=lx+ly;
723: zeronf=gscalcol_i(gzero,m);
724: z=cgetg(lz+3,t_POL);
725: z[1] = evallgef(lz+3) | evalvarn(x) | evalsigne(1);
726: for (d=0; d<=lz; d++)
727: {
728: p1=zeronf; imin=max(0,d-ly); imax=min(d,lx);
729: for (i=imin; i<=imax; i++)
730: p1=gadd(p1,element_mul(nf,(GEN)x[i+2],(GEN)y[d-i+2]));
731: z[d+2]=(long)p1;
732: }
733: tetpil=avma; return gerepile(av,tetpil,gcopy(z));
734: }
735:
736: /* division euclidienne */
737: GEN
738: polnfdeuc(GEN nf, GEN x, GEN y, GEN *ptr)
739: {
740: long av=avma,m,i,d,tx,lx,ly,lz,fl;
741: GEN z,unnf,lcy,r;
742: GEN *gptr[2];
743:
744: if (gcmp0(y)) err(talker,"division by zero in polnfdiv");
745: lx=lgef(x); ly=lgef(y); lz=lx-ly;
746: if (gcmp0(x) || lz<0) { *ptr=gcopy(x); return zeropol(varn(x)); }
747:
748: m=lgef(nf[1])-3; unnf=gscalcol_i(gun,m);
749: x=dummycopy(x); y=dummycopy(y);
750: for (i=2; i<lx; i++)
751: {
752: tx=typ(x[i]);
753: if (is_intreal_t(tx) || tx == t_INTMOD || is_frac_t(tx))
754: x[i]=lmul((GEN)x[i],unnf);
755: }
756: for (i=2; i<ly; i++)
757: {
758: tx=typ(y[i]);
759: if (is_intreal_t(tx) || tx == t_INTMOD || is_frac_t(tx))
760: y[i]=lmul((GEN)y[i],unnf);
761: }
762:
763: lz += 3;
764: z=cgetg(lz,t_POL); z[1]=evallgef(lz) | evalvarn(x) | evalsigne(1);
765: lcy=(GEN)y[ly-1];
766: if (gegal(lift(lcy),unnf)) fl=0;
767: else
768: {
769: fl=1; y=polnfmulscal(nf,element_inv(nf,lcy),y);
770: }
771: for (d=lz-1; d>=2; d--)
772: {
773: z[d]=x[d+ly-3];
774: for (i=d; i<d+ly-3; i++)
775: x[i]=lsub((GEN)x[i],element_mul(nf,(GEN)z[d],(GEN)y[i-d-2]));
776: }
777: if (fl) z=polnfmulscal(nf,lcy,z);
778:
779: for(;;)
780: {
781: if (!gcmp0((GEN)x[d]))
782: {
783: r=cgetg(d,t_POL);
784: r[1] = evallgef(d) | evalvarn(varn(x)) | evalsigne(1);
785: for (i=2; i<d; i++) r[i]=x[i];
786: break;
787: }
788: if (d==2) { r = zeropol(varn(x)); break; }
789: d--;
790: }
791: *ptr=r; gptr[0]=ptr; gptr[1]=&z;
792: gerepilemany(av,gptr,2); return z;
793: }
794:
795: GEN
796: polnfpow(GEN nf,GEN x,GEN k)
797: {
798: long s,av=avma,m;
799: GEN y,z;
800:
801: m=lgef(nf[1])-3;
802: if (typ(k)!=t_INT) err(talker,"not an integer exponent in nfpow");
803: s=signe(k); if (s<0) err(impl,"polnfpow for negative exponents");
804:
805: z=x; y=cgetg(3,t_POL);
806: y[1] = evallgef(3) | evalvarn(varn(x)) | evalsigne(1);
807: y[2] = (long)gscalcol_i(gun,m);
808: for(;;)
809: {
810: if (mpodd(k)) y=polnfmul(nf,z,y);
811: k=shifti(k,-1);
812: if (!signe(k)) { cgiv(k); return gerepileupto(av,y); }
813: z=polnfmul(nf,z,z);
814: }
815: }
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to base5.c CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM_contrib / pari / src / basemath