Changeset 7d2f4e in git


Ignore:
Timestamp:
Apr 15, 2005, 3:42:13 PM (18 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
Children:
2761f395278b788f84e5aa342e7357383e4b5430
Parents:
54f622be322e398945bc5618f6b2695330cac5e3
Message:
*hannes/lossen: new lib


git-svn-id: file:///usr/local/Singular/svn/trunk@7829 2c84dea3-7e68-4137-9b89-c4e89433aadc
Location:
Tst/Long
Files:
3 edited

Legend:

Unmodified
Added
Removed

  • Tst/Long/hnoether_l.res.gz.uu

    r54f622b r7d2f4e  
    11begin 640 hnoether_l.res.gz
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     298?>M&MSM.^E,X"P,W^8G][,Q-G+WZ8_`?#+?2HT?T`````
    254299`
    255300end

  • Tst/Long/hnoether_l.stat

    r54f622b r7d2f4e  
    1 1 >> tst_memory_0 :: 1044978306:2003021115:2-0-4:ix86-Linux:nepomuck:382256
    2 1 >> tst_memory_1 :: 1044978306:2003021115:2-0-4:ix86-Linux:nepomuck:2497416
    3 1 >> tst_memory_2 :: 1044978306:2003021115:2-0-4:ix86-Linux:nepomuck:24177544
    4 1 >> tst_timer_1 :: 1044978306:2003021115:2-0-4:ix86-Linux:nepomuck:2174
     11 >> tst_memory_0 :: 1113568891:2005041411:2-1-99:ix86-Linux:nepomuck:10468216
     21 >> tst_memory_1 :: 1113568891:2005041411:2-1-99:ix86-Linux:nepomuck:29195444
     31 >> tst_memory_2 :: 1113568891:2005041411:2-1-99:ix86-Linux:nepomuck:150830260
     41 >> tst_timer_1 :: 1113568891:2005041411:2-1-99:ix86-Linux:nepomuck:10091

  • Tst/Long/hnoether_l.tst

    r54f622b r7d2f4e  
    8282kill r;
    8383
    84 // ------------ test of reddevelop: -------------------
     84// ------------ test of hnexpansion: -------------------
    8585setring zuklein;
    86 reddevelop(x);
     86hnexpansion(x);
    8787ring r=7,(a,b),dp;
    88 reddevelop(a6+b4);
    89 kill HNEring,r;
     88hnexpansion(a6+b4);
     89kill r;
    9090ring r=0,(x,y),dp;
    91 reddevelop(x6-y4);
     91hnexpansion(x6-y4);
     92hnexpansion((x6-y4)*(y6-x4));
     93hnexpansion((y-x2+x3)*(y-x2-x3));
     94hnexpansion((x7-2x4y2+xy4-1y5)*(x7-4x4y2+4xy4-1y5));
     95hnexpansion((y2-x3)*(y2-x3-x4));
     96hnexpansion((y2-x3-x4)*(y2+x3+x4));
     97hnexpansion(((x2-y)^2+x5)*((2x2-y)^2+x5));
     98hnexpansion(x2+1+y3);
     99hnexpansion(0);
     100kill r;
     101ring r=(49,i),(x,y),dp;
     102def L=hnexpansion(x);
     103def HNring = L[1]; setring HNring;  displayHNE(hne);
     104kill L,HNring,r;
     105ring r=(7,i),(x,y),dp;
     106list hne=hnexpansion(x3+y6);
     107displayHNE(hne);
     108kill hne;
     109def L=hnexpansion((x2+y4)*(x+y4));
     110def HNring = L[1]; setring HNring;  displayHNE(hne);
    92111setring r;
    93 kill HNEring;
    94 reddevelop((x6-y4)*(y6-x4));
    95 setring r;kill HNEring;
    96 reddevelop((y-x2+x3)*(y-x2-x3));
    97 setring r;
    98 kill HNEring;
    99 reddevelop((x7-2x4y2+xy4-1y5)*(x7-4x4y2+4xy4-1y5));
    100 setring r;
    101 kill HNEring;
    102 reddevelop((y2-x3)*(y2-x3-x4));
    103 setring r;
    104 kill HNEring;
    105 reddevelop((y2-x3-x4)*(y2+x3+x4));
    106 setring r;
    107 kill HNEring;
    108 reddevelop(((x2-y)^2+x5)*((2x2-y)^2+x5));
    109 setring r;
    110 kill HNEring;
    111 reddevelop(x2+1+y3);
    112 setring r;
    113 kill HNEring;
    114 reddevelop(0);
    115 kill HNEring,r;
    116 ring r=(49,i),(x,y),dp;
    117 reddevelop(x);
    118 kill r;
    119 ring r=(7,i),(x,y),dp;
    120 list hne=reddevelop(x3+y6);
    121 hne;
    122 displayHNE(hne);
    123 setring r;
    124 kill HNEring;
    125 reddevelop((x2+y4)*(x+y4));
    126 setring r;
    127 kill HNEring;
    128 reddevelop(x2+y4);
    129 kill r,HNEring;
     112kill L,HNring;
     113hnexpansion(x2+y4);
     114kill r;
    130115ring r=(0,e),(x,y),lp;
    131 reddevelop(x2-y2);
    132 kill HNEring;
    133 setring r;
    134 reddevelop(x2-ey2);
    135 kill r,HNEring;
     116hnexpansion(x2-y2);
     117hnexpansion(x2-ey2);
     118kill r;
    136119ring r=(32003,i),(x,y),dp;
    137120minpoly=i2+1;
    138 reddevelop(x2+y4);
    139 HNEring;
    140 kill r,HNEring;
     121param(hnexpansion(x2+y4));
     122kill r;
    141123ring r=(32003,i),(x,y),dp;
    142124minpoly=i2+i+1;
    143 reddevelop(x2+y4);
    144 basering;
    145 kill r,HNEring;
     125param(hnexpansion(x2+y4));
     126kill r;
    146127ring r=real,(x,y),dp;
    147 reddevelop(x);
     128hnexpansion(x);
    148129kill r;
    149130ring r=(11,a,b,c),(d,e,f,g),dp;
    150 list hne=reddevelop(a2bd2+bce3+a2c3e4);
    151 hne;
    152 displayHNE(hne[1]);
    153 basering;
    154 kill r,HNEring;
     131list L=hnexpansion(a2bd2+bce3+a2c3e4);
     132displayHNE(L);
     133kill r;
    155134ring r=(11,a,b,c),(d,e),Ds;
    156 reddevelop(a2bd2+bce3+a2c3e4);
    157 kill r,HNEring;
     135hnexpansion(a2bd2+bce3+a2c3e4);
     136kill r;
    158137ring r=(11,a),(x,y,z),wp(1,2,3);
    159138minpoly=a2+4;
    160 list hne=reddevelop(x2+ay3);
    161 hne;
    162 displayHNE(hne[1]);
    163 basering;
    164 kill r,HNEring;
    165 ring r=(11,a),(x,y,z),wp(1,2,3);
    166 reddevelop(x2+ay3);
    167 kill HNEring,r;
     139list L=hnexpansion(x2+ay3);
     140param(L,1);
     141kill r;
     142ring F2=2,(x,y,t),ds;
     143poly f=y2+x7y+x9+x8;
     144def L=hnexpansion(f);
     145def P=param(L[1],1);
     146map phi=F2,P[1][1],P[1][2];
     147phi(f);
     148kill L,P,phi,F2;
     149
    168150//--------------- examples with change to ring extension
    169 ring F2=2,(x,y),dp;
    170 reddevelop(y2+x7y+x9+x8);
    171151ring R=32003,(x,y),dp;
    172 kill HNEring;
    173 reddevelop((x6+(y-x)^4)*(y+x));
     152poly f=(x6+(y-x)^4)*(y+x);
     153def L=hnexpansion(f);
     154def HNring = L[1]; setring HNring;  displayHNE(hne);
    174155setring R;
    175 kill HNEring;
    176 poly f=x19-4x18+3x17+8x16y-1x16-10x15y-4x14y2+6x14y+10x13y2-16x12y2+26x10y3-5x9y4-30x8y4+2x7y5+26x6y5-16x4y6+6x2y7-1y8;
    177 reddevelop(f);
     156kill HNring;
     157f=x19-4x18+3x17+8x16y-1x16-10x15y-4x14y2+6x14y+10x13y2-16x12y2+26x10y3-5x9y4
     158     -30x8y4+2x7y5+26x6y5-16x4y6+6x2y7-1y8;
     159L=hnexpansion(f);
     160def HNring = L[1]; setring HNring;  displayHNE(hne);
    178161setring R;
    179 kill HNEring;
    180 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;
    181 list hne=reddevelop(f);
    182 displayHNE(hne);
     162kill HNring;
     163f=x29-6x28+14x27+12x26y-18x26-56x25y-6x24y2+13x25+110x24y+84x23y2-5x24
     164     -108x23y-282x22y2-56x21y3+54x22y+396x21y2+390x20y3+14x19y4-266x20y2
     165     -840x19y3-310x18y4+790x18y3+1134x17y4+138x16y5-1575x16y4-1008x15y5
     166     -30x14y6+2220x14y5+588x13y6+2x12y7-2268x12y6-216x11y7+1692x10y7+45x9y8
     167     -915x8y8-4x7y9+350x6y9-90x4y10+14x2y11-1y12;
     168L=hnexpansion(f);
     169def HNring = L[1]; setring HNring;  displayHNE(hne);
    183170displayInvariants(hne);
    184171setring R;
    185 kill HNEring;
    186 reddevelop(xy6+x3y4-4x5y3+6x7y2-4x9y+x11);
    187 setring R; kill HNEring;
    188 reddevelop(y10-4x3y8+6x6y6-4x9y4+x12y2+x16);
    189 setring R; kill HNEring;
    190 reddevelop((y10-4x3y8+6x6y6-4x9y4+x12y2+x16)*(x6-y4));
    191 kill HNEring,R;
    192 //--------------- example with more than one ring change
     172kill HNring;
     173L=hnexpansion(xy6+x3y4-4x5y3+6x7y2-4x9y+x11,"ess");
     174def HNring = L[1]; setring HNring;  displayHNE(hne);
     175setring R; kill HNring;
     176L=hnexpansion(y10-4x3y8+6x6y6-4x9y4+x12y2+x16,"ess");
     177L[2];
     178def HNring = L[1]; setring HNring;
     179def P=param(hne[1]);
     180map phi=HNring,P[1][1],P[1][2];
     181phi(f);
     182kill P,phi;
     183setring R; kill HNring;
     184L=hnexpansion((y10-4x3y8+6x6y6-4x9y4+x12y2+x16)*(x6-y4),"ess");
     185L[2];
     186def HNring = L[1]; setring HNring;  displayHNE(hne);
     187ideal P; map phi;
     188for (int i=1; i<=size(hne); i++)
     189{
     190  P=param(hne[i]);
     191  phi=HNring,P[1],P[2];
     192  phi(f);
     193}
     194kill i,P,phi,L,HNring,R;
     195
     196ring r=0,(x,y),ds;
     197poly g=x12+y15+x13+x16;
     198def L=hnexpansion(g,1);
     199L[2];
     200def HNring = L[1]; setring HNring;  displayHNE(hne);
     201ideal P; map phi;
     202for (int i=1; i<=size(hne); i++)
     203{
     204  P=param(hne[i]);
     205  phi=HNring,P[1],P[2];
     206  ord(phi(f));
     207}
     208kill i,P,phi,L,HNring;
     209setring r;
     210poly f=(x2-y2)*(x2+y2)*(x2+y4);
     211def L=hnexpansion(f,"ess");
     212L[2];
     213def HNring = L[1]; setring HNring;  displayHNE(hne);
     214setring r; kill HNring;
     215f=(x2-y2)*(x2+y2)*(2y2+x4)*(y2-x7)*(2x2+y4);
     216L=hnexpansion(f,"ess");
     217L[2];
     218def HNring = L[1]; setring HNring;  displayHNE(hne);
     219setring r; kill HNring;
     220f=(y2+x2)*(x2-y3)*(x6-13y12);
     221L=hnexpansion(f,1);
     222L[2];
     223def HNring = L[1]; setring HNring;
     224ideal P; map phi;
     225for (int i=1; i<=size(hne); i++)
     226{
     227  P=param(hne[i]);
     228  phi=HNring,P[1],P[2];
     229  phi(f);
     230}
     231kill i,P,phi,HNring,L,r;
     232ring r=(0,a),(x,y),ds;
     233minpoly=a2-2;
     234poly f=(x2-y2)*(x2+y2)*(2y2+x4)*(y2-x7)*(2x2+y4);
     235def L=hnexpansion(f,1);
     236L[2];
     237def HNring = L[1]; setring HNring;
     238ideal P; map phi;
     239for (int i=1; i<=size(hne); i++)
     240{
     241  P=param(hne[i]);
     242  phi=HNring,P[1],P[2];
     243  phi(f);
     244}
     245kill i,P,phi,HNring,L;
     246
     247//--------------- examples with more than one ring change
    193248ring F3=3,(x,y),dp;
    194 list hne=reddevelop((x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4));
     249list L=hnexpansion((x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4));
     250def HNring = L[1]; setring HNring; 
    195251map T; int i;
    196 poly f=(x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4);
    197252for (i=1; i<=size(hne); i++) {
    198253 T=basering,param(hne[i]);
    … …  
    200255}
    201256displayHNE(hne);
    202 displayHNE(hne[3],1);
    203 kill displayring;
    204 kill HNEring;
    205 kill i;
     257def displayRing=displayHNE(hne[3],1);
     258setring displayRing; HNE;
     259kill displayRing,HNring,i;
    206260setring F3;
    207 reddevelop((x3-xy4+y6)*(x2+y2)*(x4-x3y+xy3+y4));
     261poly f=(x3-xy4+y6)*(x2+y2)*(x4-x3y+xy3+y4);
     262L=hnexpansion(f,1);
     263L[2];
     264def HNring = L[1]; setring HNring; 
     265map T; int i;
     266for (i=1; i<=size(hne); i++) {
     267 T=basering,param(hne[i]);
     268 T(f);
     269}
     270kill HNring,i;
    208271setring F3;
    209 kill HNEring;
    210 reddevelop((x3-xy4+y6)*(x2+y6)*(x4-x3y4+xy12+y16));
    211 kill HNEring;
     272f=(x3-xy4+y6)*(x2+y6)*(x4-x3y4+xy12+y16);
     273L=hnexpansion((x3-xy4+y6)*(x2+y6)*(x4-x3y4+xy12+y16));
     274def HNring = L[1]; setring HNring; 
     275map T; int i;
     276for (i=1; i<=size(hne); i++) {
     277 T=basering,param(hne[i]);
     278 T(f);
     279}
     280kill L,HNring,i;
     281
     282ring r=199,(x,y),ds;
     283poly g=y36+6x8y30-24x9y30+15x16y24-x17y24+20x24y18+41x18y24+42x25y18
     284 +15x32y12+31x26y18-42x33y12-86x27y18+6x40y6+23x34y12+x41y6-75x35y12
     285 +x48+31x42y6+59x36y12+24x49+75x43y6+41x50-64x44y6+86x51+25x45y6+59x52
     286 -25x53-83x54;
     287def L=hnexpansion(g);
     288invariants(L);
     289delta(L);
     290delta(g);
     291L=hnexpansion(g,1);
     292L[2];
     293invariants(L);
     294def HNring = L[1]; setring HNring;  displayHNE(hne);
     295kill L,r,HNring;
     296
    212297// -------------- bigger examples with timings
    213298ring r=0,(x,y),dp;
    … …  
    218303poly p_5 = p_4^2 + x^40 *p_3;
    219304z=timer;
    220 list hne=reddevelop(p_1*p_2*p_3*p_4);
     305list L=hnexpansion(p_1*p_2*p_3*p_4);
    221306tst_ignore(timer-z,"time");
    222307tst_ignore(kmemory(),"memory");
    223 print(hne[3][1]);
    224 print(hne[4][1]);
    225 displayInvariants(hne);
    226 setring r;
    227 kill HNEring;
    228 z=timer;
    229 list hne=reddevelop(p_5);
     308print(L[3][1]);
     309print(L[4][1]);
     310displayInvariants(L);
     311z=timer;
     312L=hnexpansion(p_5);
    230313tst_ignore(timer-z,"time");
    231314tst_ignore(kmemory(),"memory");
    232 print(hne[1][1]);
    233 displayInvariants(hne);
    234 displayInvariants(hne[1]);
    235 kill HNEring;
     315print(L[1][1]);
     316displayInvariants(L);
     317displayInvariants(L[1]);
     318kill r;
     319ring r=0,(x,y),ds;
     320poly f=(x4-2y6)*(x10+y14+x16+y17)+x30+4x24y8+y32;
     321z=timer;
     322def L=hnexpansion(f);
     323tst_ignore(timer-z,"time");
     324tst_ignore(kmemory(),"memory");
     325def HNring = L[1]; setring HNring;  displayHNE(hne);
     326kill L,HNring,r;
     327
     328ring r=32003,(x,y),ds;
     329poly p_1 = y4+x6;
     330poly p_2 = y7-2x14;
     331poly p_3 = p_1^14 + p_2^10+x100+y83;
     332z=timer;
     333def L=hnexpansion(p_3,"ess");
     334tst_ignore(timer-z,"time");
     335tst_ignore(kmemory(),"memory");
     336L[2];
     337def HNring = L[1]; setring HNring;  displayHNE(hne);
     338kill r,L,HNring;
     339
     340// irreducible example with 3 Puiseux pairs over algebraic number field
     341// (no field extension needed)
     342ring r=(199,a),(x,y,t),ds;
     343minpoly = 5+12a+3a2-4a3+3a4+a6;
     344number I = 23-94a+94a2-38a3-81a4-91a5;   // I^2 = -1
     345number sq = -23+95a-94a2+38a3+81a4+91a5; // sq^3 = 2
     346ideal J = x-t^12,
     347          y-I*t^16-sq*t^18-t^19;
     348def f=eliminate(J,t)[1];
     349def L=hnexpansion(f);
     350displayInvariants(L[1]);
     351
     352// Example with 1 field extension, 6 conjugate branches, 3 Puiseux pairs
     353ring r=199,(x,y),ds;
     354poly g=y48+24*x3y46+77*x6y44+34*x9y42+79*x12y40+56*x9y43-82*x15y38-93*x12y41
     355 +72*x18y36+12*x15y39+43*x21y34+42*x18y37-6*x15y40-33*x24y32-99*x21y35
     356 -96*x18y38+74*x27y30+56*x24y33-74*x21y36-88*x30y28-41*x27y31-70*x24y34
     357 +87*x33y26+37*x30y29+36*x27y32+81*x24y35-55*x36y24-78*x33y27-27*x30y30
     358 +91*x27y33+87*x39y22+88*x36y25-56*x33y28-87*x30y31-88*x42y20+32*x39y23
     359 -87*x36y26+14*x33y29+15*x30y32+74*x45y18+42*x42y21-2*x39y24-92*x36y27
     360 +44*x33y30-33*x48y16-86*x45y19-39*x42y22-17*x39y25+42*x36y28+43*x51y14
     361 +58*x48y17+24*x45y20-27*x42y23-2*x39y26+72*x54y12-93*x51y15+40*x48y18
     362 -28*x45y21+84*x42y24+45*x39y27-82*x57y10+80*x54y13+16*x51y16+18*x48y19
     363 -21*x45y22-19*x42y25+79*x60y8+70*x57y11+20*x54y14+31*x51y17+85*x48y20
     364 +99*x45y23+34*x63y6-9*x60y9-95*x57y12-97*x54y15+17*x51y18-33*x48y21
     365 -20*x45y24+77*x66y4-88*x63y7-57*x60y10+86*x57y13+82*x54y16+64*x51y19
     366 -58*x48y22+24*x69y2+83*x66y5-94*x63y8+25*x60y11-34*x57y14-59*x54y17
     367 -50*x51y20+x72-16*x69y3-77*x66y6+77*x63y9+83*x60y12+62*x54y18+81*x72y
     368 +73*x69y4-25*x66y7+96*x63y10+27*x60y13+56*x57y16+13*x54y19+93*x72y2
     369 +71*x69y5-46*x66y8+58*x63y11+38*x60y14-78*x57y17+77*x75+91*x72y3
     370 -5*x69y6-65*x66y9-7*x63y12+93*x60y15-40*x75y-38*x72y4-11*x69y7+31*x66y10
     371 +21*x63y13+15*x60y16+92*x75y2+29*x72y5+76*x69y8-84*x66y11+76*x63y14
     372 -34*x78+65*x75y3-42*x72y6+4*x69y9+10*x66y12-83*x78y+62*x75y4-2*x72y7
     373 +39*x69y10-48*x78y2+28*x75y5-23*x72y8+31*x69y11-41*x81+72*x78y3+14*x75y6
     374 -21*x72y9+8*x81y+94*x78y4-87*x75y7+50*x81y2+74*x78y5-6*x75y8+61*x84
     375 -79*x81y3-95*x78y6+58*x84y-35*x81y4+19*x84y2-81*x87-27*x84y3+77*x87y+x90;
     376z=timer;
     377list L=hnexpansion(g);
     378tst_ignore(timer-z,"time");
     379tst_ignore(kmemory(),"memory");
     380def HNring = L[1]; setring HNring;  displayHNE(hne);
     381setring r; kill HNring;
     382z=timer;
     383L=hnexpansion(g,"ess");
     384tst_ignore(timer-z,"time");
     385tst_ignore(kmemory(),"memory");
     386L[2];
     387
    236388// ------------ test of extdevelop: -------------------
    237 setring r;
    238389list hne=develop(x2+y3+y4-y5,-1);
    239390show(extdevelop(hne,2));
    240391show(extdevelop(hne,4));
    241392show(extdevelop(hne,10));
    242 kill r;
     393kill hne,r;
    243394ring r=(49,i),(x,y),ls;
    244395list hne=develop((x2+iy3)^7+x15);
    … …  
    247398// ------------ test of essdevelop: -------------------
    248399setring F3;
    249 list hne=essdevelop((x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4));
    250 displayHNE(hne);
     400list L=essdevelop((x3-xy2+y3)*(x2+y2)*(x4-x3y+xy3+y4));
     401L[2];
     402def HNring = L[1]; setring HNring; displayHNE(hne);
    251403setring F3;
    252 kill HNEring;
    253 list hne=essdevelop(x2+y3+xy4);
    254 displayHNE(hne);
     404kill HNring;
     405L=essdevelop(x2+y3+xy4);
     406L[2];
     407displayHNE(L[1]);
     408displayHNE(develop(x2+y3+xy4));
    255409setring r;
    256 kill HNEring;
    257 // ------------ test of HNdevelop: --------------------
    258 // list hne=HNdevelop((x2+iy3)^7+x15);  // laeuft derzeit (27.5.99) wegen einem
    259 // show(extdevelop(hne[1],8));          // Fehler in factorize endlos!
    260 list hne=HNdevelop((x2+iy3)^6+x15);     // Als Ersatz fuer die Zwischenzeit
    261 show(hne);
    262 kill r;
    263 ring r=(0,i),(a,b),dp;
     410kill F3;
     411
     412// ------------ more tests of hnexpansion: --------------------
     413list L=hnexpansion((x2+iy3)^7+x15); 
     414def HNring = L[1]; setring HNring;  displayHNE(hne);
     415show(extdevelop(hne[1],8));          // Fehler in factorize endlos!
     416map T=basering,param(hne[1]);
     417T(f);
     418setring r; kill HNring;
     419L=hnexpansion((x2+iy3)^6+x15);     // Als Ersatz fuer die Zwischenzeit
     420def HNring = L[1]; setring HNring;
     421map T=basering,param(hne[1]);
     422ord(T(f));
     423kill L,HNring,r;
     424
     425ring r=(0,i),(a,b),ds;
    264426minpoly=i2+1;
    265 list hne=HNdevelop(a2+ib3-ia3b);
    266 show(hne);
    267 kill r;
    268 ring r=0,(x,y),dp;
    269 show(HNdevelop((x3+3x2y-xy4+y10)*(x3-x2y+y8)));
    270 // ------------ test of param: ------------------------
    271 setring r;
     427list L=hnexpansion(a2+ib3-ia3b);
     428show(L);
     429kill r;
     430ring r=0,(x,y),ds;
     431displayHNE(hnexpansion((x3+3x2y-xy4+y10)*(x3-x2y+y8)));
     432// ------------ more tests of param: ------------------------
    272433param(develop(x+1+y2));
    273434param(develop(x2+y3));
    … …  
    295456list hne=develop((k3+l)^6+l7,9);
    296457displayHNE(hne);
    297 basering;
    298 displayHNE(hne,1);
    299 basering;
    300 kill displayring,r;
     458def RR=displayHNE(hne,1);
     459setring RR; HNE;
     460kill RR,r;
    301461ring r=0,(x,y),dp;
    302462displayHNE(develop(x));
    … …  
    304464displayHNE(develop(1));
    305465// ------------ test of displayInvariants: ------------
    306 list hne=reddevelop((x2+y3+y4)*(x+y2+y3-y4)*(x5+y7));
    307 displayInvariants(hne[1]);
    308 displayInvariants(hne[2]);
    309 displayInvariants(hne);
    310 kill HNEring;
     466list L=hnexpansion((x2+y3+y4)*(x+y2+y3-y4)*(x5+y7));
     467displayInvariants(L[1]);
     468displayInvariants(L[2]);
     469displayInvariants(L);
    311470// ------------ test of is_irred: ---------------------
    312 setring r;
    313471is_irred(x);
    314472is_irred(x2);
    … …  
    316474is_irred((x+y)*(x+y+xy)); // one of two HNEs found
    317475is_irred(x2+y2);          // no HNE found
    318 is_irred(1+x+y);          // not a curve
     476is_irred(1+x+y);          // unit
    319477// ----------------------------------------------------------------------------
    320 // ------- test of invariants, intersection, stripHNE, puiseux2generators,  ---
     478// ------- test of invariants, delta, intersection, puiseux2generators,     ---
    321479// -------         multiplicities, newtonpoly                               ---
     480example delta;
    322481example invariants;
    323 setring r;
    324 list hne=reddevelop((x2-y3)*(x2+y3));
    325 intersection(hne[1],hne[2]);
    326 example stripHNE;
     482poly f=(x2-y3+y5)*(x2+y3-y5);
     483L=hnexpansion(f);
     484delta(f);
     485delta(L);
     486intersection(L[1],L[2]);
    327487puiseux2generators(intvec(3,7,15,31,63,127),intvec(2,2,2,2,2,2));
    328 setring r;
    329 multiplicities(develop(x5+y7));
    330488example newtonpoly;
    331489// ------- test of getnm, T_Transform, T1_Transform, T2_Transform, koeff, -----
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