=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/PU.c,v retrieving revision 1.1 retrieving revision 1.16 diff -u -p -r1.1 -r1.16 --- OpenXM_contrib2/asir2000/engine/PU.c 1999/12/03 07:39:08 1.1 +++ OpenXM_contrib2/asir2000/engine/PU.c 2018/03/29 01:32:51 1.16 @@ -1,993 +1,1103 @@ -/* $OpenXM: OpenXM/src/asir99/engine/PU.c,v 1.1.1.1 1999/11/10 08:12:26 noro Exp $ */ +/* + * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED + * All rights reserved. + * + * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited, + * non-exclusive and royalty-free license to use, copy, modify and + * redistribute, solely for non-commercial and non-profit purposes, the + * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and + * conditions of this Agreement. For the avoidance of doubt, you acquire + * only a limited right to use the SOFTWARE hereunder, and FLL or any + * third party developer retains all rights, including but not limited to + * copyrights, in and to the SOFTWARE. + * + * (1) FLL does not grant you a license in any way for commercial + * purposes. You may use the SOFTWARE only for non-commercial and + * non-profit purposes only, such as academic, research and internal + * business use. + * (2) The SOFTWARE is protected by the Copyright Law of Japan and + * international copyright treaties. If you make copies of the SOFTWARE, + * with or without modification, as permitted hereunder, you shall affix + * to all such copies of the SOFTWARE the above copyright notice. + * (3) An explicit reference to this SOFTWARE and its copyright owner + * shall be made on your publication or presentation in any form of the + * results obtained by use of the SOFTWARE. + * (4) In the event that you modify the SOFTWARE, you shall notify FLL by + * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification + * for such modification or the source code of the modified part of the + * SOFTWARE. + * + * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL + * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND + * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS + * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES' + * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY + * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY. + * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT, + * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY + * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL + * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES + * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES + * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY + * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF + * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART + * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY + * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, + * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. + * + * $OpenXM: OpenXM_contrib2/asir2000/engine/PU.c,v 1.15 2018/02/28 03:55:38 noro Exp $ +*/ #include "ca.h" -void reorderp(nvl,ovl,p,pr) -VL nvl,ovl; -P p; -P *pr; +void reorderp(VL nvl,VL ovl,P p,P *pr) { - DCP dc; - P x,m,s,t,c; - - if ( !p ) - *pr = 0; - else if ( NUM(p) ) - *pr = p; - else { - MKV(VR(p),x); - for ( s = 0, dc = DC(p); dc; dc = NEXT(dc) ) { - reorderp(nvl,ovl,COEF(dc),&c); - if ( DEG(dc) ) { - pwrp(nvl,x,DEG(dc),&t); mulp(nvl,c,t,&m); - addp(nvl,m,s,&t); - } else - addp(nvl,s,c,&t); - s = t; - } - *pr = s; - } + DCP dc; + P x,m,s,t,c; + + if ( !p ) + *pr = 0; + else if ( NUM(p) ) + *pr = p; + else { + MKV(VR(p),x); + for ( s = 0, dc = DC(p); dc; dc = NEXT(dc) ) { + reorderp(nvl,ovl,COEF(dc),&c); + if ( DEG(dc) ) { + pwrp(nvl,x,DEG(dc),&t); mulp(nvl,c,t,&m); + addp(nvl,m,s,&t); + } else + addp(nvl,s,c,&t); + s = t; + } + *pr = s; + } } - -void substp(vl,p,v0,p0,pr) -VL vl; -V v0; -P p,p0; -P *pr; + +void substp(VL vl,P p,V v0,P p0,P *pr) { - P x,t,m,c,s,a; - DCP dc; - Q d; + P x,t,m,c,s,a; + DCP dc; + Q d; - if ( !p ) - *pr = 0; - else if ( NUM(p) ) - *pr = p; - else if ( VR(p) != v0 ) { - MKV(VR(p),x); - for ( c = 0, dc = DC(p); dc; dc = NEXT(dc) ) { - substp(vl,COEF(dc),v0,p0,&t); - if ( DEG(dc) ) { - pwrp(vl,x,DEG(dc),&s); mulp(vl,s,t,&m); - addp(vl,m,c,&a); - c = a; - } else { - addp(vl,t,c,&a); - c = a; - } - } - *pr = c; - } else { - dc = DC(p); - c = COEF(dc); - for ( d = DEG(dc), dc = NEXT(dc); - dc; d = DEG(dc), dc = NEXT(dc) ) { - subq(d,DEG(dc),(Q *)&t); pwrp(vl,p0,(Q)t,&s); - mulp(vl,s,c,&m); - addp(vl,m,COEF(dc),&c); - } - if ( d ) { - pwrp(vl,p0,d,&t); mulp(vl,t,c,&m); - c = m; - } - *pr = c; - } + if ( !p ) + *pr = 0; + else if ( NUM(p) ) + *pr = p; + else if ( VR(p) != v0 ) { + MKV(VR(p),x); + for ( c = 0, dc = DC(p); dc; dc = NEXT(dc) ) { + substp(vl,COEF(dc),v0,p0,&t); + if ( DEG(dc) ) { + pwrp(vl,x,DEG(dc),&s); mulp(vl,s,t,&m); + addp(vl,m,c,&a); + c = a; + } else { + addp(vl,t,c,&a); + c = a; + } + } + *pr = c; + } else { + dc = DC(p); + c = COEF(dc); + for ( d = DEG(dc), dc = NEXT(dc); + dc; d = DEG(dc), dc = NEXT(dc) ) { + subq(d,DEG(dc),(Q *)&t); pwrp(vl,p0,(Q)t,&s); + mulp(vl,s,c,&m); + addp(vl,m,COEF(dc),&c); + } + if ( d ) { + pwrp(vl,p0,d,&t); mulp(vl,t,c,&m); + c = m; + } + *pr = c; + } } -void detp(vl,rmat,n,dp) -VL vl; -P **rmat; -int n; -P *dp; +void substpp(VL vl,P p,V *vvect,P *svect,int nv,P *pr); + +void substpp(VL vl,P p,V *vvect,P *svect,int nv,P *pr) { - int i,j,k,sgn; - P mjj,mij,t,s,u,d; - P **mat; - P *mi,*mj; + P x,t,m,c,s,a,p0,c1; + DCP dc; + Q d; + V v; + int i; - mat = (P **)almat_pointer(n,n); - for ( i = 0; i < n; i++ ) - for ( j = 0; j < n; j++ ) - mat[i][j] = rmat[i][j]; - for ( j = 0, d = (P)ONE, sgn = 1; j < n; j++ ) { - for ( i = j; (i < n) && !mat[i][j]; i++ ); - if ( i == n ) { - *dp = 0; return; - } - for ( k = i; k < n; k++ ) - if ( mat[k][j] && (nmonop(mat[k][j]) < nmonop(mat[i][j]) ) ) - i = k; - if ( j != i ) { - mj = mat[j]; mat[j] = mat[i]; mat[i] = mj; sgn = -sgn; - } - for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ ) - for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n; k++ ) { - mulp(vl,mi[k],mjj,&t); mulp(vl,mj[k],mij,&s); - subp(vl,t,s,&u); divsp(vl,u,d,&mi[k]); - } - d = mjj; - } - if ( sgn < 0 ) - chsgnp(d,dp); - else - *dp = d; + if ( !p ) + *pr = 0; + else if ( NUM(p) ) + *pr = p; + else { + v = VR(p); + for ( i = 0; i < nv; i++ ) if ( vvect[i] == v ) break; + if ( svect[i] && OID(svect[i]) < 0 ) { + MKV(VR(p),x); + for ( c = 0, dc = DC(p); dc; dc = NEXT(dc) ) { + substpp(vl,COEF(dc),vvect,svect,nv,&t); + if ( DEG(dc) ) { + pwrp(vl,x,DEG(dc),&s); mulp(vl,s,t,&m); + addp(vl,m,c,&a); + c = a; + } else { + addp(vl,t,c,&a); + c = a; + } + } + *pr = c; + } else { + p0 = svect[i]; + dc = DC(p); + substpp(vl,COEF(dc),vvect,svect,nv,&c); + for ( d = DEG(dc), dc = NEXT(dc); + dc; d = DEG(dc), dc = NEXT(dc) ) { + subq(d,DEG(dc),(Q *)&t); pwrp(vl,p0,(Q)t,&s); + mulp(vl,s,c,&m); + substpp(vl,COEF(dc),vvect,svect,nv,&c1); + addp(vl,m,c1,&c); + } + if ( d ) { + pwrp(vl,p0,d,&t); mulp(vl,t,c,&m); + c = m; + } + *pr = c; + } + } } -void reordvar(vl,v,nvlp) -VL vl; -V v; -VL *nvlp; +void detp(VL vl,P **rmat,int n,P *dp) { - VL nvl,nvl0; + int i,j,k,l,sgn,nmin,kmin,lmin,ntmp; + P mjj,mij,t,s,u,d; + P **mat; + P *mi,*mj; - for ( NEWVL(nvl0), nvl0->v = v, nvl = nvl0; - vl; vl = NEXT(vl) ) - if ( vl->v == v ) - continue; - else { - NEWVL(NEXT(nvl)); - nvl = NEXT(nvl); - nvl->v = vl->v; - } - NEXT(nvl) = 0; - *nvlp = nvl0; + mat = (P **)almat_pointer(n,n); + for ( i = 0; i < n; i++ ) + for ( j = 0; j < n; j++ ) + mat[i][j] = rmat[i][j]; + for ( j = 0, d = (P)ONE, sgn = 1; j < n; j++ ) { + for ( i = j; (i < n) && !mat[i][j]; i++ ); + if ( i == n ) { + *dp = 0; return; + } + nmin = nmonop(mat[i][j]); + kmin=i; lmin=j; + for ( k = j; k < n; k++ ) + for ( l = j; l < n; l++ ) + if ( mat[k][l] && ((ntmp=nmonop(mat[k][l])) < nmin) ) { + kmin = k; lmin = l; nmin = ntmp; + } + if ( kmin != j ) { + mj = mat[j]; mat[j] = mat[kmin]; mat[kmin] = mj; sgn = -sgn; + } + if ( lmin != j ) { + for ( k = j; k < n; k++ ) { + t = mat[k][j]; mat[k][j] = mat[k][lmin]; mat[k][lmin] = t; + } + sgn = -sgn; + } + for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ ) + for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n; k++ ) { + mulp(vl,mi[k],mjj,&t); mulp(vl,mj[k],mij,&s); + subp(vl,t,s,&u); divsp(vl,u,d,&mi[k]); + } + d = mjj; + } + if ( sgn < 0 ) + chsgnp(d,dp); + else + *dp = d; } -void gcdprsp(vl,p1,p2,pr) -VL vl; -P p1,p2,*pr; +void invmatp(VL vl,P **rmat,int n,P ***imatp,P *dnp) { - P g1,g2,gc1,gc2,gp1,gp2,g,gc,gp,gcr; - V v1,v2; + int i,j,k,l,n2; + P mjj,mij,t,s,u,d; + P **mat,**imat; + P *mi,*mj,*w; + + n2 = n<<1; + mat = (P **)almat_pointer(n,n2); + for ( i = 0; i < n; i++ ) { + for ( j = 0; j < n; j++ ) + mat[i][j] = rmat[i][j]; + mat[i][i+n] = (P)ONE; + } + for ( j = 0, d = (P)ONE; j < n; j++ ) { + for ( i = j; (i < n) && !mat[i][j]; i++ ); + if ( i == n ) { + error("invmatp : input is singular"); + } + for ( k = i; k < n; k++ ) + if ( mat[k][j] && (nmonop(mat[k][j]) < nmonop(mat[i][j]) ) ) + i = k; + if ( j != i ) { + mj = mat[j]; mat[j] = mat[i]; mat[i] = mj; + } + for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ ) + for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n2; k++ ) { + mulp(vl,mi[k],mjj,&t); mulp(vl,mj[k],mij,&s); + subp(vl,t,s,&u); divsp(vl,u,d,&mi[k]); + } + d = mjj; + } + /* backward substitution */ + w = (P *)ALLOCA(n2*sizeof(P)); + for ( i = n-2; i >= 0; i-- ) { + bzero(w,n2*sizeof(P)); + for ( k = i+1; k < n; k++ ) + for ( l = k, u = mat[i][l]; l < n2; l++ ) { + mulp(vl,mat[k][l],u,&t); addp(vl,w[l],t,&s); w[l] = s; + } + for ( j = i, u = mat[i][j]; j < n2; j++ ) { + mulp(vl,mat[i][j],d,&t); subp(vl,t,w[j],&s); + divsp(vl,s,u,&mat[i][j]); + } + } + imat = (P **)almat_pointer(n,n); + for ( i = 0; i < n; i++ ) + for ( j = 0; j < n; j++ ) + imat[i][j] = mat[i][j+n]; + *imatp = imat; + *dnp = d; +} - if ( !p1 ) - ptozp0(p2,pr); - else if ( !p2 ) - ptozp0(p1,pr); - else if ( NUM(p1) || NUM(p2) ) - *pr = (P)ONE; - else { - ptozp0(p1,&g1); ptozp0(p2,&g2); - if ( ( v1 = VR(g1) ) == ( v2 = VR(g2) ) ) { - gcdcp(vl,g1,&gc1); divsp(vl,g1,gc1,&gp1); - gcdcp(vl,g2,&gc2); divsp(vl,g2,gc2,&gp2); - gcdprsp(vl,gc1,gc2,&gcr); - sprs(vl,v1,gp1,gp2,&g); +void reordvar(VL vl,V v,VL *nvlp) +{ + VL nvl,nvl0; - if ( VR(g) == v1 ) { - ptozp0(g,&gp); - gcdcp(vl,gp,&gc); divsp(vl,gp,gc,&gp1); - mulp(vl,gp1,gcr,pr); + for ( NEWVL(nvl0), nvl0->v = v, nvl = nvl0; + vl; vl = NEXT(vl) ) + if ( vl->v == v ) + continue; + else { + NEWVL(NEXT(nvl)); + nvl = NEXT(nvl); + nvl->v = vl->v; + } + NEXT(nvl) = 0; + *nvlp = nvl0; +} - } else - *pr = gcr; - } else { - while ( v1 != vl->v && v2 != vl->v ) - vl = NEXT(vl); - if ( v1 == vl->v ) { - gcdcp(vl,g1,&gc1); gcdprsp(vl,gc1,g2,pr); - } else { - gcdcp(vl,g2,&gc2); gcdprsp(vl,gc2,g1,pr); - } - } - } +void gcdprsp(VL vl,P p1,P p2,P *pr) +{ + P g1,g2,gc1,gc2,gp1,gp2,g,gc,gp,gcr; + V v1,v2; + + if ( !p1 ) + ptozp0(p2,pr); + else if ( !p2 ) + ptozp0(p1,pr); + else if ( NUM(p1) || NUM(p2) ) + *pr = (P)ONE; + else { + ptozp0(p1,&g1); ptozp0(p2,&g2); + if ( ( v1 = VR(g1) ) == ( v2 = VR(g2) ) ) { + gcdcp(vl,g1,&gc1); divsp(vl,g1,gc1,&gp1); + gcdcp(vl,g2,&gc2); divsp(vl,g2,gc2,&gp2); + gcdprsp(vl,gc1,gc2,&gcr); + sprs(vl,v1,gp1,gp2,&g); + + if ( VR(g) == v1 ) { + ptozp0(g,&gp); + gcdcp(vl,gp,&gc); divsp(vl,gp,gc,&gp1); + mulp(vl,gp1,gcr,pr); + + } else + *pr = gcr; + } else { + while ( v1 != vl->v && v2 != vl->v ) + vl = NEXT(vl); + if ( v1 == vl->v ) { + gcdcp(vl,g1,&gc1); gcdprsp(vl,gc1,g2,pr); + } else { + gcdcp(vl,g2,&gc2); gcdprsp(vl,gc2,g1,pr); + } + } + } } -void gcdcp(vl,p,pr) -VL vl; -P p,*pr; +void gcdcp(VL vl,P p,P *pr) { - P g,g1; - DCP dc; + P g,g1; + DCP dc; - if ( NUM(p) ) - *pr = (P)ONE; - else { - dc = DC(p); - g = COEF(dc); - for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) { - gcdprsp(vl,g,COEF(dc),&g1); - g = g1; - } - *pr = g; - } + if ( NUM(p) ) + *pr = (P)ONE; + else { + dc = DC(p); + g = COEF(dc); + for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) { + gcdprsp(vl,g,COEF(dc),&g1); + g = g1; + } + *pr = g; + } } -void sprs(vl,v,p1,p2,pr) -VL vl; -V v; -P p1,p2,*pr; +void sprs(VL vl,V v,P p1,P p2,P *pr) { - P q1,q2,m,m1,m2,x,h,r,g1,g2; - int d; - Q dq; - VL nvl; + P q1,q2,m,m1,m2,x,h,r,g1,g2; + int d; + Q dq; + VL nvl; - reordvar(vl,v,&nvl); - reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); + reordvar(vl,v,&nvl); + reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); - if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) { - *pr = 0; - return; - } + if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) { + *pr = 0; + return; + } - if ( deg(v,q1) >= deg(v,q2) ) { - g1 = q1; g2 = q2; - } else { - g2 = q1; g1 = q2; - } - - for ( h = (P)ONE, x = (P)ONE; ; ) { - if ( !deg(v,g2) ) - break; + if ( deg(v,q1) >= deg(v,q2) ) { + g1 = q1; g2 = q2; + } else { + g2 = q1; g1 = q2; + } + + for ( h = (P)ONE, x = (P)ONE; ; ) { + if ( !deg(v,g2) ) + break; - premp(nvl,g1,g2,&r); - if ( !r ) - break; + premp(nvl,g1,g2,&r); + if ( !r ) + break; - d = deg(v,g1) - deg(v,g2); STOQ(d,dq); - pwrp(nvl,h,dq,&m); mulp(nvl,m,x,&m1); g1 = g2; - divsp(nvl,r,m1,&g2); x = LC(g1); /* g1 is not const w.r.t v */ - pwrp(nvl,x,dq,&m1); mulp(nvl,m1,h,&m2); - divsp(nvl,m2,m,&h); - } - *pr = g2; + d = deg(v,g1) - deg(v,g2); STOQ(d,dq); + pwrp(nvl,h,dq,&m); mulp(nvl,m,x,&m1); g1 = g2; + divsp(nvl,r,m1,&g2); x = LC(g1); /* g1 is not const w.r.t v */ + pwrp(nvl,x,dq,&m1); mulp(nvl,m1,h,&m2); + divsp(nvl,m2,m,&h); + } + *pr = g2; } -void resultp(vl,v,p1,p2,pr) -VL vl; -V v; -P p1,p2,*pr; +void resultp(VL vl,V v,P p1,P p2,P *pr) { - P q1,q2,m,m1,m2,lc,q,r,t,g1,g2,adj; - int d,d1,d2,j,k; - VL nvl; - Q dq; + P q1,q2,m,m1,m2,lc,q,r,t,g1,g2,adj; + int d,d1,d2,j,k; + VL nvl; + Q dq; - if ( !p1 || !p2 ) { - *pr = 0; return; - } - reordvar(vl,v,&nvl); - reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); + if ( !p1 || !p2 ) { + *pr = 0; return; + } + reordvar(vl,v,&nvl); + reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); - if ( VR(q1) != v ) - if ( VR(q2) != v ) { - *pr = 0; - return; - } else { - d = deg(v,q2); STOQ(d,dq); - pwrp(vl,q1,dq,pr); - return; - } - else if ( VR(q2) != v ) { - d = deg(v,q1); STOQ(d,dq); - pwrp(vl,q2,dq,pr); - return; - } - - if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) { - *pr = 0; - return; - } + if ( VR(q1) != v ) + if ( VR(q2) != v ) { + *pr = 0; + return; + } else { + d = deg(v,q2); STOQ(d,dq); + pwrp(vl,q1,dq,pr); + return; + } + else if ( VR(q2) != v ) { + d = deg(v,q1); STOQ(d,dq); + pwrp(vl,q2,dq,pr); + return; + } + + if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) { + *pr = 0; + return; + } - d1 = deg(v,q1); d2 = deg(v,q2); - if ( d1 > d2 ) { - g1 = q1; g2 = q2; adj = (P)ONE; - } else if ( d1 < d2 ) { - g2 = q1; g1 = q2; - if ( (d1 % 2) && (d2 % 2) ) { - STOQ(-1,dq); adj = (P)dq; - } else - adj = (P)ONE; - } else { - premp(nvl,q1,q2,&t); - d = deg(v,t); STOQ(d,dq); pwrp(nvl,LC(q2),dq,&adj); - g1 = q2; g2 = t; - if ( d1 % 2 ) { - chsgnp(adj,&t); adj = t; - } - } - d1 = deg(v,g1); j = d1 - 1; + d1 = deg(v,q1); d2 = deg(v,q2); + if ( d1 > d2 ) { + g1 = q1; g2 = q2; adj = (P)ONE; + } else if ( d1 < d2 ) { + g2 = q1; g1 = q2; + if ( (d1 % 2) && (d2 % 2) ) { + STOQ(-1,dq); adj = (P)dq; + } else + adj = (P)ONE; + } else { + premp(nvl,q1,q2,&t); + d = deg(v,t); STOQ(d,dq); pwrp(nvl,LC(q2),dq,&adj); + g1 = q2; g2 = t; + if ( d1 % 2 ) { + chsgnp(adj,&t); adj = t; + } + } + d1 = deg(v,g1); j = d1 - 1; - for ( lc = (P)ONE; ; ) { - if ( ( k = deg(v,g2) ) < 0 ) { - *pr = 0; - return; - } + for ( lc = (P)ONE; ; ) { + if ( ( k = deg(v,g2) ) < 0 ) { + *pr = 0; + return; + } - if ( k == j ) - if ( !k ) { - divsp(nvl,g2,adj,pr); - return; - } else { - premp(nvl,g1,g2,&r); mulp(nvl,lc,lc,&m); - divsp(nvl,r,m,&q); - g1 = g2; g2 = q; - lc = LC(g1); /* g1 is not const */ - j = k - 1; - } - else { - d = j - k; STOQ(d,dq); - pwrp(nvl,(VR(g2)==v?LC(g2):g2),dq,&m); - mulp(nvl,g2,m,&m1); - pwrp(nvl,lc,dq,&m); divsp(nvl,m1,m,&t); - if ( k == 0 ) { - divsp(nvl,t,adj,pr); - return; - } else { - premp(nvl,g1,g2,&r); - mulp(nvl,lc,lc,&m1); mulp(nvl,m,m1,&m2); - divsp(nvl,r,m2,&q); - g1 = t; g2 = q; - if ( d % 2 ) { - chsgnp(g2,&t); g2 = t; - } - lc = LC(g1); /* g1 is not const */ - j = k - 1; - } - } - } + if ( k == j ) + if ( !k ) { + divsp(nvl,g2,adj,pr); + return; + } else { + premp(nvl,g1,g2,&r); mulp(nvl,lc,lc,&m); + divsp(nvl,r,m,&q); + g1 = g2; g2 = q; + lc = LC(g1); /* g1 is not const */ + j = k - 1; + } + else { + d = j - k; STOQ(d,dq); + pwrp(nvl,(VR(g2)==v?LC(g2):g2),dq,&m); + mulp(nvl,g2,m,&m1); + pwrp(nvl,lc,dq,&m); divsp(nvl,m1,m,&t); + if ( k == 0 ) { + divsp(nvl,t,adj,pr); + return; + } else { + premp(nvl,g1,g2,&r); + mulp(nvl,lc,lc,&m1); mulp(nvl,m,m1,&m2); + divsp(nvl,r,m2,&q); + g1 = t; g2 = q; + if ( d % 2 ) { + chsgnp(g2,&t); g2 = t; + } + lc = LC(g1); /* g1 is not const */ + j = k - 1; + } + } + } } -void srch2(vl,v,p1,p2,pr) -VL vl; -V v; -P p1,p2,*pr; +void srch2(VL vl,V v,P p1,P p2,P *pr) { - P q1,q2,m,m1,m2,lc,q,r,t,s,g1,g2,adj; - int d,d1,d2,j,k; - VL nvl; - Q dq; + P q1,q2,m,m1,m2,lc,q,r,t,s,g1,g2,adj; + int d,d1,d2,j,k; + VL nvl; + Q dq; - reordvar(vl,v,&nvl); - reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); + reordvar(vl,v,&nvl); + reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); - if ( VR(q1) != v ) - if ( VR(q2) != v ) { - *pr = 0; - return; - } else { - d = deg(v,q2); STOQ(d,dq); - pwrp(vl,q1,dq,pr); - return; - } - else if ( VR(q2) != v ) { - d = deg(v,q1); STOQ(d,dq); - pwrp(vl,q2,dq,pr); - return; - } - - if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) { - *pr = 0; - return; - } + if ( VR(q1) != v ) + if ( VR(q2) != v ) { + *pr = 0; + return; + } else { + d = deg(v,q2); STOQ(d,dq); + pwrp(vl,q1,dq,pr); + return; + } + else if ( VR(q2) != v ) { + d = deg(v,q1); STOQ(d,dq); + pwrp(vl,q2,dq,pr); + return; + } + + if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) { + *pr = 0; + return; + } - if ( deg(v,q1) >= deg(v,q2) ) { - g1 = q1; g2 = q2; - } else { - g2 = q1; g1 = q2; - } + if ( deg(v,q1) >= deg(v,q2) ) { + g1 = q1; g2 = q2; + } else { + g2 = q1; g1 = q2; + } - - if ( ( d1 = deg(v,g1) ) > ( d2 = deg(v,g2) ) ) { - j = d1 - 1; - adj = (P)ONE; - } else { - premp(nvl,g1,g2,&t); - d = deg(v,t); STOQ(d,dq); - pwrp(nvl,LC(g2),dq,&adj); - g1 = g2; g2 = t; - j = deg(v,g1) - 1; - } + + if ( ( d1 = deg(v,g1) ) > ( d2 = deg(v,g2) ) ) { + j = d1 - 1; + adj = (P)ONE; + } else { + premp(nvl,g1,g2,&t); + d = deg(v,t); STOQ(d,dq); + pwrp(nvl,LC(g2),dq,&adj); + g1 = g2; g2 = t; + j = deg(v,g1) - 1; + } - for ( lc = (P)ONE; ; ) { - if ( ( k = deg(v,g2) ) < 0 ) { - *pr = 0; - return; - } + for ( lc = (P)ONE; ; ) { + if ( ( k = deg(v,g2) ) < 0 ) { + *pr = 0; + return; + } - ptozp(g1,1,(Q *)&t,&s); g1 = s; ptozp(g2,1,(Q *)&t,&s); g2 = s; - if ( k == j ) - if ( !k ) { - divsp(nvl,g2,adj,pr); - return; - } else { - premp(nvl,g1,g2,&r); mulp(nvl,lc,lc,&m); - divsp(nvl,r,m,&q); - g1 = g2; g2 = q; - lc = LC(g1); /* g1 is not const */ - j = k - 1; - } - else { - d = j - k; STOQ(d,dq); - pwrp(nvl,(VR(g2)==v?LC(g2):g2),dq,&m); - mulp(nvl,g2,m,&m1); - pwrp(nvl,lc,dq,&m); divsp(nvl,m1,m,&t); - if ( k == 0 ) { - divsp(nvl,t,adj,pr); - return; - } else { - premp(nvl,g1,g2,&r); - mulp(nvl,lc,lc,&m1); mulp(nvl,m,m1,&m2); - divsp(nvl,r,m2,&q); - g1 = t; g2 = q; - if ( d % 2 ) { - chsgnp(g2,&t); g2 = t; - } - lc = LC(g1); /* g1 is not const */ - j = k - 1; - } - } - } + ptozp(g1,1,(Q *)&t,&s); g1 = s; ptozp(g2,1,(Q *)&t,&s); g2 = s; + if ( k == j ) + if ( !k ) { + divsp(nvl,g2,adj,pr); + return; + } else { + premp(nvl,g1,g2,&r); mulp(nvl,lc,lc,&m); + divsp(nvl,r,m,&q); + g1 = g2; g2 = q; + lc = LC(g1); /* g1 is not const */ + j = k - 1; + } + else { + d = j - k; STOQ(d,dq); + pwrp(nvl,(VR(g2)==v?LC(g2):g2),dq,&m); + mulp(nvl,g2,m,&m1); + pwrp(nvl,lc,dq,&m); divsp(nvl,m1,m,&t); + if ( k == 0 ) { + divsp(nvl,t,adj,pr); + return; + } else { + premp(nvl,g1,g2,&r); + mulp(nvl,lc,lc,&m1); mulp(nvl,m,m1,&m2); + divsp(nvl,r,m2,&q); + g1 = t; g2 = q; + if ( d % 2 ) { + chsgnp(g2,&t); g2 = t; + } + lc = LC(g1); /* g1 is not const */ + j = k - 1; + } + } + } } -void srcr(vl,v,p1,p2,pr) -VL vl; -V v; -P p1,p2,*pr; +void srcr(VL vl,V v,P p1,P p2,P *pr) { - P q1,q2,c,c1; - P tg,tg1,tg2,resg; - int index,mod; - Q a,b,f,q,t,s,u,n,m; - VL nvl; + P q1,q2,c,c1; + P tg,tg1,tg2,resg; + int index,mod; + Q a,b,f,q,t,s,u,n,m; + VL nvl; - reordvar(vl,v,&nvl); - reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); + reordvar(vl,v,&nvl); + reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); - if ( ( VR(q1) != v ) && ( VR(q2) != v ) ) { - *pr = 0; - return; - } - if ( VR(q1) != v ) { - pwrp(vl,q1,DEG(DC(q2)),pr); - return; - } - if ( VR(q2) != v ) { - pwrp(vl,q2,DEG(DC(q1)),pr); - return; - } - norm1c(q1,&a); norm1c(q2,&b); - n = DEG(DC(q1)); m = DEG(DC(q2)); - pwrq(a,m,&t); pwrq(b,n,&s); mulq(t,s,&u); - factorial(QTOS(n)+QTOS(m),&t); - mulq(u,t,&s); addq(s,s,&f); - for ( index = 0, q = ONE, c = 0; cmpq(f,q) >= 0; ) { - mod = lprime[index++]; - if ( !mod ) - error("sqfrum : lprime[] exhausted."); - ptomp(mod,LC(q1),&tg); - if ( !tg ) - continue; - ptomp(mod,LC(q2),&tg); - if ( !tg ) - continue; - ptomp(mod,q1,&tg1); ptomp(mod,q2,&tg2); - srchmp(nvl,mod,v,tg1,tg2,&resg); - chnremp(nvl,mod,c,q,resg,&c1); c = c1; - STOQ(mod,t); mulq(q,t,&s); q = s; - } - *pr = c; + if ( ( VR(q1) != v ) && ( VR(q2) != v ) ) { + *pr = 0; + return; + } + if ( VR(q1) != v ) { + pwrp(vl,q1,DEG(DC(q2)),pr); + return; + } + if ( VR(q2) != v ) { + pwrp(vl,q2,DEG(DC(q1)),pr); + return; + } + norm1c(q1,&a); norm1c(q2,&b); + n = DEG(DC(q1)); m = DEG(DC(q2)); + pwrq(a,m,&t); pwrq(b,n,&s); mulq(t,s,&u); + factorial(QTOS(n)+QTOS(m),&t); + mulq(u,t,&s); addq(s,s,&f); + for ( index = 0, q = ONE, c = 0; cmpq(f,q) >= 0; ) { + mod = get_lprime(index++); + ptomp(mod,LC(q1),&tg); + if ( !tg ) + continue; + ptomp(mod,LC(q2),&tg); + if ( !tg ) + continue; + ptomp(mod,q1,&tg1); ptomp(mod,q2,&tg2); + srchmp(nvl,mod,v,tg1,tg2,&resg); + chnremp(nvl,mod,c,q,resg,&c1); c = c1; + STOQ(mod,t); mulq(q,t,&s); q = s; + } + *pr = c; } -void res_ch_det(vl,v,p1,p2,pr) -VL vl; -V v; -P p1,p2,*pr; +void res_ch_det(VL vl,V v,P p1,P p2,P *pr) { - P q1,q2,c,c1; - P tg,tg1,tg2,resg; - int index,mod; - Q a,b,f,q,t,s,u,n,m; - VL nvl; + P q1,q2,c,c1; + P tg,tg1,tg2,resg; + int index,mod; + Q a,b,f,q,t,s,u,n,m; + VL nvl; - reordvar(vl,v,&nvl); - reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); + reordvar(vl,v,&nvl); + reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2); - if ( ( VR(q1) != v ) && ( VR(q2) != v ) ) { - *pr = 0; - return; - } - if ( VR(q1) != v ) { - pwrp(vl,q1,DEG(DC(q2)),pr); - return; - } - if ( VR(q2) != v ) { - pwrp(vl,q2,DEG(DC(q1)),pr); - return; - } - norm1c(q1,&a); norm1c(q2,&b); - n = DEG(DC(q1)); m = DEG(DC(q2)); - pwrq(a,m,&t); pwrq(b,n,&s); mulq(t,s,&u); - factorial(QTOS(n)+QTOS(m),&t); - mulq(u,t,&s); addq(s,s,&f); - for ( index = 0, q = ONE, c = 0; cmpq(f,q) >= 0; ) { - mod = lprime[index++]; - if ( !mod ) - error("sqfrum : lprime[] exhausted."); - ptomp(mod,LC(q1),&tg); - if ( !tg ) - continue; - ptomp(mod,LC(q2),&tg); - if ( !tg ) - continue; - ptomp(mod,q1,&tg1); ptomp(mod,q2,&tg2); - res_detmp(nvl,mod,v,tg1,tg2,&resg); - chnremp(nvl,mod,c,q,resg,&c1); c = c1; - STOQ(mod,t); mulq(q,t,&s); q = s; - } - *pr = c; + if ( ( VR(q1) != v ) && ( VR(q2) != v ) ) { + *pr = 0; + return; + } + if ( VR(q1) != v ) { + pwrp(vl,q1,DEG(DC(q2)),pr); + return; + } + if ( VR(q2) != v ) { + pwrp(vl,q2,DEG(DC(q1)),pr); + return; + } + norm1c(q1,&a); norm1c(q2,&b); + n = DEG(DC(q1)); m = DEG(DC(q2)); + pwrq(a,m,&t); pwrq(b,n,&s); mulq(t,s,&u); + factorial(QTOS(n)+QTOS(m),&t); + mulq(u,t,&s); addq(s,s,&f); + for ( index = 0, q = ONE, c = 0; cmpq(f,q) >= 0; ) { + mod = get_lprime(index++); + ptomp(mod,LC(q1),&tg); + if ( !tg ) + continue; + ptomp(mod,LC(q2),&tg); + if ( !tg ) + continue; + ptomp(mod,q1,&tg1); ptomp(mod,q2,&tg2); + res_detmp(nvl,mod,v,tg1,tg2,&resg); + chnremp(nvl,mod,c,q,resg,&c1); c = c1; + STOQ(mod,t); mulq(q,t,&s); q = s; + } + *pr = c; } -void res_detmp(vl,mod,v,p1,p2,dp) -VL vl; -int mod; -V v; -P p1,p2; -P *dp; +void res_detmp(VL vl,int mod,V v,P p1,P p2,P *dp) { - int n1,n2,n,sgn; - int i,j,k; - P mjj,mij,t,s,u,d; - P **mat; - P *mi,*mj; - DCP dc; + int n1,n2,n,sgn; + int i,j,k; + P mjj,mij,t,s,u,d; + P **mat; + P *mi,*mj; + DCP dc; - n1 = UDEG(p1); n2 = UDEG(p2); n = n1+n2; - mat = (P **)almat_pointer(n,n); - for ( dc = DC(p1); dc; dc = NEXT(dc) ) - mat[0][n1-QTOS(DEG(dc))] = COEF(dc); - for ( i = 1; i < n2; i++ ) - for ( j = 0; j <= n1; j++ ) - mat[i][i+j] = mat[0][j]; - for ( dc = DC(p2); dc; dc = NEXT(dc) ) - mat[n2][n2-QTOS(DEG(dc))] = COEF(dc); - for ( i = 1; i < n1; i++ ) - for ( j = 0; j <= n2; j++ ) - mat[i+n2][i+j] = mat[n2][j]; - for ( j = 0, d = (P)ONEM, sgn = 1; j < n; j++ ) { - for ( i = j; (i < n) && !mat[i][j]; i++ ); - if ( i == n ) { - *dp = 0; return; - } - for ( k = i; k < n; k++ ) - if ( mat[k][j] && (nmonop(mat[k][j]) < nmonop(mat[i][j]) ) ) - i = k; - if ( j != i ) { - mj = mat[j]; mat[j] = mat[i]; mat[i] = mj; sgn = -sgn; - } - for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ ) - for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n; k++ ) { - mulmp(vl,mod,mi[k],mjj,&t); mulmp(vl,mod,mj[k],mij,&s); - submp(vl,mod,t,s,&u); divsmp(vl,mod,u,d,&mi[k]); - } - d = mjj; - } - if ( sgn > 0 ) - *dp = d; - else - chsgnmp(mod,d,dp); + n1 = UDEG(p1); n2 = UDEG(p2); n = n1+n2; + mat = (P **)almat_pointer(n,n); + for ( dc = DC(p1); dc; dc = NEXT(dc) ) + mat[0][n1-QTOS(DEG(dc))] = COEF(dc); + for ( i = 1; i < n2; i++ ) + for ( j = 0; j <= n1; j++ ) + mat[i][i+j] = mat[0][j]; + for ( dc = DC(p2); dc; dc = NEXT(dc) ) + mat[n2][n2-QTOS(DEG(dc))] = COEF(dc); + for ( i = 1; i < n1; i++ ) + for ( j = 0; j <= n2; j++ ) + mat[i+n2][i+j] = mat[n2][j]; + for ( j = 0, d = (P)ONEM, sgn = 1; j < n; j++ ) { + for ( i = j; (i < n) && !mat[i][j]; i++ ); + if ( i == n ) { + *dp = 0; return; + } + for ( k = i; k < n; k++ ) + if ( mat[k][j] && (nmonop(mat[k][j]) < nmonop(mat[i][j]) ) ) + i = k; + if ( j != i ) { + mj = mat[j]; mat[j] = mat[i]; mat[i] = mj; sgn = -sgn; + } + for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ ) + for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n; k++ ) { + mulmp(vl,mod,mi[k],mjj,&t); mulmp(vl,mod,mj[k],mij,&s); + submp(vl,mod,t,s,&u); divsmp(vl,mod,u,d,&mi[k]); + } + d = mjj; + } + if ( sgn > 0 ) + *dp = d; + else + chsgnmp(mod,d,dp); } #if 0 -showmat(vl,mat,n) -VL vl; -P **mat; -int n; +showmat(VL vl,P **mat,int n) { - int i,j; - P t; + int i,j; + P t; - for ( i = 0; i < n; i++ ) { - for ( j = 0; j < n; j++ ) { - mptop(mat[i][j],&t); printp(vl,t); fprintf(out," "); - } - fprintf(out,"\n"); - } - fflush(out); + for ( i = 0; i < n; i++ ) { + for ( j = 0; j < n; j++ ) { + mptop(mat[i][j],&t); asir_printp(vl,t); fprintf(out," "); + } + fprintf(out,"\n"); + } + fflush(out); } -showmp(vl,p) -VL vl; -P p; +showmp(VL vl,P p) { - P t; + P t; - mptop(p,&t); printp(vl,t); fprintf(out,"\n"); + mptop(p,&t); asir_printp(vl,t); fprintf(out,"\n"); } #endif -void premp(vl,p1,p2,pr) -VL vl; -P p1,p2,*pr; +void premp(VL vl,P p1,P p2,P *pr) { - P m,m1,m2; - P *pw; - DCP dc; - V v1,v2; - register int i,j; - int n1,n2,d; + P m,m1,m2; + P *pw; + DCP dc; + V v1,v2; + register int i,j; + int n1,n2,d; - if ( NUM(p1) ) - if ( NUM(p2) ) - *pr = 0; - else - *pr = p1; - else if ( NUM(p2) ) - *pr = 0; - else if ( ( v1 = VR(p1) ) == ( v2 = VR(p2) ) ) { - n1 = deg(v1,p1); n2 = deg(v1,p2); - pw = (P *)ALLOCA((n1+1)*sizeof(P)); - bzero((char *)pw,(int)((n1+1)*sizeof(P))); + if ( NUM(p1) ) + if ( NUM(p2) ) + *pr = 0; + else + *pr = p1; + else if ( NUM(p2) ) + *pr = 0; + else if ( ( v1 = VR(p1) ) == ( v2 = VR(p2) ) ) { + n1 = deg(v1,p1); n2 = deg(v1,p2); + if ( n1 < n2 ) { + *pr = p1; + return; + } + pw = (P *)ALLOCA((n1+1)*sizeof(P)); + bzero((char *)pw,(int)((n1+1)*sizeof(P))); - for ( dc = DC(p1); dc; dc = NEXT(dc) ) - pw[QTOS(DEG(dc))] = COEF(dc); + for ( dc = DC(p1); dc; dc = NEXT(dc) ) + pw[QTOS(DEG(dc))] = COEF(dc); - for ( i = n1; i >= n2; i-- ) { - if ( pw[i] ) { - m = pw[i]; - for ( j = i; j >= 0; j-- ) { - mulp(vl,pw[j],LC(p2),&m1); pw[j] = m1; - } + for ( i = n1; i >= n2; i-- ) { + if ( pw[i] ) { + m = pw[i]; + for ( j = i; j >= 0; j-- ) { + mulp(vl,pw[j],LC(p2),&m1); pw[j] = m1; + } - for ( dc = DC(p2), d = i - n2; dc; dc = NEXT(dc) ) { - mulp(vl,COEF(dc),m,&m1); - subp(vl,pw[QTOS(DEG(dc))+d],m1,&m2); - pw[QTOS(DEG(dc))+d] = m2; - } - } else - for ( j = i; j >= 0; j-- ) - if ( pw[j] ) { - mulp(vl,pw[j],LC(p2),&m1); pw[j] = m1; - } - } - plisttop(pw,v1,n2-1,pr); - } else { - while ( v1 != vl->v && v2 != vl->v ) - vl = NEXT(vl); - if ( v1 == vl->v ) - *pr = 0; - else - *pr = p1; - } + for ( dc = DC(p2), d = i - n2; dc; dc = NEXT(dc) ) { + mulp(vl,COEF(dc),m,&m1); + subp(vl,pw[QTOS(DEG(dc))+d],m1,&m2); + pw[QTOS(DEG(dc))+d] = m2; + } + } else + for ( j = i; j >= 0; j-- ) + if ( pw[j] ) { + mulp(vl,pw[j],LC(p2),&m1); pw[j] = m1; + } + } + plisttop(pw,v1,n2-1,pr); + } else { + while ( v1 != vl->v && v2 != vl->v ) + vl = NEXT(vl); + if ( v1 == vl->v ) + *pr = 0; + else + *pr = p1; + } } -void ptozp0(p,pr) -P p; -P *pr; +void ptozp0(P p,P *pr) { - Q c; + Q c; - ptozp(p,1,&c,pr); + if ( qpcheck((Obj)p) ) + ptozp(p,1,&c,pr); + else + *pr = p; } -void mindegp(vl,p,mvlp,pr) -VL vl,*mvlp; -P p,*pr; +void mindegp(VL vl,P p,VL *mvlp,P *pr) { - P t; - VL nvl,tvl,avl; - V v; - int n,d; + P t; + VL nvl,tvl,avl; + V v; + int n,d; - clctv(vl,p,&nvl); v = nvl->v; d = getdeg(nvl->v,p); - for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) { - n = getdeg(avl->v,p); - if ( n < d ) { - v = avl->v; d = n; - } - } - if ( v != nvl->v ) { - reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t); - *pr = t; *mvlp = tvl; - } else { - *pr = p; *mvlp = nvl; - } + clctv(vl,p,&nvl); v = nvl->v; d = getdeg(nvl->v,p); + for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) { + n = getdeg(avl->v,p); + if ( n < d ) { + v = avl->v; d = n; + } + } + if ( v != nvl->v ) { + reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t); + *pr = t; *mvlp = tvl; + } else { + *pr = p; *mvlp = nvl; + } } -void maxdegp(vl,p,mvlp,pr) -VL vl,*mvlp; -P p,*pr; +void maxdegp(VL vl,P p,VL *mvlp,P *pr) { - P t; - VL nvl,tvl,avl; - V v; - int n,d; + P t; + VL nvl,tvl,avl; + V v; + int n,d; - clctv(vl,p,&nvl); v = nvl->v; d = getdeg(nvl->v,p); - for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) { - n = getdeg(avl->v,p); - if ( n > d ) { - v = avl->v; d = n; - } - } - if ( v != nvl->v ) { - reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t); - *pr = t; *mvlp = tvl; - } else { - *pr = p; *mvlp = nvl; - } + clctv(vl,p,&nvl); v = nvl->v; d = getdeg(nvl->v,p); + for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) { + n = getdeg(avl->v,p); + if ( n > d ) { + v = avl->v; d = n; + } + } + if ( v != nvl->v ) { + reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t); + *pr = t; *mvlp = tvl; + } else { + *pr = p; *mvlp = nvl; + } } -void min_common_vars_in_coefp(vl,p,mvlp,pr) -VL vl,*mvlp; -P p,*pr; +void min_common_vars_in_coefp(VL vl,P p,VL *mvlp,P *pr) { - P u,p0; - VL tvl,cvl,svl,uvl,avl,vl0; - int n,n0,d,d0; - DCP dc; + P u,p0; + VL tvl,cvl,svl,uvl,avl,vl0; + int n,n0,d,d0; + DCP dc; - clctv(vl,p,&tvl); vl = tvl; - for ( tvl = vl, n0 = 0; tvl; tvl = NEXT(tvl), n0++ ); - for ( avl = vl; avl; avl = NEXT(avl) ) { - if ( VR(p) != avl->v ) { - reordvar(vl,avl->v,&uvl); reorderp(uvl,vl,p,&u); - } else { - uvl = vl; u = p; - } - for ( cvl = NEXT(uvl), dc = DC(u); dc && cvl; dc = NEXT(dc) ) { - clctv(uvl,COEF(dc),&tvl); intersectv(cvl,tvl,&svl); cvl = svl; - } - if ( !cvl ) { - *mvlp = uvl; *pr = u; return; - } else { - for ( tvl = cvl, n = 0; tvl; tvl = NEXT(tvl), n++ ); - if ( n < n0 ) { - vl0 = uvl; p0 = u; n0 = n; d0 = getdeg(uvl->v,u); - } else if ( (n == n0) && ((d = getdeg(uvl->v,u)) < d0) ) { - vl0 = uvl; p0 = u; n0 = n; d0 = d; - } - } - } - *pr = p0; *mvlp = vl0; + clctv(vl,p,&tvl); vl = tvl; + for ( tvl = vl, n0 = 0; tvl; tvl = NEXT(tvl), n0++ ); + for ( avl = vl; avl; avl = NEXT(avl) ) { + if ( VR(p) != avl->v ) { + reordvar(vl,avl->v,&uvl); reorderp(uvl,vl,p,&u); + } else { + uvl = vl; u = p; + } + for ( cvl = NEXT(uvl), dc = DC(u); dc && cvl; dc = NEXT(dc) ) { + clctv(uvl,COEF(dc),&tvl); intersectv(cvl,tvl,&svl); cvl = svl; + } + if ( !cvl ) { + *mvlp = uvl; *pr = u; return; + } else { + for ( tvl = cvl, n = 0; tvl; tvl = NEXT(tvl), n++ ); + if ( n < n0 ) { + vl0 = uvl; p0 = u; n0 = n; d0 = getdeg(uvl->v,u); + } else if ( (n == n0) && ((d = getdeg(uvl->v,u)) < d0) ) { + vl0 = uvl; p0 = u; n0 = n; d0 = d; + } + } + } + *pr = p0; *mvlp = vl0; } -void minlcdegp(vl,p,mvlp,pr) -VL vl,*mvlp; -P p,*pr; +void minlcdegp(VL vl,P p,VL *mvlp,P *pr) { - P u,p0; - VL tvl,uvl,avl,vl0; - int d,d0; + P u,p0; + VL tvl,uvl,avl,vl0; + int d,d0; - clctv(vl,p,&tvl); vl = tvl; - vl0 = vl; p0 = p; d0 = homdeg(COEF(DC(p))); - for ( avl = NEXT(vl); avl; avl = NEXT(avl) ) { - reordvar(vl,avl->v,&uvl); reorderp(uvl,vl,p,&u); - d = homdeg(COEF(DC(u))); - if ( d < d0 ) { - vl0 = uvl; p0 = u; d0 = d; - } - } - *pr = p0; *mvlp = vl0; + clctv(vl,p,&tvl); vl = tvl; + vl0 = vl; p0 = p; d0 = homdeg(COEF(DC(p))); + for ( avl = NEXT(vl); avl; avl = NEXT(avl) ) { + reordvar(vl,avl->v,&uvl); reorderp(uvl,vl,p,&u); + d = homdeg(COEF(DC(u))); + if ( d < d0 ) { + vl0 = uvl; p0 = u; d0 = d; + } + } + *pr = p0; *mvlp = vl0; } -void sort_by_deg(n,p,pr) -int n; -P *p,*pr; +void sort_by_deg(int n,P *p,P *pr) { - int j,k,d,k0; - V v; + int j,k,d,k0; + V v; - for ( j = 0; j < n; j++ ) { - for ( k0 = k = j, d = deg(v = VR(p[0]),p[j]); - k < n; k++ ) - if ( deg(v,p[k]) < d ) { - k0 = k; - d = deg(v,p[k]); - } - pr[j] = p[k0]; - if ( j != k0 ) - p[k0] = p[j]; - } + for ( j = 0; j < n; j++ ) { + for ( k0 = k = j, d = deg(v = VR(p[0]),p[j]); + k < n; k++ ) + if ( deg(v,p[k]) < d ) { + k0 = k; + d = deg(v,p[k]); + } + pr[j] = p[k0]; + if ( j != k0 ) + p[k0] = p[j]; + } } -void sort_by_deg_rev(n,p,pr) -int n; -P *p,*pr; +void sort_by_deg_rev(int n,P *p,P *pr) { - int j,k,d,k0; - V v; + int j,k,d,k0; + V v; - for ( j = 0; j < n; j++ ) { - for ( k0 = k = j, d = deg(v = VR(p[0]),p[j]); - k < n; k++ ) - if ( deg(v,p[k]) > d ) { - k0 = k; - d = deg(v,p[k]); - } - pr[j] = p[k0]; - if ( j != k0 ) - p[k0] = p[j]; - } + for ( j = 0; j < n; j++ ) { + for ( k0 = k = j, d = deg(v = VR(p[0]),p[j]); + k < n; k++ ) + if ( deg(v,p[k]) > d ) { + k0 = k; + d = deg(v,p[k]); + } + pr[j] = p[k0]; + if ( j != k0 ) + p[k0] = p[j]; + } } -void getmindeg(v,p,dp) -V v; -P p; -Q *dp; +void getmindeg(V v,P p,Q *dp) { - Q dt,d; - DCP dc; + Q dt,d; + DCP dc; - if ( !p || NUM(p) ) - *dp = 0; - else if ( v == VR(p) ) { - for ( dc = DC(p); NEXT(dc); dc = NEXT(dc) ); - *dp = DEG(dc); - } else { - dc = DC(p); - getmindeg(v,COEF(dc),&d); - for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) { - getmindeg(v,COEF(dc),&dt); - if ( cmpq(dt,d) < 0 ) - d = dt; - } - *dp = d; - } + if ( !p || NUM(p) ) + *dp = 0; + else if ( v == VR(p) ) { + for ( dc = DC(p); NEXT(dc); dc = NEXT(dc) ); + *dp = DEG(dc); + } else { + dc = DC(p); + getmindeg(v,COEF(dc),&d); + for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) { + getmindeg(v,COEF(dc),&dt); + if ( cmpq(dt,d) < 0 ) + d = dt; + } + *dp = d; + } } -void minchdegp(vl,p,mvlp,pr) -VL vl,*mvlp; -P p,*pr; +void minchdegp(VL vl,P p,VL *mvlp,P *pr) { - P t; - VL tvl,nvl,avl; - int n,d,z; - V v; + P t; + VL tvl,nvl,avl; + int n,d,z; + V v; - if ( NUM(p) ) { - *mvlp = vl; - *pr = p; - return; - } - clctv(vl,p,&nvl); - v = nvl->v; - d = getchomdeg(v,p) + getlchomdeg(v,p,&z); - for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) { - n = getchomdeg(avl->v,p) + getlchomdeg(avl->v,p,&z); - if ( n < d ) { - v = avl->v; d = n; - } - } - if ( v != nvl->v ) { - reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t); - *pr = t; *mvlp = tvl; - } else { - *pr = p; *mvlp = nvl; - } + if ( NUM(p) ) { + *mvlp = vl; + *pr = p; + return; + } + clctv(vl,p,&nvl); + v = nvl->v; + d = getchomdeg(v,p) + getlchomdeg(v,p,&z); + for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) { + n = getchomdeg(avl->v,p) + getlchomdeg(avl->v,p,&z); + if ( n < d ) { + v = avl->v; d = n; + } + } + if ( v != nvl->v ) { + reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t); + *pr = t; *mvlp = tvl; + } else { + *pr = p; *mvlp = nvl; + } } -int getchomdeg(v,p) -V v; -P p; +int getchomdeg(V v,P p) { - int m,m1; - DCP dc; + int m,m1; + DCP dc; - if ( !p || NUM(p) ) - return ( 0 ); - else if ( VR(p) == v ) - return ( dbound(v,p) ); - else { - for ( dc = DC(p), m = 0; dc; dc = NEXT(dc) ) { - m1 = getchomdeg(v,COEF(dc))+QTOS(DEG(dc)); - m = MAX(m,m1); - } - return ( m ); - } + if ( !p || NUM(p) ) + return ( 0 ); + else if ( VR(p) == v ) + return ( dbound(v,p) ); + else { + for ( dc = DC(p), m = 0; dc; dc = NEXT(dc) ) { + m1 = getchomdeg(v,COEF(dc))+QTOS(DEG(dc)); + m = MAX(m,m1); + } + return ( m ); + } } -int getlchomdeg(v,p,d) -V v; -P p; -int *d; +int getlchomdeg(V v,P p,int *d) { - int m0,m1,d0,d1; - DCP dc; + int m0,m1,d0,d1; + DCP dc; - if ( !p || NUM(p) ) { - *d = 0; - return ( 0 ); - } else if ( VR(p) == v ) { - *d = QTOS(DEG(DC(p))); - return ( homdeg(LC(p)) ); - } else { - for ( dc = DC(p), m0 = 0, d0 = 0; dc; dc = NEXT(dc) ) { - m1 = getlchomdeg(v,COEF(dc),&d1)+QTOS(DEG(dc)); - if ( d1 > d0 ) { - m0 = m1; - d0 = d1; - } else if ( d1 == d0 ) - m0 = MAX(m0,m1); - } - *d = d0; - return ( m0 ); - } + if ( !p || NUM(p) ) { + *d = 0; + return ( 0 ); + } else if ( VR(p) == v ) { + *d = QTOS(DEG(DC(p))); + return ( homdeg(LC(p)) ); + } else { + for ( dc = DC(p), m0 = 0, d0 = 0; dc; dc = NEXT(dc) ) { + m1 = getlchomdeg(v,COEF(dc),&d1)+QTOS(DEG(dc)); + if ( d1 > d0 ) { + m0 = m1; + d0 = d1; + } else if ( d1 == d0 ) + m0 = MAX(m0,m1); + } + *d = d0; + return ( m0 ); + } } -int nmonop(p) -P p; +int nmonop(P p) { - int s; - DCP dc; + int s; + DCP dc; - if ( !p ) - return 0; - else - switch ( OID(p) ) { - case O_N: - return 1; break; - case O_P: - for ( dc = DC((P)p), s = 0; dc; dc = NEXT(dc) ) - s += nmonop(COEF(dc)); - return s; break; - default: - return 0; - } + if ( !p ) + return 0; + else + switch ( OID(p) ) { + case O_N: + return 1; break; + case O_P: + for ( dc = DC((P)p), s = 0; dc; dc = NEXT(dc) ) + s += nmonop(COEF(dc)); + return s; break; + default: + return 0; + } } -int qpcheck(p) -Obj p; +int qpcheck(Obj p) { - DCP dc; + DCP dc; - if ( !p ) - return 1; - else - switch ( OID(p) ) { - case O_N: - return RATN((Num)p)?1:0; - case O_P: - for ( dc = DC((P)p); dc; dc = NEXT(dc) ) - if ( !qpcheck((Obj)COEF(dc)) ) - return 0; - return 1; - default: - return 0; - } + if ( !p ) + return 1; + else + switch ( OID(p) ) { + case O_N: + return RATN((Num)p)?1:0; + case O_P: + for ( dc = DC((P)p); dc; dc = NEXT(dc) ) + if ( !qpcheck((Obj)COEF(dc)) ) + return 0; + return 1; + default: + return 0; + } } /* check if p is univariate and all coeffs are INT or LM */ -int uzpcheck(p) -Obj p; +int uzpcheck(Obj p) { - DCP dc; - P c; + DCP dc; + P c; - if ( !p ) - return 1; - else - switch ( OID(p) ) { - case O_N: - return (RATN((Num)p)&&INT(p))||(NID((Num)p)==N_LM); - case O_P: - for ( dc = DC((P)p); dc; dc = NEXT(dc) ) { - c = COEF(dc); - if ( !NUM(c) || !uzpcheck(c) ) - return 0; - } - return 1; - default: - return 0; - } + if ( !p ) + return 1; + else + switch ( OID(p) ) { + case O_N: + return (RATN((Num)p)&&INT(p))||(NID((Num)p)==N_LM); + case O_P: + for ( dc = DC((P)p); dc; dc = NEXT(dc) ) { + c = COEF(dc); + if ( !NUM(c) || !uzpcheck((Obj)c) ) + return 0; + } + return 1; + default: + return 0; + } } -int p_mag(p) -P p; +int p_mag(P p) { - int s; - DCP dc; + int s; + DCP dc; - if ( !p ) - return 0; - else if ( OID(p) == O_N ) - return n_bits(NM((Q)p))+(INT((Q)p)?0:n_bits(DN((Q)p))); - else { - for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) - s += p_mag(COEF(dc)); - return s; - } + if ( !p ) + return 0; + else if ( OID(p) == O_N ) + return n_bits(NM((Q)p))+(INT((Q)p)?0:n_bits(DN((Q)p))); + else { + for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) + s += p_mag(COEF(dc)); + return s; + } +} + +int maxblenp(P p) +{ + int s,t; + DCP dc; + + if ( !p ) + return 0; + else if ( OID(p) == O_N ) + return n_bits(NM((Q)p))+(INT((Q)p)?0:n_bits(DN((Q)p))); + else { + for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) { + t = maxblenp(COEF(dc)); + s = MAX(t,s); + } + return s; + } }