Code coverage tests

This page documents the degree to which the PARI/GP source code is tested by our public test suite, distributed with the source distribution in directory src/test/. This is measured by the gcov utility; we then process gcov output using the lcov frond-end.

We test a few variants depending on Configure flags on the pari.math.u-bordeaux.fr machine (x86_64 architecture), and agregate them in the final report:

The target is to exceed 90% coverage for all mathematical modules (given that branches depending on DEBUGLEVEL or DEBUGMEM are not covered). This script is run to produce the results below.

LCOV - code coverage report
Current view: top level - basemath - RgV.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.18.1 lcov report (development 30005-fc14bb602a) Lines: 509 578 88.1 %
Date: 2025-02-18 09:22:46 Functions: 95 104 91.3 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2000  The PARI group.
       2             : 
       3             : This file is part of the PARI/GP package.
       4             : 
       5             : PARI/GP is free software; you can redistribute it and/or modify it under the
       6             : terms of the GNU General Public License as published by the Free Software
       7             : Foundation; either version 2 of the License, or (at your option) any later
       8             : version. It is distributed in the hope that it will be useful, but WITHOUT
       9             : ANY WARRANTY WHATSOEVER.
      10             : 
      11             : Check the License for details. You should have received a copy of it, along
      12             : with the package; see the file 'COPYING'. If not, write to the Free Software
      13             : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
      14             : 
      15             : #include "pari.h"
      16             : #include "paripriv.h"
      17             : 
      18             : int
      19     1233258 : RgM_is_ZM(GEN x)
      20             : {
      21     1233258 :   long i, j, h, l = lg(x);
      22     1233258 :   if (l == 1) return 1;
      23     1232593 :   h = lgcols(x);
      24     1232579 :   if (h == 1) return 1;
      25     4670320 :   for (j = l-1; j > 0; j--)
      26    22322262 :     for (i = h-1; i > 0; i--)
      27    18884360 :       if (typ(gcoeff(x,i,j)) != t_INT) return 0;
      28     1074823 :   return 1;
      29             : }
      30             : 
      31             : int
      32         203 : RgM_is_QM(GEN x)
      33             : {
      34         203 :   long i, j, h, l = lg(x);
      35         203 :   if (l == 1) return 1;
      36         189 :   h = lgcols(x);
      37         189 :   if (h == 1) return 1;
      38        1218 :   for (j = l-1; j > 0; j--)
      39       15057 :     for (i = h-1; i > 0; i--)
      40       14028 :       if (!is_rational_t(typ(gcoeff(x,i,j)))) return 0;
      41         175 :   return 1;
      42             : }
      43             : 
      44             : int
      45          49 : RgV_is_ZMV(GEN V)
      46             : {
      47          49 :   long i, l = lg(V);
      48         399 :   for (i=1; i<l; i++)
      49         350 :     if (typ(gel(V,i))!=t_MAT || !RgM_is_ZM(gel(V,i)))
      50           0 :       return 0;
      51          49 :   return 1;
      52             : }
      53             : 
      54             : /********************************************************************/
      55             : /**                                                                **/
      56             : /**                   GENERIC LINEAR ALGEBRA                       **/
      57             : /**                                                                **/
      58             : /********************************************************************/
      59             : /*           GENERIC  MULTIPLICATION involving zc/zm                */
      60             : 
      61             : /* x[i,] * y */
      62             : static GEN
      63     8351427 : RgMrow_zc_mul_i(GEN x, GEN y, long c, long i)
      64             : {
      65     8351427 :   pari_sp av = avma;
      66     8351427 :   GEN s = NULL;
      67             :   long j;
      68   835297806 :   for (j=1; j<c; j++)
      69             :   {
      70   826949523 :     long t = y[j];
      71   826949523 :     if (!t) continue;
      72    29016860 :     if (!s) { s = gmulgs(gcoeff(x,i,j),t); continue; }
      73    20880814 :     switch(t)
      74             :     {
      75    15092642 :       case  1: s = gadd(s, gcoeff(x,i,j)); break;
      76      239922 :       case -1: s = gsub(s, gcoeff(x,i,j)); break;
      77     5548250 :       default: s = gadd(s, gmulgs(gcoeff(x,i,j), t)); break;
      78             :     }
      79             :   }
      80     8348283 :   return s? gerepileupto(av, s): gc_const(av, gen_0);
      81             : }
      82             : GEN
      83       70028 : RgMrow_zc_mul(GEN x, GEN y, long i) { return RgMrow_zc_mul_i(x,y,lg(y),i); }
      84             : /* x nonempty t_MAT, y a compatible zc (dimension > 0). */
      85             : static GEN
      86      239837 : RgM_zc_mul_i(GEN x, GEN y, long c, long l)
      87             : {
      88      239837 :   GEN z = cgetg(l,t_COL);
      89             :   long i;
      90     8521216 :   for (i = 1; i < l; i++) gel(z,i) = RgMrow_zc_mul_i(x,y,c,i);
      91      239833 :   return z;
      92             : }
      93             : GEN
      94       71981 : RgM_zc_mul(GEN x, GEN y) { return RgM_zc_mul_i(x,y, lg(x), lgcols(x)); }
      95             : /* x t_MAT, y a compatible zm (dimension > 0). */
      96             : GEN
      97       57113 : RgM_zm_mul(GEN x, GEN y)
      98             : {
      99       57113 :   long j, c, l = lg(x), ly = lg(y);
     100       57113 :   GEN z = cgetg(ly, t_MAT);
     101       57113 :   if (l == 1) return z;
     102       57113 :   c = lgcols(x);
     103      224968 :   for (j = 1; j < ly; j++) gel(z,j) = RgM_zc_mul_i(x, gel(y,j), l,c);
     104       57112 :   return z;
     105             : }
     106             : 
     107             : /* x[i,]*y, l = lg(y) > 1 */
     108             : static GEN
     109    32305586 : RgMrow_ZC_mul_i(GEN x, GEN y, long i, long l)
     110             : {
     111    32305586 :   pari_sp av = avma;
     112    32305586 :   GEN t = gmul(gcoeff(x,i,1), gel(y,1)); /* l > 1 ! */
     113             :   long j;
     114  5021588583 :   for (j=2; j<l; j++)
     115  4989603110 :     if (signe(gel(y,j))) t = gadd(t, gmul(gcoeff(x,i,j), gel(y,j)));
     116    31985473 :   return gerepileupto(av,t);
     117             : }
     118             : 
     119             : /* compatible t_MAT * t_COL, lx = lg(x) = lg(y) > 1, l = lgcols(x) */
     120             : static GEN
     121     1928449 : RgM_ZC_mul_i(GEN x, GEN y, long lx, long l)
     122             : {
     123     1928449 :   GEN z = cgetg(l,t_COL);
     124             :   long i;
     125    34235001 :   for (i=1; i<l; i++) gel(z,i) = RgMrow_ZC_mul_i(x,y,i,lx);
     126     1925818 :   return z;
     127             : }
     128             : 
     129             : GEN
     130     1928483 : RgM_ZM_mul_worker(GEN y, GEN x)
     131     1928483 : { return RgM_ZC_mul_i(x, y, lg(x), lgcols(x)); }
     132             : 
     133             : /* mostly useful when y is sparse */
     134             : GEN
     135      354882 : RgM_ZM_mul(GEN x, GEN y)
     136             : {
     137      354882 :   pari_sp av = avma;
     138             :   GEN worker;
     139      354882 :   if (lg(x) == 1) return cgetg(lg(y), t_MAT);
     140      354882 :   worker = snm_closure(is_entry("_RgM_ZM_mul_worker"),mkvec(x));
     141      354888 :   return gerepileupto(av, gen_parapply(worker, y));
     142             : }
     143             : 
     144             : static GEN
     145      210025 : RgV_zc_mul_i(GEN x, GEN y, long l)
     146             : {
     147             :   long i;
     148      210025 :   GEN z = gen_0;
     149      210025 :   pari_sp av = avma;
     150     8213714 :   for (i = 1; i < l; i++) z = gadd(z, gmulgs(gel(x,i), y[i]));
     151      210024 :   return gerepileupto(av, z);
     152             : }
     153             : GEN
     154       83384 : RgV_zc_mul(GEN x, GEN y) { return RgV_zc_mul_i(x, y, lg(x)); }
     155             : 
     156             : GEN
     157       34216 : RgV_zm_mul(GEN x, GEN y)
     158             : {
     159       34216 :   long j, l = lg(x), ly = lg(y);
     160       34216 :   GEN z = cgetg(ly, t_VEC);
     161      160856 :   for (j = 1; j < ly; j++) gel(z,j) = RgV_zc_mul_i(x, gel(y,j), l);
     162       34215 :   return z;
     163             : }
     164             : 
     165             : /* scalar product x.x */
     166             : GEN
     167     9449959 : RgV_dotsquare(GEN x)
     168             : {
     169     9449959 :   long i, lx = lg(x);
     170     9449959 :   pari_sp av = avma;
     171             :   GEN z;
     172     9449959 :   if (lx == 1) return gen_0;
     173     9449959 :   z = gsqr(gel(x,1));
     174    21171017 :   for (i=2; i<lx; i++)
     175             :   {
     176    11721281 :     z = gadd(z, gsqr(gel(x,i)));
     177    11721252 :     if (gc_needed(av,3))
     178             :     {
     179           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgV_dotsquare, i = %ld",i);
     180           0 :       z = gerepileupto(av, z);
     181             :     }
     182             :   }
     183     9449736 :   return gerepileupto(av,z);
     184             : }
     185             : 
     186             : /* scalar product x.y, lx = lg(x) = lg(y) */
     187             : static GEN
     188    13620969 : RgV_dotproduct_i(GEN x, GEN y, long lx)
     189             : {
     190    13620969 :   pari_sp av = avma;
     191             :   long i;
     192             :   GEN z;
     193    13620969 :   if (lx == 1) return gen_0;
     194    13620570 :   z = gmul(gel(x,1),gel(y,1));
     195   219050376 :   for (i=2; i<lx; i++)
     196             :   {
     197   205431354 :     z = gadd(z, gmul(gel(x,i), gel(y,i)));
     198   205431834 :     if (gc_needed(av,3))
     199             :     {
     200           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgV_dotproduct, i = %ld",i);
     201           0 :       z = gerepileupto(av, z);
     202             :     }
     203             :   }
     204    13619022 :   return gerepileupto(av,z);
     205             : }
     206             : GEN
     207     1013399 : RgV_dotproduct(GEN x,GEN y)
     208             : {
     209     1013399 :   if (x == y) return RgV_dotsquare(x);
     210     1013399 :   return RgV_dotproduct_i(x, y, lg(x));
     211             : }
     212             : /* v[1] + ... + v[lg(v)-1] */
     213             : GEN
     214     3032830 : RgV_sum(GEN v)
     215             : {
     216             :   GEN p;
     217     3032830 :   long i, l = lg(v);
     218     3032830 :   if (l == 1) return gen_0;
     219     7381328 :   p = gel(v,1); for (i=2; i<l; i++) p = gadd(p, gel(v,i));
     220     3032787 :   return p;
     221             : }
     222             : /* v[1] + ... + v[n]. Assume lg(v) > n. */
     223             : GEN
     224           0 : RgV_sumpart(GEN v, long n)
     225             : {
     226             :   GEN p;
     227             :   long i;
     228           0 :   if (!n) return gen_0;
     229           0 :   p = gel(v,1); for (i=2; i<=n; i++) p = gadd(p, gel(v,i));
     230           0 :   return p;
     231             : }
     232             : /* v[m] + ... + v[n]. Assume lg(v) > n, m > 0. */
     233             : GEN
     234           0 : RgV_sumpart2(GEN v, long m, long n)
     235             : {
     236             :   GEN p;
     237             :   long i;
     238           0 :   if (n < m) return gen_0;
     239           0 :   p = gel(v,m); for (i=m+1; i<=n; i++) p = gadd(p, gel(v,i));
     240           0 :   return p;
     241             : }
     242             : GEN
     243         400 : RgM_sumcol(GEN A)
     244             : {
     245         400 :   long i,j,m,l = lg(A);
     246             :   GEN v;
     247             : 
     248         400 :   if (l == 1) return cgetg(1,t_MAT);
     249         400 :   if (l == 2) return gcopy(gel(A,1));
     250         216 :   m = lgcols(A);
     251         216 :   v = cgetg(m, t_COL);
     252         718 :   for (i = 1; i < m; i++)
     253             :   {
     254         502 :     pari_sp av = avma;
     255         502 :     GEN s = gcoeff(A,i,1);
     256        1214 :     for (j = 2; j < l; j++) s = gadd(s, gcoeff(A,i,j));
     257         502 :     gel(v, i) = gerepileupto(av, s);
     258             :   }
     259         216 :   return v;
     260             : }
     261             : 
     262             : static GEN
     263     3336121 : _gmul(void *data, GEN x, GEN y)
     264     3336121 : { (void)data; return gmul(x,y); }
     265             : 
     266             : GEN
     267      453210 : RgV_prod(GEN x)
     268             : {
     269      453210 :   return gen_product(x, NULL, _gmul);
     270             : }
     271             : 
     272             : /*                    ADDITION SCALAR + MATRIX                     */
     273             : /* x square matrix, y scalar; create the square matrix x + y*Id */
     274             : GEN
     275        7623 : RgM_Rg_add(GEN x, GEN y)
     276             : {
     277        7623 :   long l = lg(x), i, j;
     278        7623 :   GEN z = cgetg(l,t_MAT);
     279             : 
     280        7623 :   if (l==1) return z;
     281        7623 :   if (l != lgcols(x)) pari_err_OP("+", x, y);
     282       57358 :   for (i=1; i<l; i++)
     283             :   {
     284       49735 :     GEN zi = cgetg(l,t_COL), xi = gel(x,i);
     285       49735 :     gel(z,i) = zi;
     286     2057170 :     for (j=1; j<l; j++)
     287     2007435 :       gel(zi,j) = i==j? gadd(y,gel(xi,j)): gcopy(gel(xi,j));
     288             :   }
     289        7623 :   return z;
     290             : }
     291             : GEN
     292           0 : RgM_Rg_sub(GEN x, GEN y)
     293             : {
     294           0 :   long l = lg(x), i, j;
     295           0 :   GEN z = cgetg(l,t_MAT);
     296             : 
     297           0 :   if (l==1) return z;
     298           0 :   if (l != lgcols(x)) pari_err_OP("-", x, y);
     299           0 :   for (i=1; i<l; i++)
     300             :   {
     301           0 :     GEN zi = cgetg(l,t_COL), xi = gel(x,i);
     302           0 :     gel(z,i) = zi;
     303           0 :     for (j=1; j<l; j++)
     304           0 :       gel(zi,j) = i==j? gsub(gel(xi,j), y): gcopy(gel(xi,j));
     305             :   }
     306           0 :   return z;
     307             : }
     308             : GEN
     309         739 : RgM_Rg_add_shallow(GEN x, GEN y)
     310             : {
     311         739 :   long l = lg(x), i, j;
     312         739 :   GEN z = cgetg(l,t_MAT);
     313             : 
     314         739 :   if (l==1) return z;
     315         739 :   if (l != lgcols(x)) pari_err_OP( "+", x, y);
     316        2384 :   for (i=1; i<l; i++)
     317             :   {
     318        1645 :     GEN zi = cgetg(l,t_COL), xi = gel(x,i);
     319        1645 :     gel(z,i) = zi;
     320        9456 :     for (j=1; j<l; j++) gel(zi,j) = gel(xi,j);
     321        1645 :     gel(zi,i) = gadd(gel(zi,i), y);
     322             :   }
     323         739 :   return z;
     324             : }
     325             : GEN
     326      314460 : RgM_Rg_sub_shallow(GEN x, GEN y)
     327             : {
     328      314460 :   long l = lg(x), i, j;
     329      314460 :   GEN z = cgetg(l,t_MAT);
     330             : 
     331      314458 :   if (l==1) return z;
     332      314458 :   if (l != lgcols(x)) pari_err_OP( "-", x, y);
     333     2029643 :   for (i=1; i<l; i++)
     334             :   {
     335     1715214 :     GEN zi = cgetg(l,t_COL), xi = gel(x,i);
     336     1715222 :     gel(z,i) = zi;
     337    27273821 :     for (j=1; j<l; j++) gel(zi,j) = gel(xi,j);
     338     1715222 :     gel(zi,i) = gsub(gel(zi,i), y);
     339             :   }
     340      314429 :   return z;
     341             : }
     342             : 
     343             : GEN
     344     2390850 : RgC_Rg_add(GEN x, GEN y)
     345             : {
     346     2390850 :   long k, lx = lg(x);
     347     2390850 :   GEN z = cgetg(lx, t_COL);
     348     2390851 :   if (lx == 1)
     349             :   {
     350           0 :     if (isintzero(y)) return z;
     351           0 :     pari_err_TYPE2("+",x,y);
     352             :   }
     353     2390851 :   gel(z,1) = gadd(y,gel(x,1));
     354     6746918 :   for (k = 2; k < lx; k++) gel(z,k) = gcopy(gel(x,k));
     355     2390842 :   return z;
     356             : }
     357             : GEN
     358       24029 : RgC_Rg_sub(GEN x, GEN y)
     359             : {
     360       24029 :   long k, lx = lg(x);
     361       24029 :   GEN z = cgetg(lx, t_COL);
     362       24029 :   if (lx == 1)
     363             :   {
     364           0 :     if (isintzero(y)) return z;
     365           0 :     pari_err_TYPE2("-",x,y);
     366             :   }
     367       24029 :   gel(z,1) = gsub(gel(x,1), y);
     368       69113 :   for (k = 2; k < lx; k++) gel(z,k) = gcopy(gel(x,k));
     369       24029 :   return z;
     370             : }
     371             : /* a - x */
     372             : GEN
     373       32759 : Rg_RgC_sub(GEN a, GEN x)
     374             : {
     375       32759 :   long k, lx = lg(x);
     376       32759 :   GEN z = cgetg(lx,t_COL);
     377       32759 :   if (lx == 1)
     378             :   {
     379           0 :     if (isintzero(a)) return z;
     380           0 :     pari_err_TYPE2("-",a,x);
     381             :   }
     382       32759 :   gel(z,1) = gsub(a, gel(x,1));
     383       74745 :   for (k = 2; k < lx; k++) gel(z,k) = gneg(gel(x,k));
     384       32759 :   return z;
     385             : }
     386             : 
     387             : static GEN
     388    18683207 : RgC_add_i(GEN x, GEN y, long lx)
     389             : {
     390    18683207 :   GEN A = cgetg(lx, t_COL);
     391             :   long i;
     392   142201076 :   for (i=1; i<lx; i++) gel(A,i) = gadd(gel(x,i), gel(y,i));
     393    18682885 :   return A;
     394             : }
     395             : GEN
     396    15419974 : RgC_add(GEN x, GEN y) { return RgC_add_i(x, y, lg(x)); }
     397             : GEN
     398     2546889 : RgV_add(GEN x, GEN y)
     399    10435388 : { pari_APPLY_type(t_VEC, gadd(gel(x,i), gel(y,i))) }
     400             : 
     401             : static GEN
     402     5754281 : RgC_sub_i(GEN x, GEN y, long lx)
     403             : {
     404             :   long i;
     405     5754281 :   GEN A = cgetg(lx, t_COL);
     406   634341351 :   for (i=1; i<lx; i++) gel(A,i) = gsub(gel(x,i), gel(y,i));
     407     5753036 :   return A;
     408             : }
     409             : GEN
     410     4846684 : RgC_sub(GEN x, GEN y) { return RgC_sub_i(x, y, lg(x)); }
     411             : GEN
     412      356526 : RgV_sub(GEN x, GEN y)
     413     3032044 : { pari_APPLY_type(t_VEC, gsub(gel(x,i), gel(y,i))) }
     414             : 
     415             : GEN
     416      690767 : RgM_add(GEN x, GEN y)
     417             : {
     418      690767 :   long lx = lg(x), l, j;
     419             :   GEN z;
     420      690767 :   if (lx == 1) return cgetg(1, t_MAT);
     421      690767 :   z = cgetg(lx, t_MAT); l = lgcols(x);
     422     3953999 :   for (j = 1; j < lx; j++) gel(z,j) = RgC_add_i(gel(x,j), gel(y,j), l);
     423      690767 :   return z;
     424             : }
     425             : GEN
     426      173205 : RgM_sub(GEN x, GEN y)
     427             : {
     428      173205 :   long lx = lg(x), l, j;
     429             :   GEN z;
     430      173205 :   if (lx == 1) return cgetg(1, t_MAT);
     431      173205 :   z = cgetg(lx, t_MAT); l = lgcols(x);
     432     1080839 :   for (j = 1; j < lx; j++) gel(z,j) = RgC_sub_i(gel(x,j), gel(y,j), l);
     433      173200 :   return z;
     434             : }
     435             : 
     436             : static GEN
     437     3920438 : RgC_neg_i(GEN x, long lx)
     438             : {
     439             :   long i;
     440     3920438 :   GEN y = cgetg(lx, t_COL);
     441    29928715 :   for (i=1; i<lx; i++) gel(y,i) = gneg(gel(x,i));
     442     3920439 :   return y;
     443             : }
     444             : GEN
     445      932309 : RgC_neg(GEN x) { return RgC_neg_i(x, lg(x)); }
     446             : GEN
     447        4515 : RgV_neg(GEN x)
     448       60473 : { pari_APPLY_type(t_VEC, gneg(gel(x,i))) }
     449             : GEN
     450      542310 : RgM_neg(GEN x)
     451             : {
     452      542310 :   long i, hx, lx = lg(x);
     453      542310 :   GEN y = cgetg(lx, t_MAT);
     454      542310 :   if (lx == 1) return y;
     455      542303 :   hx = lgcols(x);
     456     3530432 :   for (i=1; i<lx; i++) gel(y,i) = RgC_neg_i(gel(x,i), hx);
     457      542303 :   return y;
     458             : }
     459             : 
     460             : GEN
     461     4735512 : RgV_RgC_mul(GEN x, GEN y)
     462             : {
     463     4735512 :   long lx = lg(x);
     464     4735512 :   if (lx != lg(y)) pari_err_OP("operation 'RgV_RgC_mul'", x, y);
     465     4735428 :   return RgV_dotproduct_i(x, y, lx);
     466             : }
     467             : GEN
     468        1687 : RgC_RgV_mul(GEN x, GEN y)
     469             : {
     470        1687 :   long i, ly = lg(y);
     471        1687 :   GEN z = cgetg(ly,t_MAT);
     472        5061 :   for (i=1; i<ly; i++) gel(z,i) = RgC_Rg_mul(x, gel(y,i));
     473        1687 :   return z;
     474             : }
     475             : GEN
     476           0 : RgC_RgM_mul(GEN x, GEN y)
     477             : {
     478           0 :   long i, ly = lg(y);
     479           0 :   GEN z = cgetg(ly,t_MAT);
     480           0 :   if (ly != 1 && lgcols(y) != 2) pari_err_OP("operation 'RgC_RgM_mul'",x,y);
     481           0 :   for (i=1; i<ly; i++) gel(z,i) = RgC_Rg_mul(x, gcoeff(y,1,i));
     482           0 :   return z;
     483             : }
     484             : GEN
     485           0 : RgM_RgV_mul(GEN x, GEN y)
     486             : {
     487           0 :   if (lg(x) != 2) pari_err_OP("operation 'RgM_RgV_mul'", x,y);
     488           0 :   return RgC_RgV_mul(gel(x,1), y);
     489             : }
     490             : 
     491             : /* x[i,]*y, l = lg(y) > 1 */
     492             : static GEN
     493   115959228 : RgMrow_RgC_mul_i(GEN x, GEN y, long i, long l)
     494             : {
     495   115959228 :   pari_sp av = avma;
     496   115959228 :   GEN t = gmul(gcoeff(x,i,1), gel(y,1)); /* l > 1 ! */
     497             :   long j;
     498   987631715 :   for (j=2; j<l; j++)
     499             :   {
     500   871681623 :     GEN c = gcoeff(x,i,j);
     501   871681623 :     if (!isintzero(c)) t = gadd(t, gmul(c, gel(y,j)));
     502             :   }
     503   115950092 :   return gerepileupto(av,t);
     504             : }
     505             : GEN
     506        4655 : RgMrow_RgC_mul(GEN x, GEN y, long i)
     507        4655 : { return RgMrow_RgC_mul_i(x, y, i, lg(x)); }
     508             : 
     509             : static GEN
     510          28 : RgM_RgC_mul_FpM(GEN x, GEN y, GEN p)
     511             : {
     512          28 :   pari_sp av = avma;
     513             :   GEN r;
     514          28 :   if (lgefint(p) == 3)
     515             :   {
     516          14 :     ulong pp = uel(p, 2);
     517          14 :     r = Flm_Flc_mul(RgM_to_Flm(x, pp), RgV_to_Flv(y, pp), pp);
     518          14 :     r = Flc_to_ZC_inplace(r);
     519             :   }
     520             :   else
     521          14 :     r = FpM_FpC_mul(RgM_to_FpM(x, p), RgC_to_FpC(y, p), p);
     522          28 :   return gerepileupto(av, FpC_to_mod(r, p));
     523             : }
     524             : 
     525             : static GEN
     526          28 : RgM_RgC_mul_FqM(GEN x, GEN y, GEN pol, GEN p)
     527             : {
     528          28 :   pari_sp av = avma;
     529          28 :   GEN b, T = RgX_to_FpX(pol, p);
     530          28 :   if (signe(T) == 0) pari_err_OP("*", x, y);
     531          28 :   b = FqM_FqC_mul(RgM_to_FqM(x, T, p), RgC_to_FqC(y, T, p), T, p);
     532          28 :   return gerepileupto(av, FqC_to_mod(b, T, p));
     533             : }
     534             : 
     535             : static GEN
     536    31184662 : RgM_RgC_mul_fast(GEN x, GEN y)
     537             : {
     538             :   GEN p, pol;
     539             :   long pa;
     540    31184662 :   long t = RgM_RgC_type(x,y, &p,&pol,&pa);
     541    31184902 :   switch(t)
     542             :   {
     543     8835435 :     case t_INT:    return ZM_ZC_mul(x,y);
     544      126811 :     case t_FRAC:   return QM_QC_mul(x,y);
     545          91 :     case t_FFELT:  return FFM_FFC_mul(x, y, pol);
     546          28 :     case t_INTMOD: return RgM_RgC_mul_FpM(x, y, p);
     547          27 :     case RgX_type_code(t_POLMOD, t_INTMOD):
     548          27 :                    return RgM_RgC_mul_FqM(x, y, pol, p);
     549    22222510 :     default:       return NULL;
     550             :   }
     551             : }
     552             : 
     553             : /* compatible t_MAT * t_COL, lx = lg(x) = lg(y) > 1, l = lgcols(x) */
     554             : static GEN
     555    34021973 : RgM_RgC_mul_i(GEN x, GEN y, long lx, long l)
     556             : {
     557    34021973 :   GEN z = cgetg(l,t_COL);
     558             :   long i;
     559   149971363 :   for (i=1; i<l; i++) gel(z,i) = RgMrow_RgC_mul_i(x,y,i,lx);
     560    34017269 :   return z;
     561             : }
     562             : 
     563             : GEN
     564    31184662 : RgM_RgC_mul(GEN x, GEN y)
     565             : {
     566    31184662 :   long lx = lg(x);
     567             :   GEN z;
     568    31184662 :   if (lx != lg(y)) pari_err_OP("operation 'RgM_RgC_mul'", x,y);
     569    31184668 :   if (lx == 1) return cgetg(1,t_COL);
     570    31184668 :   z = RgM_RgC_mul_fast(x, y);
     571    31184898 :   if (z) return z;
     572    22222505 :   return RgM_RgC_mul_i(x, y, lx, lgcols(x));
     573             : }
     574             : 
     575             : GEN
     576      296033 : RgV_RgM_mul(GEN x, GEN y)
     577             : {
     578      296033 :   long i, lx, ly = lg(y);
     579             :   GEN z;
     580      296033 :   if (ly == 1) return cgetg(1,t_VEC);
     581      296026 :   lx = lg(x);
     582      296026 :   if (lx != lgcols(y)) pari_err_OP("operation 'RgV_RgM_mul'", x,y);
     583      296019 :   z = cgetg(ly, t_VEC);
     584     3424920 :   for (i=1; i<ly; i++) gel(z,i) = RgV_dotproduct_i(x, gel(y,i), lx);
     585      295929 :   return z;
     586             : }
     587             : 
     588             : static GEN
     589       57148 : RgM_mul_FpM_i(GEN x, GEN y, GEN p)
     590             : {
     591       57148 :   if (lgefint(p) == 3)
     592             :   {
     593       57076 :     ulong pp = uel(p, 2);
     594       57076 :     if (pp==2) return F2m_to_mod(F2m_mul(RgM_to_F2m(x), RgM_to_F2m(y)));
     595       57027 :     if (pp==3) return F3m_to_mod(F3m_mul(RgM_to_F3m(x), RgM_to_F3m(y)));
     596       56873 :     return Flm_to_mod(Flm_mul(RgM_to_Flm(x, pp), RgM_to_Flm(y, pp), pp), pp);
     597             :   }
     598          72 :   return FpM_to_mod(FpM_mul(RgM_to_FpM(x,p), RgM_to_FpM(y,p), p), p);
     599             : }
     600             : static GEN
     601       57148 : RgM_mul_FpM(GEN x, GEN y, GEN p)
     602       57148 : { pari_sp av = avma; return gerepileupto(av, RgM_mul_FpM_i(x, y, p)); }
     603             : 
     604             : static GEN
     605       26005 : RgM_mul_FqM(GEN x, GEN y, GEN pol, GEN p)
     606             : {
     607       26005 :   pari_sp av = avma;
     608       26005 :   GEN b, T = RgX_to_FpX(pol, p);
     609       26005 :   if (signe(T) == 0) pari_err_OP("*", x, y);
     610       26005 :   b = FqM_mul(RgM_to_FqM(x, T, p), RgM_to_FqM(y, T, p), T, p);
     611       26005 :   return gerepileupto(av, FqM_to_mod(b, T, p));
     612             : }
     613             : 
     614             : static GEN
     615       12516 : RgM_liftred(GEN x, GEN T)
     616       12516 : { return RgXQM_red(liftpol_shallow(x), T); }
     617             : 
     618             : static GEN
     619        1463 : RgM_mul_ZXQM(GEN x, GEN y, GEN T)
     620             : {
     621        1463 :   pari_sp av = avma;
     622        1463 :   GEN b = ZXQM_mul(RgM_liftred(x,T), RgM_liftred(y, T), T);
     623        1463 :   return gerepilecopy(av, QXQM_to_mod_shallow(b,T));
     624             : }
     625             : 
     626             : static GEN
     627         133 : RgM_sqr_ZXQM(GEN x, GEN T)
     628             : {
     629         133 :   pari_sp av = avma;
     630         133 :   GEN b = ZXQM_sqr(RgM_liftred(x, T), T);
     631         133 :   return gerepilecopy(av, QXQM_to_mod_shallow(b,T));
     632             : }
     633             : 
     634             : static GEN
     635        4725 : RgM_mul_QXQM(GEN x, GEN y, GEN T)
     636             : {
     637        4725 :   pari_sp av = avma;
     638        4725 :   GEN b = QXQM_mul(RgM_liftred(x, T), RgM_liftred(y, T), T);
     639        4725 :   return gerepilecopy(av, QXQM_to_mod_shallow(b,T));
     640             : }
     641             : 
     642             : static GEN
     643           7 : RgM_sqr_QXQM(GEN x, GEN T)
     644             : {
     645           7 :   pari_sp av = avma;
     646           7 :   GEN b = QXQM_sqr(RgM_liftred(x, T), T);
     647           7 :   return gerepilecopy(av, QXQM_to_mod_shallow(b,T));
     648             : }
     649             : 
     650             : INLINE int
     651        4774 : RgX_is_monic_ZX(GEN pol)
     652        4774 : { return RgX_is_ZX(pol) && ZX_is_monic(pol); }
     653             : 
     654             : static GEN
     655     7575452 : RgM_mul_fast(GEN x, GEN y)
     656             : {
     657             :   GEN p, pol;
     658             :   long pa;
     659     7575452 :   long t = RgM_type2(x,y, &p,&pol,&pa);
     660     7575508 :   switch(t)
     661             :   {
     662     2689608 :     case t_INT:    return ZM_mul(x,y);
     663      117138 :     case t_FRAC:   return QM_mul(x,y);
     664        4389 :     case t_FFELT:  return FFM_mul(x, y, pol);
     665       57085 :     case t_INTMOD: return RgM_mul_FpM(x, y, p);
     666        1470 :     case RgX_type_code(t_POLMOD, t_INT):
     667        1470 :                    return ZX_is_monic(pol)? RgM_mul_ZXQM(x, y, pol): NULL;
     668        4746 :     case RgX_type_code(t_POLMOD, t_FRAC):
     669        4746 :                    return RgX_is_monic_ZX(pol)? RgM_mul_QXQM(x, y, pol): NULL;
     670       26003 :     case RgX_type_code(t_POLMOD, t_INTMOD):
     671       26003 :                    return RgM_mul_FqM(x, y, pol, p);
     672     4675069 :     default:       return NULL;
     673             :   }
     674             : }
     675             : 
     676             : static GEN
     677        1365 : RgM_sqr_fast(GEN x)
     678             : {
     679             :   GEN p, pol;
     680             :   long pa;
     681        1365 :   long t = RgM_type(x, &p,&pol,&pa);
     682        1365 :   switch(t)
     683             :   {
     684         231 :     case t_INT:    return ZM_sqr(x);
     685         700 :     case t_FRAC:   return QM_sqr(x);
     686         105 :     case t_FFELT:  return FFM_mul(x, x, pol);
     687          63 :     case t_INTMOD: return RgM_mul_FpM(x, x, p);
     688         140 :     case RgX_type_code(t_POLMOD, t_INT):
     689         140 :                    return ZX_is_monic(pol)? RgM_sqr_ZXQM(x, pol): NULL;
     690          28 :     case RgX_type_code(t_POLMOD, t_FRAC):
     691          28 :                    return RgX_is_monic_ZX(pol)? RgM_sqr_QXQM(x, pol): NULL;
     692           0 :     case RgX_type_code(t_POLMOD, t_INTMOD):
     693           0 :                    return RgM_mul_FqM(x, x, pol, p);
     694          98 :     default:       return NULL;
     695             :   }
     696             : }
     697             : 
     698             : /* lx, ly > 1 */
     699             : static GEN
     700     4675095 : RgM_mul_i(GEN x, GEN y, long lx, long ly)
     701             : {
     702     4675095 :   GEN z = cgetg(ly, t_MAT);
     703     4675089 :   long j, l = lgcols(x);
     704    16474374 :   for (j = 1; j < ly; j++) gel(z,j) = RgM_RgC_mul_i(x, gel(y,j), lx, l);
     705     4675041 :   return z;
     706             : }
     707             : GEN
     708     7591229 : RgM_mul(GEN x, GEN y)
     709             : {
     710     7591229 :   long lx, ly = lg(y);
     711             :   GEN z;
     712     7591229 :   if (ly == 1) return cgetg(1,t_MAT);
     713     7575479 :   lx = lg(x);
     714     7575479 :   if (lx != lgcols(y)) pari_err_OP("operation 'RgM_mul'", x,y);
     715     7575478 :   if (lx == 1) return zeromat(0,ly-1);
     716     7575450 :   z = RgM_mul_fast(x, y);
     717     7575506 :   if (z) return z;
     718     4675094 :   return RgM_mul_i(x, y, lx, ly);
     719             : }
     720             : 
     721             : GEN
     722        1400 : RgM_sqr(GEN x)
     723             : {
     724        1400 :   long j, lx = lg(x);
     725             :   GEN z;
     726        1400 :   if (lx == 1) return cgetg(1, t_MAT);
     727        1365 :   if (lx != lgcols(x)) pari_err_OP("operation 'RgM_mul'", x,x);
     728        1365 :   z = RgM_sqr_fast(x);
     729        1365 :   if (z) return z;
     730         126 :   z = cgetg(lx, t_MAT);
     731         497 :   for (j=1; j<lx; j++) gel(z,j) = RgM_RgC_mul_i(x, gel(x,j), lx, lx);
     732         126 :   return z;
     733             : }
     734             : 
     735             : /* assume result is symmetric */
     736             : GEN
     737           0 : RgM_multosym(GEN x, GEN y)
     738             : {
     739           0 :   long j, lx, ly = lg(y);
     740             :   GEN M;
     741           0 :   if (ly == 1) return cgetg(1,t_MAT);
     742           0 :   lx = lg(x);
     743           0 :   if (lx != lgcols(y)) pari_err_OP("operation 'RgM_multosym'", x,y);
     744           0 :   if (lx == 1) return cgetg(1,t_MAT);
     745           0 :   if (ly != lgcols(x)) pari_err_OP("operation 'RgM_multosym'", x,y);
     746           0 :   M = cgetg(ly, t_MAT);
     747           0 :   for (j=1; j<ly; j++)
     748             :   {
     749           0 :     GEN z = cgetg(ly,t_COL), yj = gel(y,j);
     750             :     long i;
     751           0 :     for (i=1; i<j; i++) gel(z,i) = gcoeff(M,j,i);
     752           0 :     for (i=j; i<ly; i++)gel(z,i) = RgMrow_RgC_mul_i(x,yj,i,lx);
     753           0 :     gel(M,j) = z;
     754             :   }
     755           0 :   return M;
     756             : }
     757             : /* x~ * y, assuming result is symmetric */
     758             : GEN
     759        7663 : RgM_transmultosym(GEN x, GEN y)
     760             : {
     761        7663 :   long i, j, l, ly = lg(y);
     762             :   GEN M;
     763        7663 :   if (ly == 1) return cgetg(1,t_MAT);
     764        7663 :   if (lg(x) != ly) pari_err_OP("operation 'RgM_transmultosym'", x,y);
     765        7663 :   l = lgcols(y);
     766        7663 :   if (lgcols(x) != l) pari_err_OP("operation 'RgM_transmultosym'", x,y);
     767        7663 :   M = cgetg(ly, t_MAT);
     768       30820 :   for (i=1; i<ly; i++)
     769             :   {
     770       23157 :     GEN xi = gel(x,i), c = cgetg(ly,t_COL);
     771       23157 :     gel(M,i) = c;
     772       47490 :     for (j=1; j<i; j++)
     773       24333 :       gcoeff(M,i,j) = gel(c,j) = RgV_dotproduct_i(xi,gel(y,j),l);
     774       23157 :     gel(c,i) = RgV_dotproduct_i(xi,gel(y,i),l);
     775             :   }
     776        7663 :   return M;
     777             : }
     778             : /* x~ * y */
     779             : GEN
     780           0 : RgM_transmul(GEN x, GEN y)
     781             : {
     782           0 :   long i, j, l, lx, ly = lg(y);
     783             :   GEN M;
     784           0 :   if (ly == 1) return cgetg(1,t_MAT);
     785           0 :   lx = lg(x);
     786           0 :   l = lgcols(y);
     787           0 :   if (lgcols(x) != l) pari_err_OP("operation 'RgM_transmul'", x,y);
     788           0 :   M = cgetg(ly, t_MAT);
     789           0 :   for (i=1; i<ly; i++)
     790             :   {
     791           0 :     GEN yi = gel(y,i), c = cgetg(lx,t_COL);
     792           0 :     gel(M,i) = c;
     793           0 :     for (j=1; j<lx; j++) gel(c,j) = RgV_dotproduct_i(yi,gel(x,j),l);
     794             :   }
     795           0 :   return M;
     796             : }
     797             : 
     798             : GEN
     799     4695734 : gram_matrix(GEN x)
     800             : {
     801     4695734 :   long i,j, l, lx = lg(x);
     802             :   GEN M;
     803     4695734 :   if (!is_matvec_t(typ(x))) pari_err_TYPE("gram",x);
     804     4695730 :   if (lx == 1) return cgetg(1,t_MAT);
     805     4695716 :   l = lgcols(x);
     806     4695714 :   M = cgetg(lx,t_MAT);
     807    14087089 :   for (i=1; i<lx; i++)
     808             :   {
     809     9391382 :     GEN xi = gel(x,i), c = cgetg(lx,t_COL);
     810     9391379 :     gel(M,i) = c;
     811    14087060 :     for (j=1; j<i; j++)
     812     4695688 :       gcoeff(M,i,j) = gel(c,j) = RgV_dotproduct_i(xi,gel(x,j),l);
     813     9391372 :     gel(c,i) = RgV_dotsquare(xi);
     814             :   }
     815     4695707 :   return M;
     816             : }
     817             : 
     818             : static GEN
     819        3717 : _RgM_add(void *E, GEN x, GEN y) { (void)E; return RgM_add(x, y); }
     820             : 
     821             : static GEN
     822           0 : _RgM_sub(void *E, GEN x, GEN y) { (void)E; return RgM_sub(x, y); }
     823             : 
     824             : static GEN
     825        5600 : _RgM_cmul(void *E, GEN P, long a, GEN x) { (void)E; return RgM_Rg_mul(x,gel(P,a+2)); }
     826             : 
     827             : static GEN
     828         231 : _RgM_sqr(void *E, GEN x) { (void) E; return RgM_sqr(x); }
     829             : 
     830             : static GEN
     831         735 : _RgM_mul(void *E, GEN x, GEN y) { (void) E; return RgM_mul(x, y); }
     832             : 
     833             : static GEN
     834        4039 : _RgM_one(void *E) { long *n = (long*) E; return matid(*n); }
     835             : 
     836             : static GEN
     837           0 : _RgM_zero(void *E) { long *n = (long*) E; return zeromat(*n,*n); }
     838             : 
     839             : static GEN
     840        2821 : _RgM_red(void *E, GEN x) { (void)E; return x; }
     841             : 
     842             : static struct bb_algebra RgM_algebra = { _RgM_red, _RgM_add, _RgM_sub,
     843             :        _RgM_mul, _RgM_sqr, _RgM_one, _RgM_zero };
     844             : 
     845             : /* generates the list of powers of x of degree 0,1,2,...,l*/
     846             : GEN
     847         168 : RgM_powers(GEN x, long l)
     848             : {
     849         168 :   long n = lg(x)-1;
     850         168 :   return gen_powers(x,l,1,(void *) &n, &_RgM_sqr, &_RgM_mul, &_RgM_one);
     851             : }
     852             : 
     853             : GEN
     854         490 : RgX_RgMV_eval(GEN Q, GEN x)
     855             : {
     856         490 :   long n = lg(x)>1 ? lg(gel(x,1))-1:0;
     857         490 :   return gen_bkeval_powers(Q,degpol(Q),x,(void*)&n,&RgM_algebra,&_RgM_cmul);
     858             : }
     859             : 
     860             : GEN
     861        1393 : RgX_RgM_eval(GEN Q, GEN x)
     862             : {
     863        1393 :   long n = lg(x)-1;
     864        1393 :   return gen_bkeval(Q,degpol(Q),x,1,(void*)&n,&RgM_algebra,&_RgM_cmul);
     865             : }
     866             : 
     867             : GEN
     868     4413016 : RgC_Rg_div(GEN x, GEN y)
     869    19050316 : { pari_APPLY_type(t_COL, gdiv(gel(x,i),y)) }
     870             : 
     871             : GEN
     872    11844615 : RgC_Rg_mul(GEN x, GEN y)
     873    75470419 : { pari_APPLY_type(t_COL, gmul(gel(x,i),y)) }
     874             : 
     875             : GEN
     876       31157 : RgV_Rg_mul(GEN x, GEN y)
     877     1200766 : { pari_APPLY_type(t_VEC, gmul(gel(x,i),y)) }
     878             : 
     879             : GEN
     880      604183 : RgM_Rg_div(GEN X, GEN c) {
     881      604183 :   long i, j, h, l = lg(X);
     882      604183 :   GEN A = cgetg(l, t_MAT);
     883      604183 :   if (l == 1) return A;
     884      604183 :   h = lgcols(X);
     885     2784120 :   for (j=1; j<l; j++)
     886             :   {
     887     2179958 :     GEN a = cgetg(h, t_COL), x = gel(X, j);
     888    17358388 :     for (i = 1; i < h; i++) gel(a,i) = gdiv(gel(x,i), c);
     889     2179937 :     gel(A,j) = a;
     890             :   }
     891      604162 :   return A;
     892             : }
     893             : GEN
     894     1248841 : RgM_Rg_mul(GEN X, GEN c) {
     895     1248841 :   long i, j, h, l = lg(X);
     896     1248841 :   GEN A = cgetg(l, t_MAT);
     897     1248851 :   if (l == 1) return A;
     898     1248851 :   h = lgcols(X);
     899     4084272 :   for (j=1; j<l; j++)
     900             :   {
     901     2835500 :     GEN a = cgetg(h, t_COL), x = gel(X, j);
     902    12930312 :     for (i = 1; i < h; i++) gel(a,i) = gmul(gel(x,i), c);
     903     2835418 :     gel(A,j) = a;
     904             :   }
     905     1248772 :   return A;
     906             : }
     907             : 
     908             : /********************************************************************/
     909             : /*                                                                  */
     910             : /*                    SCALAR TO MATRIX/VECTOR                       */
     911             : /*                                                                  */
     912             : /********************************************************************/
     913             : /* fill the square nxn matrix equal to t*Id */
     914             : static void
     915    12724438 : fill_scalmat(GEN y, GEN t, long n)
     916             : {
     917             :   long i;
     918    47966190 :   for (i = 1; i <= n; i++)
     919             :   {
     920    35242117 :     gel(y,i) = zerocol(n);
     921    35241752 :     gcoeff(y,i,i) = t;
     922             :   }
     923    12724073 : }
     924             : 
     925             : GEN
     926      869702 : scalarmat(GEN x, long n) {
     927      869702 :   GEN y = cgetg(n+1, t_MAT);
     928      869679 :   if (!n) return y;
     929      869679 :   fill_scalmat(y, gcopy(x), n); return y;
     930             : }
     931             : GEN
     932     3154048 : scalarmat_shallow(GEN x, long n) {
     933     3154048 :   GEN y = cgetg(n+1, t_MAT);
     934     3154120 :   fill_scalmat(y, x, n); return y;
     935             : }
     936             : GEN
     937         217 : scalarmat_s(long x, long n) {
     938         217 :   GEN y = cgetg(n+1, t_MAT);
     939         217 :   if (!n) return y;
     940         217 :   fill_scalmat(y, stoi(x), n); return y;
     941             : }
     942             : GEN
     943     8701064 : matid(long n) {
     944             :   GEN y;
     945     8701064 :   if (n < 0) pari_err_DOMAIN("matid", "size", "<", gen_0, stoi(n));
     946     8701057 :   y = cgetg(n+1, t_MAT);
     947     8701095 :   fill_scalmat(y, gen_1, n); return y;
     948             : }
     949             : 
     950             : INLINE GEN
     951     2265812 : scalarcol_i(GEN x, long n, long c)
     952             : {
     953             :   long i;
     954     2265812 :   GEN y = cgetg(n+1,t_COL);
     955     2265807 :   if (!n) return y;
     956     2265807 :   gel(y,1) = c? gcopy(x): x;
     957     6758249 :   for (i=2; i<=n; i++) gel(y,i) = gen_0;
     958     2265805 :   return y;
     959             : }
     960             : 
     961             : GEN
     962      785693 : scalarcol(GEN x, long n) { return scalarcol_i(x,n,1); }
     963             : 
     964             : GEN
     965     1480122 : scalarcol_shallow(GEN x, long n) { return scalarcol_i(x,n,0); }
     966             : 
     967             : int
     968       17597 : RgM_isscalar(GEN x, GEN s)
     969             : {
     970       17597 :   long i, j, lx = lg(x);
     971             : 
     972       17597 :   if (lx == 1) return 1;
     973       17597 :   if (lx != lgcols(x)) return 0;
     974       17597 :   if (!s) s = gcoeff(x,1,1);
     975             : 
     976       49797 :   for (j=1; j<lx; j++)
     977             :   {
     978       40505 :     GEN c = gel(x,j);
     979      154099 :     for (i=1; i<j; )
     980      120492 :       if (!gequal0(gel(c,i++))) return 0;
     981             :     /* i = j */
     982       33607 :     if (!gequal(gel(c,i++),s)) return 0;
     983      176003 :     for (   ; i<lx; )
     984      143803 :       if (!gequal0(gel(c,i++))) return 0;
     985             :   }
     986        9292 :   return 1;
     987             : }
     988             : 
     989             : int
     990        3664 : RgM_isidentity(GEN x)
     991             : {
     992        3664 :   long i,j, lx = lg(x);
     993             : 
     994        3664 :   if (lx == 1) return 1;
     995        3664 :   if (lx != lgcols(x)) return 0;
     996        8798 :   for (j=1; j<lx; j++)
     997             :   {
     998        8518 :     GEN c = gel(x,j);
     999       40052 :     for (i=1; i<j; )
    1000       33373 :       if (!gequal0(gel(c,i++))) return 0;
    1001             :     /* i = j */
    1002        6679 :     if (!gequal1(gel(c,i++))) return 0;
    1003       49750 :     for (   ; i<lx; )
    1004       44616 :       if (!gequal0(gel(c,i++))) return 0;
    1005             :   }
    1006         280 :   return 1;
    1007             : }
    1008             : 
    1009             : long
    1010         644 : RgC_is_ei(GEN x)
    1011             : {
    1012         644 :   long i, j = 0, l = lg(x);
    1013        3472 :   for (i = 1; i < l; i++)
    1014             :   {
    1015        2828 :     GEN c = gel(x,i);
    1016        2828 :     if (gequal0(c)) continue;
    1017         644 :     if (!gequal1(c) || j) return 0;
    1018         644 :     j = i;
    1019             :   }
    1020         644 :   return j;
    1021             : }
    1022             : 
    1023             : int
    1024         336 : RgM_isdiagonal(GEN x)
    1025             : {
    1026         336 :   long i,j, lx = lg(x);
    1027         336 :   if (lx == 1) return 1;
    1028         336 :   if (lx != lgcols(x)) return 0;
    1029             : 
    1030        3220 :   for (j=1; j<lx; j++)
    1031             :   {
    1032        2891 :     GEN c = gel(x,j);
    1033       18452 :     for (i=1; i<j; i++)
    1034       15561 :       if (!gequal0(gel(c,i))) return 0;
    1035       18452 :     for (i++; i<lx; i++)
    1036       15568 :       if (!gequal0(gel(c,i))) return 0;
    1037             :   }
    1038         329 :   return 1;
    1039             : }
    1040             : int
    1041         315 : isdiagonal(GEN x) { return (typ(x)==t_MAT) && RgM_isdiagonal(x); }
    1042             : 
    1043             : GEN
    1044       22358 : RgM_det_triangular(GEN mat)
    1045             : {
    1046       22358 :   long i,l = lg(mat);
    1047             :   pari_sp av;
    1048             :   GEN s;
    1049             : 
    1050       22358 :   if (l<3) return l<2? gen_1: gcopy(gcoeff(mat,1,1));
    1051       20671 :   av = avma; s = gcoeff(mat,1,1);
    1052      121695 :   for (i=2; i<l; i++) s = gmul(s,gcoeff(mat,i,i));
    1053       20671 :   return av==avma? gcopy(s): gerepileupto(av,s);
    1054             : }
    1055             : 
    1056             : GEN
    1057      478032 : RgV_kill0(GEN v)
    1058             : {
    1059             :   long i, l;
    1060      478032 :   GEN w = cgetg_copy(v, &l);
    1061   130113800 :   for (i = 1; i < l; i++)
    1062             :   {
    1063   129636000 :     GEN a = gel(v,i);
    1064   129636000 :     gel(w,i) = gequal0(a) ? NULL: a;
    1065             :   }
    1066      477800 :   return w;
    1067             : }

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