// File: hnoether_l.tst
// Intensive tests for hnoether lib
LIB "tst.lib";
tst_init();
LIB "hnoether.lib";
// ------------ test of develop: -------------------
ring zuklein=0,x,dp;
develop(x2+2x3);
ring r=0,(x,y),ds;
develop(x2+2x+3+y);
develop(0);
develop(x2+y2);
develop(x2+y+y2);
develop(2x2+3xy+4xy3-x2y);
poly p_1 = y2+x3;
poly p_2 = p_1^2 + x5y;
poly p_3 = p_2^2 + x^10 *p_1;
poly p_4 = p_3^2 + x^20 *p_2;
poly p_5 = p_4^2 + x^40 *p_3;
param(develop(p_2));
int z=timer;
param(develop(p_4));
tst_ignore(timer-z,"time");
z=timer;
list hne=develop(p_4,-1);
tst_ignore(timer-z,"time");
print(extdevelop(hne,4)[1]);
tst_ignore(timer-z,"time");
z=timer;
print(develop(p_4,4)[1]);
tst_ignore(timer-z,"time");
poly heme=xy8+y8+x4y6+4x3y6+2x5y5+6x6y4+4x8y3+x10y2+4x9y2+2x11y+x12;
hne=develop(heme);
print(hne[1]);
ring R=32003,(x,y),dp;
poly p_5=imap(r,p_5);
z=timer;
print(develop(p_5,-1)[1]);
tst_ignore(timer-z,"time");
kill r;
ring r=32003,(x,y),ls;
poly p_5=fetch(R,p_5);
z=timer;
print(develop(p_5,-1)[1]);
tst_ignore(timer-z,"time");
kill r,R;
ring r=2,(x,y,t),ds;
poly f=y2+x7y+x9+x8;
param(develop(f));
kill r;
ring r=7,(x,y),dp;
poly f=2*(y-3x7)^14;
develop(f+x12y14);
develop(f+x7y14);
kill r;
ring r=(0,i),(a,b),dp;
develop(a2+ib3);
develop(a5+i2*a4+2i*a2b+b2);
kill r;
ring r=(0,i),(a,b),dp;
minpoly=i2+1;
develop(a2+ib3);
develop(a5+i2*a4+2i*a2b+b2);
develop((a+2b)^2+ib5);
kill r;
ring r=(7,i),(x,y),dp;
develop(x+y);
kill r;
ring r=(7,i),(x,y),dp;
minpoly=i2+1;
develop(x);
kill r;
ring r=(49,k),(g,h),Dp;
develop(g3+h4);
develop((g2+2h)^7+h9);
kill r;
ring r=real,(x,y),dp;
develop(x-y);
kill r;
ring r=(11,a,b,c),(d,e,f),ls;
develop(ad2+a2b3e3+2bc4e4);
kill r;

// ------------ test of reddevelop: -------------------
setring zuklein;
reddevelop(x);
ring r=7,(a,b),dp;
reddevelop(a6+b4);
kill HNEring,r;
ring r=0,(x,y),dp;
reddevelop(x6-y4);
setring r;
kill HNEring;
reddevelop((x6-y4)*(y6-x4));
setring r;kill HNEring;
reddevelop((y-x2+x3)*(y-x2-x3));
setring r;
kill HNEring;
reddevelop((x7-2x4y2+xy4-1y5)*(x7-4x4y2+4xy4-1y5));
setring r;
kill HNEring;
reddevelop((y2-x3)*(y2-x3-x4));
setring r;
kill HNEring;
reddevelop((y2-x3-x4)*(y2+x3+x4));
setring r;
kill HNEring;
reddevelop(((x2-y)^2+x5)*((2x2-y)^2+x5));
setring r;
kill HNEring;
reddevelop(x2+1+y3);
setring r;
kill HNEring;
reddevelop(0);
kill HNEring,r;
ring r=(49,i),(x,y),dp;
reddevelop(x);
kill r;
ring r=(7,i),(x,y),dp;
list hne=reddevelop(x3+y6);
hne;
displayHNE(hne);
setring r;
kill HNEring;
reddevelop((x2+y4)*(x+y4));
setring r;
kill HNEring;
reddevelop(x2+y4);
kill r,HNEring;
ring r=(0,e),(x,y),lp;
reddevelop(x2-y2);
kill HNEring;
setring r;
reddevelop(x2-ey2);
kill r,HNEring;
ring r=(32003,i),(x,y),dp;
minpoly=i2+1;
reddevelop(x2+y4);
HNEring;
kill r,HNEring;
ring r=(32003,i),(x,y),dp;
minpoly=i2+i+1;
reddevelop(x2+y4);
basering;
kill r,HNEring;
ring r=real,(x,y),dp;
reddevelop(x);
kill r;
ring r=(11,a,b,c),(d,e,f,g),dp;
list hne=reddevelop(a2bd2+bce3+a2c3e4);
hne;
displayHNE(hne[1]);
basering;
kill r,HNEring;
ring r=(11,a,b,c),(d,e),Ds;
reddevelop(a2bd2+bce3+a2c3e4);
kill r,HNEring;
ring r=(11,a),(x,y,z),wp(1,2,3);
minpoly=a2+4;
list hne=reddevelop(x2+ay3);
hne;
displayHNE(hne[1]);
basering;
kill r,HNEring;
ring r=(11,a),(x,y,z),wp(1,2,3);
reddevelop(x2+ay3);
kill HNEring,r;
//--------------- examples with change to ring extension
ring F2=2,(x,y),dp;
reddevelop(y2+x7y+x9+x8);
ring R=32003,(x,y),dp;
kill HNEring;
reddevelop((x6+(y-x)^4)*(y+x));
setring R;
kill HNEring;
poly f=x19-4x18+3x17+8x16y-1x16-10x15y-4x14y2+6x14y+10x13y2-16x12y2+26x10y3-5x9y4-30x8y4+2x7y5+26x6y5-16x4y6+6x2y7-1y8;
reddevelop(f);
setring R;
kill HNEring;
f=x29-6x28+14x27+12x26y-18x26-56x25y-6x24y2+13x25+110x24y+84x23y2-5x24-108x23y-282x22y2-56x21y3+54x22y+396x21y2+390x20y3+14x19y4-266x20y2-840x19y3-310x18y4+790x18y3+1134x17y4+138x16y5-1575x16y4-1008x15y5-30x14y6+2220x14y5+588x13y6+2x12y7-2268x12y6-216x11y7+1692x10y7+45x9y8-915x8y8-4x7y9+350x6y9-90x4y10+14x2y11-1y12;
list hne=reddevelop(f);
displayHNE(hne);
displayInvariants(hne);
setring R;
kill HNEring;
reddevelop(xy6+x3y4-4x5y3+6x7y2-4x9y+x11);
setring R; kill HNEring;
reddevelop(y10-4x3y8+6x6y6-4x9y4+x12y2+x16);
setring R; kill HNEring;
reddevelop((y10-4x3y8+6x6y6-4x9y4+x12y2+x16)*(x6-y4));
kill HNEring,R;
//--------------- example with more than one ring change
ring F3=3,(x,y),dp;
list hne=reddevelop((x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4));
map T; int i;
poly f=(x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4);
for (i=1; i<=size(hne); i++) {
 T=basering,param(hne[i]);
 T(f);
}
displayHNE(hne);
displayHNE(hne[3],1);
kill displayring;
kill HNEring;
kill i;
setring F3;
reddevelop((x3-xy4+y6)*(x2+y2)*(x4-x3y+xy3+y4));
setring F3;
kill HNEring;
reddevelop((x3-xy4+y6)*(x2+y6)*(x4-x3y4+xy12+y16));
kill HNEring;
// -------------- bigger examples with timings
ring r=0,(x,y),dp;
poly p_1 = y2+x3;
poly p_2 = p_1^2 + x5y;
poly p_3 = p_2^2 + x^10 *p_1;
poly p_4 = p_3^2 + x^20 *p_2;
poly p_5 = p_4^2 + x^40 *p_3;
z=timer;
list hne=reddevelop(p_1*p_2*p_3*p_4);
tst_ignore(timer-z,"time");
tst_ignore(kmemory(),"memory");
print(hne[3][1]);
print(hne[4][1]);
displayInvariants(hne);
setring r;
kill HNEring;
z=timer;
list hne=reddevelop(p_5);
tst_ignore(timer-z,"time");
tst_ignore(kmemory(),"memory");
print(hne[1][1]);
displayInvariants(hne);
displayInvariants(hne[1]);
kill HNEring;
// ------------ test of extdevelop: -------------------
setring r;
list hne=develop(x2+y3+y4-y5,-1);
show(extdevelop(hne,2));
show(extdevelop(hne,4));
show(extdevelop(hne,10));
kill r;
ring r=(49,i),(x,y),ls;
list hne=develop((x2+iy3)^7+x15);
show(extdevelop(hne,8));
kill hne;
// ------------ test of essdevelop: -------------------
setring F3;
list hne=essdevelop((x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4));
displayHNE(hne);
setring F3;
kill HNEring;
list hne=essdevelop(x2+y3+xy4);
displayHNE(hne);
setring r;
kill HNEring;
// ------------ test of HNdevelop: --------------------
// list hne=HNdevelop((x2+iy3)^7+x15);  // laeuft derzeit (27.5.99) wegen einem
// show(extdevelop(hne[1],8));          // Fehler in factorize endlos!
list hne=HNdevelop((x2+iy3)^6+x15);     // Als Ersatz fuer die Zwischenzeit
show(hne);
kill r;
ring r=(0,i),(a,b),dp;
minpoly=i2+1;
list hne=HNdevelop(a2+ib3-ia3b);
show(hne);
kill r;
ring r=0,(x,y),dp;
show(HNdevelop((x3+3x2y-xy4+y10)*(x3-x2y+y8)));
// ------------ test of param: ------------------------
setring r;
param(develop(x+1+y2));
param(develop(x2+y3));
param(develop(y2+x3));
param(develop(x+y2-y3));
param(develop(x2+y3+y4));
param(develop((x-2y3)^2+x3));
param(develop(y+x2-y3));
param(develop((y-2x3)^2+x7));
param(develop((y-2x3)^2+x7),0);
param(develop(x+y2-y3),0);
param(develop(x2+y3+y4),"Fritz");
param(develop(y2+x3+x4),x);
z=timer;
param(develop((y-2x3)^2+y5));
tst_ignore(timer-z,"time");
kill r;
ring r=(27,j),(k,l,t),lp;
list hne=develop((k3-jl)^6+l7,9);
param(hne);
// ------------ test of displayHNE: -------------------
displayHNE(hne);
kill r;
ring r=3,(k,l,t),lp;
list hne=develop((k3+l)^6+l7,9);
displayHNE(hne);
basering;
displayHNE(hne,1);
basering;
kill displayring,r;
ring r=0,(x,y),dp;
displayHNE(develop(x));
displayHNE(develop(y));
displayHNE(develop(1));
// ------------ test of displayInvariants: ------------
list hne=reddevelop((x2+y3+y4)*(x+y2+y3-y4)*(x5+y7));
displayInvariants(hne[1]);
displayInvariants(hne[2]);
displayInvariants(hne);
kill HNEring;
// ------------ test of is_irred: ---------------------
setring r;
is_irred(x);
is_irred(x2);
is_irred((x+y)*(1+x+y));  // one HNE
is_irred((x+y)*(x+y+xy)); // one of two HNEs found
is_irred(x2+y2);          // no HNE found
is_irred(1+x+y);          // not a curve
// ----------------------------------------------------------------------------
// ------- test of invariants, intersection, stripHNE, puiseux2generators,  ---
// -------         multiplicities, newtonpoly                               ---
example invariants;
setring r;
list hne=reddevelop((x2-y3)*(x2+y3));
intersection(hne[1],hne[2]);
example stripHNE;
puiseux2generators(intvec(3,7,15,31,63,127),intvec(2,2,2,2,2,2));
setring r;
multiplicities(develop(x5+y7));
example newtonpoly;
// ------- test of getnm, T_Transform, T1_Transform, T2_Transform, koeff, -----
// ------------  redleit, squarefree, allsquarefree, referencepoly   ----------
example getnm;
T_Transform(y2+x3,1,2);
T1_Transform(y-x2+x3,1,2);
T2_Transform(y2+x3-x2y,-1,3,2,referencepoly(newtonpoly(y2+x3-x2y)));
koeff(x2+2xy+3xy2-x2y-2y3,1,2);
example redleit;
example squarefree;
ring R=(27,k),(x,y),dp;
squarefree(x2);
squarefree(y3);
squarefree((x2+y)^3*(x-y)^2*(x+y));

example allsquarefree;
tst_status(1);$