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#include "def.h"
#include "macro.h"
INT all_points_phg();
INT scan_galois(OP v)
{
OP d=callocobject();
INT i,erg=OK;
printf("degree:");scan(INTEGER,d);
erg += m_il_v(S_I_I(d)+2,v); C_O_K(v,GALOISRING);
erg += copy(d,S_V_I(v,0));
printf("characteristic:");scan(INTEGER,S_V_I(v,1));
for (i=0;i<S_I_I(d);i++)
{
erg += scan(INTEGER,S_V_I(v,i+2));
}
erg += freeall(d);
ENDR("scan_galois");
}
INT add_galois(OP p1,OP p2, OP p3) //p3 = p2+p1
{
INT erg =OK,i;
// funktioniert auch mit p1=p2.....
copy(p1,p3);
for (i=2;i<S_V_LI(p3);i++)
{
M_I_I((S_V_II(p1,i)+S_V_II(p2,i))%S_GR_CI(p3), S_V_I(p3,i)) ;
}
ENDR("add_galois");
}
INT t_galois_polynom(OP g, OP p)
{
INT i,erg=OK;
OP z;
init(MONOPOLY,p);
z=p;
for (i=2;i<S_V_LI(g);i++)
{
OP mo;
mo = callocobject();
b_sk_mo(callocobject(),callocobject(),mo);
C_L_S(z,mo);
M_I_I(S_V_II(g,i),S_PO_K(z));
M_I_I(i-2,S_PO_S(z));
if (i+1 <S_V_LI(g)) { C_L_N(z,callocobject()); z=S_L_N(z); init(MONOPOLY,z); }
}
ENDR("t_galois_polynom");
}
static OP mgg_c=NULL; //charakteristik zu multiplikationstafel
static OP mgg_d=NULL; // degree zu multiplikationstafel
static OP mgg_mt=NULL; //multiplikationstafel
static OP mgg_pl=NULL; //irred polynom
static INT mgg_change_counter; // count the new entries in the mult table
INT get_galois_irred(OP g, OP ip) // irreduzible zu galois ring
{
INT erg =OK;
OP v;
if (
(S_I_I(mgg_c)==S_GR_CI(g))
&&
(S_I_I(mgg_d)==S_GR_DI(g))
&&
(not EMPTYP(mgg_pl))
) {
copy(mgg_pl,ip);
goto endr_ende;
}
v=callocobject();
factorize(S_GR_C(g),v);
get_ff_irred(S_V_I(v,0) ,S_GR_D(g),ip);
copy(S_GR_C(g),mgg_c);
copy(S_GR_D(g),mgg_d);
copy(ip,mgg_pl);
freeall(v);
ENDR("get_galois_irred");
}
INT t_polynom_galois(OP p ,INT c, INT d, OP g)
{
INT erg =OK,i=2;
OP z=p;
m_il_nv(d+2,g); C_O_K(g,GALOISRING);
m_i_i(d,S_V_I(g,0));
m_i_i(c,S_V_I(g,1));
if (S_L_S(z) == NULL) goto endr_ende;
while (z!=NULL)
{
M_I_I( S_I_I(S_PO_K(z)),
S_V_I(g,2+S_I_I(S_PO_S(z)) )
);
z = S_L_N(z);
}
ENDR("t_polynom_galois");
}
INT init_galois_global( OP charac, OP deg )
{
INT erg =OK;
if ((S_I_I(mgg_c)==S_I_I(charac)) && (S_I_I(mgg_d)==S_I_I(deg))) return OK;
if (S_I_I(mgg_c) != 0) // previously different galois ring
{
// store mult table
if (mgg_change_counter>0)
store_result_2(charac,deg,"galois_mult",mgg_mt);
}
freeself(mgg_mt);
// load mult table
check_result_2(charac,deg,"galois_mult",mgg_mt);
if (emptyp(mgg_mt)) // first time
{
OP h=callocobject();
hoch(charac,deg,h);
if (S_I_I(h) <= 256) // only table in small cases
m_lh_m(h,h,mgg_mt);
freeall(h);
}
copy(charac,mgg_c);
copy(deg,mgg_d);
mgg_change_counter=0;
ENDR("init_galois_global");
}
INT galois_anfang()
{
INT erg =OK;
CALLOCOBJECT4(mgg_c,mgg_d,mgg_mt,mgg_pl);
M_I_I(0,mgg_c);
M_I_I(0,mgg_d);
mgg_change_counter=0;
ENDR("galois_anfang");
}
INT galois_ende()
{
INT erg =OK;
if (S_I_I(mgg_c) != 0) // previously different galois ring
{
// store mult table
if (mgg_change_counter>0)
S2R(mgg_c,mgg_d,"galois_mult",mgg_mt);
}
FREEALL4(mgg_c,mgg_d,mgg_mt,mgg_pl);
ENDR("galois_ende");
}
INT index_galois(OP g)
// index of galois ring element
{
INT d=S_GR_DI(g);
INT c=S_GR_CI(g);
INT res=0,i,m;
for (i=0,m=1;i<d;i++,m*=c)
res += S_V_II(g,2+i)*m;
return res;
}
INT mult_galois_galois(OP p1, OP p2, OP p3)
{
INT erg = OK,p1i,p2i;
CTO(GALOISRING,"mult_galois(1)",p1);
CTO(GALOISRING,"mult_galois(2)",p2);
SYMCHECK(S_GR_CI(p1)!=S_GR_CI(p2),"mult_galois_galois:different characteristics");
SYMCHECK(S_GR_DI(p1)!=S_GR_DI(p2),"mult_galois_galois:different degrees");
{
OP poly1,poly2,poly3,poly4,irred,diverg;
if (S_GR_DI(p1)==1) {
copy(p1,p3);
M_I_I((S_V_II(p1,2)*S_V_II(p2,2))%S_GR_CI(p1), S_V_I(p3,2));
goto endr_ende;
}
if (
(S_GR_CI(p1)!=S_I_I(mgg_c)) || (S_GR_DI(p1)!=S_I_I(mgg_d))
)
init_galois_global(S_GR_C(p1),S_GR_D(p1)); // initialize irred polynomial and mult_table
if (not EMPTYP(mgg_mt)) // check if result available
{
p1i=index_galois(p1);
p2i=index_galois(p2);
if (p1i >= S_M_HI(mgg_mt)) error("mult_galois_galois:I1");
if (p2i >= S_M_HI(mgg_mt)) error("mult_galois_galois:I2");
if (not EMPTYP(S_M_IJ(mgg_mt,p1i,p2i))) // result of multiplicazion is known
{
copy(S_M_IJ(mgg_mt,p1i,p2i),p3);
goto endr_ende;
}
}
CALLOCOBJECT6(poly1,poly2,poly3,poly4,irred,diverg);
t_galois_polynom(p1,poly1);
t_galois_polynom(p2,poly2);
mult(poly1,poly2,poly3);
mod(poly3,S_GR_C(p1),poly3);
get_galois_irred(p1,irred);
quores(poly3,irred,diverg,poly4);
mod(poly4,S_GR_C(p1),poly4);
t_polynom_galois(poly4,S_GR_CI(p1),S_GR_DI(p1),p3);
FREEALL6(poly1,poly2,poly3,poly4,irred,diverg);
if (not EMPTYP(mgg_mt)) // check if result available
{
mgg_change_counter++;
copy(p3,S_M_IJ(mgg_mt,p1i,p2i));
}
}
ENDR("mult_galois");
}
INT mult_galois(OP a, OP b, OP c)
{
INT erg = OK;
switch (S_O_K(b)) {
case GALOISRING:
erg += mult_galois_galois(a,b,c);
break;
case VECTOR:
{
INT i;
copy(b,c);
for (i=0;i<S_V_LI(c);i++)
erg += mult_galois(a,S_V_I(b,i),S_V_I(c,i));
}
break;
default:
printobjectkind(b);
error("mult_galois(2): wrong second type");
erg = ERROR;
}
ENDR("mult_galois");
}
INT unitp_galois(OP g)
{
INT j,erg =OK;
for (j=2;j<S_V_LI(g);j++)
{
if (ggt_i(S_V_II(g,j), S_GR_CI(g)) == 1) return TRUE;
}
return FALSE;
ENDR("unitp_galois");
}
INT nullp_galois(OP g)
/* AK 131206 V3.1 */
{
INT erg = OK;
INT i;
for (i=2;i<S_V_LI(g);i++)
if (S_V_II(g,i) != 0) return FALSE;
return TRUE;
ENDR("nullp_galois");
}
INT null_galois(OP a,OP b)
{
INT erg =OK,i;
copy(a,b);
for (i=2;i<S_V_LI(b);i++) M_I_I(0,S_V_I(b,i));
ENDR("null_galois");
}
INT einsp_galois(OP g)
{
INT erg = OK;
INT i;
if (S_V_II(g,2) != 1) return FALSE;
for (i=3;i<S_V_LI(g);i++)
if (S_V_II(g,i) != 0) return FALSE;
return TRUE;
ENDR("einsp_galois");
}
INT first_gr_given_c_d(OP c, OP d, OP gr)
{
INT erg =OK;
m_il_nv(S_I_I(d)+2,gr); C_O_K(gr,GALOISRING);
copy(d,S_V_I(gr,0));
copy(c,S_V_I(gr,1));
ENDR("first_gr_given_c_d");
}
INT null_gr_given_c_d(OP c, OP d, OP gr)
{
return first_gr_given_c_d(c,d,gr);
}
INT eins_gr_given_c_d(OP c, OP d, OP gr)
{
INT erg = OK;
first_gr_given_c_d(c,d,gr);
m_i_i(1,S_V_I(gr,2));
ENDR("eins_gr_given_c_d");
}
INT eins_galois(OP a,OP b)
{
INT erg = OK;
if (a==b)
{
INT i;
M_I_I(1,S_V_I(b,2));
for (i=3;i<S_V_LI(b);i++) M_I_I(0,S_V_I(b,i));
}
else
erg += eins_gr_given_c_d(S_GR_C(a),S_GR_D(a),b);
ENDR("eins_galois");
}
INT invers_galois(a,b) OP a,b;
{
INT erg = OK;
CE2(a,b,invers_galois);
{
OP c;
c=CALLOCOBJECT();
copy(a,c);
copy(a,b);
while (! einsp_galois(c))
{
SWAP(b,c);
mult_galois(a,b,c);
}
FREEALL(c);
}
ENDR("invers_galois");
}
INT addinvers_apply_galois(OP a)
/* AK 200307 */
{
INT erg =OK,i,ai;
CTO(GALOISRING,"addinvers_apply_galois(1)",a);
for (i=2;i<S_V_LI(a);i++)
{
if (S_V_II(a,i)!=0)
{
ai = S_GR_CI(a)-S_V_II(a,i);
M_I_I(ai,S_V_I(a,i));
}
}
ENDR("addinvers_apply_galois");
}
INT random_gr_given_c_d(c,d,b) OP c,d; OP b;
{
INT erg = OK;
CTO(INTEGER,"random_gr_given_c_d(1)",c);
CTO(INTEGER,"random_gr_given_c_d(2)",d);
SYMCHECK(prime_power_p(c) ==FALSE,"random_gr_given_c_d:c no prime power");
{
INT i;
m_il_v(S_I_I(d)+2,b); C_O_K(b,GALOISRING);
m_i_i(S_I_I(d),S_V_I(b,0));
m_i_i(S_I_I(c),S_V_I(b,1));
for (i=2;i<S_V_LI(b);i++)
m_i_i(rand()%S_I_I(c),S_V_I(b,i));
}
ENDR("random_gr_given_c_d");
}
INT next_apply_gr(OP gr1)
/* AK 150307 */
{
INT erg =OK,i,j,c;
CTO(GALOISRING,"next_apply_gr(1)",gr1);
c=S_V_II(gr1,1);
for (i=S_V_LI(gr1)-1; i>=2;i--)
if (S_V_II(gr1,i) < c-1) {
INC_INTEGER(S_V_I(gr1,i));
for (j=i+1;j<S_V_LI(gr1);j++) M_I_I(0,S_V_I(gr1,j));
return OK;
}
return LAST_FF;
ENDR("next_apply_gr");
}
INT next_gr(OP gr1, OP gr2)
{
INT erg =OK,i,j,c;
CTO(GALOISRING,"next_gr(1)",gr1);
if (gr1!=gr2) copy(gr1,gr2);
return next_apply_gr(gr2);
/*
c=S_V_II(gr2,1);
for (i=S_V_LI(gr2)-1; i>=2;i--)
if (S_V_II(gr2,i) < c-1) {
INC_INTEGER(S_V_I(gr2,i));
for (j=i+1;j<S_V_LI(gr2);j++) M_I_I(0,S_V_I(gr2,j));
return OK;
}
return LAST_FF;
*/
ENDR("next_gr");
}
INT vectorofzerodivisors_galois(OP c, OP d, OP v)
/* vector with all non unit elements */
{
INT erg =OK;
OP sl=callocobject();
m_il_v(0,v);
first_gr_given_c_d(c,d,sl);
do {
if (! unitp_galois(sl)) { inc(v); copy(sl,S_V_I(v,S_V_LI(v)-1)); }
} while(next_gr(sl,sl)!=LAST_FF);
ENDR("vectorofzerodivisors_galois");
}
INT random_subgroup_glk_grcd_smaller_k(k,c,d,a) OP k,c,d,a;
/* erzeuger fuer kleinere glnk-1 */
{
INT erg = OK;
CTO(INTEGER,"random_subgroup_glk_grcd_smaller_k(1)",k);
SYMCHECK(S_I_I(k)<1,"random_subgroup_glk_grcd_smaller_k(1): k<1");
SYMCHECK(S_I_I(d)<1,"random_subgroup_glk_grcd_smaller_k(3): d<1");
SYMCHECK(prime_power_p(c)==FALSE,"random_subgroup_glk_grcd_smaller_k(2): no prime power");
{
INT i,j;
if (S_I_I(k)<=2)
erg += random_subgroup_glk_grcd_cyclic(k,c,d,a);
else
{
DEC(k);
erg += random_subgroup_glk_grcd(k,c,d,a);
for (i=0;i<S_V_LI(a);i++)
{
OP mat;
mat = S_V_I(a,i);
erg += inc(mat);
erg += eins_gr_given_c_d(c,d,S_M_IJ(mat,S_M_HI(mat)-1,S_M_LI(mat)-1));
for (j=0;j<S_M_HI(mat)-1;j++)
{
erg += null_gr_given_c_d(c,d,S_M_IJ(mat,j,S_M_LI(mat)-1));
erg += null_gr_given_c_d(c,d,S_M_IJ(mat,S_M_HI(mat)-1,j));
}
}
INC(k);
}
}
ENDR("random_subgroup_glk_grcd_smaller_k");
}
INT random_subgroup_glk_grcd_diagonal(k,c,d,a) OP k,c,d,a;
/* subgroup generated by diagonal matrix */
/* AK 110804 */
{
INT erg = OK;
CTO(INTEGER,"random_subgroup_glk_grcd_diagonal(1)",k);
SYMCHECK(S_I_I(k)<1,"random_subgroup_glk_grcd_diagonal(1): k<1");
SYMCHECK(S_I_I(d)<1,"random_subgroup_glk_grcd_diagonal(3): d<1");
SYMCHECK(prime_power_p(c)==FALSE,
"random_subgroup_glk_grcd_diagonal(2): no prime power");
{
OP z;
INT ii,jj;
erg += m_il_v(1,a);
z = S_V_I(a,0);
erg += m_lh_m(k,k,z);
for (ii=0;ii<S_M_HI(z);ii++)
for (jj=0;jj<S_M_HI(z);jj++)
if (ii!=jj) erg += null_gr_given_c_d(c,d,S_M_IJ(z,ii,jj));
for (jj=0;jj<S_M_HI(z);jj++)
{
nn:
erg += random_gr_given_c_d(c,d,S_M_IJ(z,jj,jj));
if (! unitp_galois(S_M_IJ(z,jj,jj))) goto nn;
}
}
printf("diag generator:");println(a);
ENDR("random_subgroup_glk_grcd_diagonal");
}
INT random_subgroup_glk_grcd_2gen(k,c,d,a) OP k,d,c,a;
/* AK 170407 V3.1 */
{
INT erg =OK;
CTO(INTEGER,"random_subgroup_glk_grcd_2gen(1)",k);
CTO(INTEGER,"random_subgroup_glk_grcd_2gen(2)",c);
CTO(INTEGER,"random_subgroup_glk_grcd_2gen(3)",d);
{
OP v1,v2;
CALLOCOBJECT2(v1,v2);
erg += random_subgroup_glk_grcd_cyclic(k,c,d,v1);
erg += random_subgroup_glk_grcd_cyclic(k,c,d,v2);
erg += append(v1,v2,a);
FREEALL2(v1,v2);
}
ENDR("random_subgroup_glk_grcd_2gen");
}
INT random_subgroup_glk_grcd_cyclic(k,c,d,a) OP k,d,c,a;
/* findet zufllige erzeuger einer zyklischen
untergruppe von glk ueber GR characteristik c und degree d */
/* AK 241106 V3.1 */
{
INT erg = OK;
CTO(INTEGER,"random_subgroup_glk_grcd_cyclic(1)",k);
CTO(INTEGER,"random_subgroup_glk_grcd_cyclic(2)",c);
CTO(INTEGER,"random_subgroup_glk_grcd_cyclic(3)",d);
{
OP mat;INT i,j;
mat = CALLOCOBJECT();
m_lh_m(k,k,mat);
ag:
for (i=0;i<S_M_HI(mat);i++)
for (j=0;j<S_M_LI(mat);j++)
{
random_gr_given_c_d(c,d,S_M_IJ(mat,i,j));
}
m_o_v(mat,a);
{
OP d;
d=CALLOCOBJECT();
det_mat_imm(mat,d); printf("det=");println(d);
if (! unitp_galois(d)) { freeall(d); goto ag; }
//order(mat,d); printf("ordnung:"); println(d);
FREEALL(d);
}
FREEALL(mat);
}
ENDR("random_subgroup_glk_grcd_cyclic");
}
static INT multscal_221106(mat,point,res) OP mat,point,res;
{
INT i; INT erg = OK;
OP inv;
//println(point);
inv = CALLOCOBJECT();
MULT(mat,point,res);
for (i=0;i<S_V_LI(res);i++) if (unitp_galois(S_V_I(res,i))) break;
// bei i eintrag != null
if (i==S_V_LI(res)) { println(res); error("no unit found"); }
INVERS(S_V_I(res,i),inv); // printf("break bei %d, mult mit:",i);println(inv);
MULT_APPLY(inv,res);
FREEALL(inv);
//println(res);
ENDR("multscal_151104");
}
INT random_subgroup_glk_grcd_stabilizer(k,phgc,phgd,a) OP k,phgc,phgd,a;
/* subgroup generated as stabilizer of operation on 1-dim subspaces over Galoisring *
/
/* AK 281106 */
{
INT erg = OK;
CTO(INTEGER,"random_subgroup_glk_grcd_stabilizer(1)",k);
CTO(INTEGER,"random_subgroup_glk_grcd_stabilizer(3)",phgd);
SYMCHECK(S_I_I(k)<1,"random_subgroup_glk_grcd_stabilizer(1): k<1");
SYMCHECK(S_I_I(phgd)<1,"random_subgroup_glk_grcd_stabilizer(3): degree<1");
SYMCHECK(prime_power_p(phgc)==FALSE,
"random_subgroup_glk_grcd_stabilizer(2): no prime power");
{
/* first step onedim random element */
OP z=callocobject(),v;
INT i,np=-1;
all_points_phg(k,phgc,phgd,z);
i = rand()%S_V_LI(z);
v = S_V_I(z,i);
// println(v);
/* jetzt ist v ein kanonischer 1-dim subspace */
/* orbit mit stabilizer */
{
OP g = callocobject();
OP res = callocobject();
nochmal:
random_subgroup_glk_grcd(k,phgc,phgd,g);
println(g); println(v);
orbit(g,v,res,multscal_221106,a);
println(res); println(S_V_L(res));
/* check ob gesamte punkte */
if (S_V_LI(res)==S_V_LI(z)) goto nochmal;
FREEALL2(g,res);
}
FREEALL(z);
}
ENDR("random_subgroup_glk_grcd_stabilizer");
}
INT random_subgroup_glk_grcd(k,c,d,a) OP k,d,c,a;
{
INT erg = OK;
CTO(INTEGER,"random_subgroup_glk_grcd(1)",k);
CTO(INTEGER,"random_subgroup_glk_grcd(2)",c);
CTO(INTEGER,"random_subgroup_glk_grcd(3)",d);
{
INT i;
i = rand();
i = i%6;
if (i==0)
return random_subgroup_glk_grcd_diagonal(k,c,d,a);
else if (i==1)
return random_subgroup_glk_grcd_smaller_k(k,c,d,a);
else if (i==2)
return random_subgroup_glk_grcd_stabilizer(k,c,d,a);
else if (i==3)
return random_subgroup_glk_grcd_2gen(k,c,d,a);
else
return random_subgroup_glk_grcd_cyclic(k,c,d,a);
}
ENDR("random_subgroup_glk_grcd");
}
INT get_incidence_phg(OP k,OP phg_c, OP phg_d,OP erz,OP matrix,OP bahnsizes,
OP eindim /*mybe NULL*/, OP eindimbahnen,
OP hyper /*mybe NULL*/, OP hyperbahnen)
{
INT erg =OK,i,j;
INT edf=0;
OP c,hyprep,anzbahn,transerz;
CALLOCOBJECT4(c,hyprep,anzbahn,transerz);
if (eindim==NULL) { edf=1; eindim=CALLOCOBJECT(); }
all_points_phg(k,phg_c,phg_d,eindim);
printf("anzahl punkte:"); println(S_V_L(eindim));
all_orbits(eindim,erz,eindimbahnen,NULL,multscal_221106); // f bahnen von 1dim uvr nummeriert 1,2,...
//println(eindimbahnen);
erg +=max(eindimbahnen,anzbahn); // c ist anzahl bahnen
printf("anzahl der bahnen = "); println(anzbahn);
erg += m_lh_nm(anzbahn,anzbahn,matrix);
erg += m_l_nv(anzbahn,bahnsizes);
m_il_v(S_V_LI(erz),transerz);
for (i=0;i<S_V_LI(transerz);i++) transpose(S_V_I(erz,i),S_V_I(transerz,i));
if (hyper!=NULL) copy(eindim,hyper);
else hyper=eindim;
all_orbits(hyper,transerz,hyperbahnen,NULL,multscal_221106); // f bahnen von 1dim uvr nummeriert 1,2,...
//printf("bahnen der hyperebenen:");println(hyperbahnen);
max(hyperbahnen,c);
printf("anzahl der hyperbahnen = "); println(c);
m_l_v(c,hyprep); // vektor fr reprsentanten der hyperebenen
for (i=0;i<S_V_LI(hyperbahnen);i++) { M_I_I(i,S_V_I(hyprep, S_V_II(hyperbahnen,i)-1)); }
println(hyprep);
for (j=0;j<S_V_LI(eindimbahnen);j++)
{
for (i=0;i<S_V_LI(hyprep);i++)
{
OP y,x;
x = S_V_I(eindim,S_V_II(hyprep,i));
y = S_V_I(eindim,j);
erg +=scalarproduct(x,y,c);
if (NULLP(c)) INC(S_M_IJ(matrix,i,S_V_II(eindimbahnen,j)-1));
}
INC(S_V_I(bahnsizes,S_V_II(eindimbahnen,j)-1));
}
if (edf==1) FREEALL(eindim);
FREEALL4(c,hyprep,anzbahn,transerz);
ENDR("get_incidence_phg");
}
INT all_points_phg(k,phg_c,phg_d,res) OP k,phg_c,phg_d,res;
/* alle 1 dimensionalen uvr von GR(c,d)^k */
/* in sortierter folge */
/* AK 211106 */
{
INT erg = OK;
CTO(INTEGER,"all_points_phg(1)",k);
CTO(INTEGER,"all_points_phg(2)",phg_c);
CTO(INTEGER,"all_points_phg(3)",phg_d);
C3R(k,phg_c,phg_d,"all_points_phg_store",res);
{
INT i,j; OP z,h,v,nv;
CALLOCOBJECT2(v,nv);
vectorofzerodivisors_galois(phg_c, phg_d, nv);
//printf("nullteiler sind:");println(nv);
m_il_v(0,res);
for (i=0;i<S_I_I(k);i++)
{
m_il_v(0,v);
inc(v);
z = S_V_I(v,S_V_LI(v)-1);
m_l_v(k,z);
for (j=0;j<i;j++) null_gr_given_c_d(phg_c,phg_d,S_V_I(z,j));
eins_gr_given_c_d(phg_c,phg_d,S_V_I(z,i));
for (j=i+1;j<S_I_I(k);j++)
first_gr_given_c_d(phg_c,phg_d,S_V_I(z,j));
// das war der erste mit der 1 an der stelle i
h = CALLOCOBJECT();
if (i<(S_I_I(k)-1))
while (1) {
INT res;
copy(z,h);
j=S_V_LI(h)-1;
nochmal:
res = next_gr(S_V_I(z,j),S_V_I(h,j));
if (res == LAST_FF) {
if (j==(i+1)) break;
j--; goto nochmal;
}
else {
INT jj;
for (jj=j+1;jj<S_V_LI(h);jj++)
first_gr_given_c_d(phg_c,phg_d,S_V_I(h,jj));
inc(v); z = S_V_I(v,S_V_LI(v)-1);
copy(h,z);
}
}
FREEALL(h);
/* v ist jetzt der vektor mit 0'en bis platz i
jetzt mssen davor alle mglichen nullteiler in allen permutationen kommen */
append_apply(res,v); // v an res anhngen
if ((S_V_LI(nv)>1)&&(i>0)) {
OP lv;
lv=CALLOCOBJECT();
m_il_nv(i,lv); // nv ist die schleife ber alle fllungen , nullvektor ist start
nn:
for (j=S_V_LI(lv)-1;j>=0;j--)
{
if (S_V_II(lv,j)+1 < S_V_LI(nv)) { inc(S_V_I(lv,j));
for (++j;j<S_V_LI(lv);j++) M_I_I(0,S_V_I(lv,j));
// lv hat jetzt die indices der nullteiler
for (j=0;j<S_V_LI(v);j++)
{
INT k;
for (k=0;k<S_V_LI(lv);k++)
copy(S_V_I(nv,S_V_II(lv,k)), S_V_I(S_V_I(v,j),k));
}
append_apply(res,v); // v an res anhngen
// println(lv);
goto nn;
}
// das war die letzte nullteiler verteilung
}
FREEALL(lv);
}
}
FREEALL2(v,nv);
SYM_sort(res);
}
S3R(k,phg_c,phg_d,"all_points_phg_store",res);
ENDR("all_points");
}
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