|
|
D.15.33.1 borderBasis
Procedure from library rstandard.lib (see rstandard_lib).
- Usage:
- borderBasis(I); I is an ideal.
- Return:
- ideal, a border basis for I.
- Purpose:
- Computes a border basis for the ideal given by the generators in I.
Example:
| | LIB "rstandard.lib";
ring R=32003,(x,y,z),ds;
poly f=x3y+x5+x3y2+2x2y3+x2yz2+xy5+x12+y16+z20;
ideal i= jacob(f);
i=i,f;
ideal j=borderBasis(i); j;
==> j[1]=y4z20
==> j[2]=y5z19
==> j[3]=xy4z19
==> j[4]=y6z18
==> j[5]=xy5z18
==> j[6]=y3z20
==> j[7]=xy3z19
==> j[8]=xy4z18
==> j[9]=y6z17-12804y4z19
==> j[10]=xy5z17
==> j[11]=y7z16+16001y5z18
==> j[12]=xy6z16
==> j[13]=y8z15-6401y4z19
==> j[14]=y9z14
==> j[15]=xy8z14
==> j[16]=z22
==> j[17]=yz21-2461y4z19-6336y5z19
==> j[18]=xz21+7364y5z19
==> j[19]=y2z20
==> j[20]=xyz20-2178z24
==> j[21]=xy2z19+y4z19-3742z23+3141y5z19
==> j[22]=xy3z18+8001y5z18+8282z24
==> j[23]=xy4z17+8001y6z17+16001y4z19+1871z23+14431y5z19
==> j[24]=xy5z16
==> j[25]=y7z15+16001y5z17+y3z19+6153y4z19-1510z23+5835y5z19
==> j[26]=xy6z15
==> j[27]=xy7z14
==> j[28]=y9z13
==> j[29]=xy8z13
==> j[30]=xz20+5047z22-12685yz22+14070y6z18-3219z24
==> j[31]=xyz19+y3z19+13336yz21-10668y4z19-1025z23-3141y5z19+12930yz23
==> j[32]=xy2z18-y8z14-16001y6z16
==> j[33]=xy3z17+8001y5z17+16001y3z19-6668yz21+5334y4z19-15489z23-14431y5z19-\
6465yz23
==> j[34]=xy4z16-16001y8z14
==> j[35]=xy5z15
==> j[36]=xy6z14
==> j[37]=xy7z13
==> j[38]=y9z12
==> j[39]=xy8z12
==> j[40]=xz19+y2z19+13336z21-10668y3z19-13486yz21+14070y6z17-7509y4z19+3931z\
23-7282y5z19+14267yz23
==> j[41]=xyz18-y7z14-16001y5z16
==> j[42]=x2z18+15999y8z14
==> j[43]=xy2z17-y8z13-16001y6z15
==> j[44]=xy3z16-16001y7z14
==> j[45]=xy4z15-16001y8z13
==> j[46]=xy5z14
==> j[47]=xy6z13
==> j[48]=xy7z12
==> j[49]=y9z11
==> j[50]=xy8z11
==> j[51]=xyz17-y7z13-16001y5z15
==> j[52]=x2z17+15999y8z13
==> j[53]=xy2z16-y8z12-16001y6z14
==> j[54]=xy3z15-16001y7z13
==> j[55]=xy4z14-16001y8z12
==> j[56]=xy5z13
==> j[57]=xy6z12
==> j[58]=xy7z11
==> j[59]=y9z10
==> j[60]=xy8z10
==> j[61]=xyz16-y7z12-16001y5z14
==> j[62]=x2z16+15999y8z12
==> j[63]=xy2z15-y8z11-16001y6z13
==> j[64]=xy3z14-16001y7z12
==> j[65]=xy4z13-16001y8z11
==> j[66]=xy5z12
==> j[67]=xy6z11
==> j[68]=xy7z10
==> j[69]=y9z9
==> j[70]=xy8z9
==> j[71]=xyz15-y7z11-16001y5z13
==> j[72]=x2z15+15999y8z11
==> j[73]=xy2z14-y8z10-16001y6z12
==> j[74]=xy3z13-16001y7z11
==> j[75]=xy4z12-16001y8z10
==> j[76]=xy5z11
==> j[77]=xy6z10
==> j[78]=xy7z9
==> j[79]=y9z8
==> j[80]=xy8z8
==> j[81]=xyz14-y7z10-16001y5z12
==> j[82]=x2z14+15999y8z10
==> j[83]=xy2z13-y8z9-16001y6z11
==> j[84]=xy3z12-16001y7z10
==> j[85]=xy4z11-16001y8z9
==> j[86]=xy5z10
==> j[87]=xy6z9
==> j[88]=xy7z8
==> j[89]=y9z7
==> j[90]=xy8z7
==> j[91]=xyz13-y7z9-16001y5z11
==> j[92]=x2z13+15999y8z9
==> j[93]=xy2z12-y8z8-16001y6z10
==> j[94]=xy3z11-16001y7z9
==> j[95]=xy4z10-16001y8z8
==> j[96]=xy5z9
==> j[97]=xy6z8
==> j[98]=xy7z7
==> j[99]=y9z6
==> j[100]=xy8z6
==> j[101]=xyz12-y7z8-16001y5z10
==> j[102]=x2z12+15999y8z8
==> j[103]=xy2z11-y8z7-16001y6z9
==> j[104]=xy3z10-16001y7z8
==> j[105]=xy4z9-16001y8z7
==> j[106]=xy5z8
==> j[107]=xy6z7
==> j[108]=xy7z6
==> j[109]=y9z5
==> j[110]=xy8z5
==> j[111]=xyz11-y7z7-16001y5z9
==> j[112]=x2z11+15999y8z7
==> j[113]=xy2z10-y8z6-16001y6z8
==> j[114]=xy3z9-16001y7z7
==> j[115]=xy4z8-16001y8z6
==> j[116]=xy5z7
==> j[117]=xy6z6
==> j[118]=xy7z5
==> j[119]=y9z4
==> j[120]=xy8z4
==> j[121]=xyz10-y7z6-16001y5z8
==> j[122]=x2z10+15999y8z6-10672z24
==> j[123]=xy2z9-y8z5-16001y6z7
==> j[124]=xy3z8-16001y7z6
==> j[125]=xy4z7-16001y8z5
==> j[126]=xy5z6
==> j[127]=xy6z5
==> j[128]=xy7z4
==> j[129]=y9z3-13yz23
==> j[130]=xy8z3
==> j[131]=xyz9-y7z5-16001y5z7
==> j[132]=x2z9+15999y8z5-10672z23-10671y3z21-6848yz23
==> j[133]=xy2z8-y8z4-16001y6z6
==> j[134]=xy3z7-16001y7z5
==> j[135]=xy4z6-16001y8z4
==> j[136]=xy5z5
==> j[137]=xy6z4
==> j[138]=xy7z3+8004yz23
==> j[139]=y9z2-13yz22-15947y2z22+10666z24
==> j[140]=xy8z2+8004y2z22
==> j[141]=xyz8-y7z4-16001y5z6-10y2z22+5333z24
==> j[142]=x2z8+15999y8z4-10672z22-10671y3z20-6848yz22+12688y6z18-11084y4z20-\
14680y2z22-7035z24
==> j[143]=xy2z7-y8z3-16001y6z5-10y3z21-5550yz23
==> j[144]=xy3z6-16001y7z4+5y2z22+10666z24
==> j[145]=xy4z5-16001y8z3+5y3z21-13234yz23
==> j[146]=xy5z4-10y2z22-5333z24
==> j[147]=xy6z3-10y3z21+6617yz23
==> j[148]=xy7z2+8004yz22+15994y4z20-4009y2z22
==> j[149]=y9z-13yz21-15947y2z21+10666z23-887y3z21-3742yz23
==> j[150]=xy8z+8004y2z21+15994y5z19-4009y3z21-15711yz23
==> j[151]=xyz7-y7z3-16001y5z5-10y2z21+5333z23-10616y3z21-4203yz23
==> j[152]=x2z7+15999y8z3-10672z21-10671y3z19-6848yz21+12688y6z17-11084y4z19-\
14680y2z21-7035z23+13095y5z19-13524y3z21-15272yz23
==> j[153]=xy2z6-y8z2-16001y6z4+10y7z16-5y5z18-202yz22+7268y4z20-14207y2z22
==> j[154]=x2yz6+10z24
==> j[155]=x3z6+10672z22+7898y7z16-3949y5z18-13434y3z20+12703yz22-99y8z16+336\
3y6z18-12983y4z20+95y2z22+7035z24
==> j[156]=xy3z5-16001y7z3+5y2z21+10666z23+7861y7z17+12071y5z19-13496y3z21+31\
22yz23
==> j[157]=xy4z4-16001y8z2-5y7z16-15999y5z18-15908yz22-3634y4z20+7096y2z22
==> j[158]=xy5z3-10y2z21-5333z23+3273y7z17+14365y5z19+13944y3z21-12333yz23
==> j[159]=xy6z2-15999y7z16-8002y5z18+15994y3z20+7954yz22-14192y4z20-3548y2z2\
2
==> j[160]=xy7z+8004yz21+15994y4z19-4009y2z21+15994y5z19+2887y3z21+5420yz23
==> j[161]=y9-13yz20-15947y2z20+10666z22-6546y7z16+3273y5z18-11792y3z20-10836\
yz22-14621y8z16-243y6z18+782y4z20+7500y2z22+9136z24
==> j[162]=xy8+13y2z20+15y3z20+11425yz22-13712y8z16+6856y6z18-39y4z20-14861y2\
z22
==> j[163]=xyz6-y7z2-16001y5z4+10354xz20+10344y2z20-6668z22+7268y3z20+1098xz2\
2-9158yz22-9948y4z20-11817y2z22-14446z24
==> j[164]=xy2z5-y8z-16001y6z3+10y7z15-5y5z17+7797xz21-202yz21+7268y4z19-6410\
y2z21+3045z23+2599y7z17+13179y5z19-7833y3z21+11027xz23-9572yz23
==> j[165]=x2yz5+10z23
==> j[166]=x3z5+10xz19+10y2z19-15983z21+308y2z21+14825y7z17-13320y5z19-15774y\
3z21+8567xz23-1580yz23
==> j[167]=xy3z4-16001y7z2+10837xz20+10842y2z20+7350z22-3634y3z20-4951xz22-11\
430yz22+4974y4z20-14110y2z22-4347z24
==> j[168]=xy4z3-16001y8z-5y7z15-15999y5z17+12103xz21-15908yz21-3634y4z19-128\
04y2z21+14479z23+14702y7z17+9412y5z19-12085y3z21+3708xz23-7337yz23
==> j[169]=xy5z2-14848xz20-14858y2z20-15700z22-8477y7z16-11763y5z18-14192y3z2\
0+5715yz22-2487y4z20-12081y2z22
==> j[170]=xy6z-15999y7z15-8002y5z17+15994y3z19+7954yz21-14192y4z19-3548y2z21\
+7620y5z19+9921y3z21+14270xz23-8292yz23
==> j[171]=xy7+13yz20+15y2z20-39y3z20+1301xz22+52yz22-15y8z16-15994y6z18+598y\
4z20+10292y2z22-11449z24
==> j[172]=xyz5-y7z-16001y5z3+10354xz19+10344y2z19-6668z21+7268y3z19+1098xz21\
-9158yz21-9948y4z19-11817y2z21-14446z23-3211y7z17+2210y5z19+5101y3z21-988\
0xz23+15179yz23
==> j[173]=xy2z4-y8-16001y6z2-3x2z6-15994y8z2+10293x2z8-9731y8z4+2153x2z10+10\
619y8z6-14606x2z12+4512y8z8+13109x2z14+15232y8z10+3573x2z16+7069y8z12+36x\
2z18+13z20+15952yz20-90y8z14+6744x2z20+15892y2z20-12600z22+2257y7z16+1487\
3y5z18+689y3z20-13569xz22+6739yz22+10754y8z16-13807y6z18-15560y4z20+15767\
x2z22+15779y2z22-1380z24
==> j[174]=x2yz4+10z22
==> j[175]=x3z4+x2z6+15999y8z2+15994x2z8-8477y9z2-11523y10z2-7982y8z4-2953x2z\
10-14969y11z2+9602y9z4-4512y12z2+10793y10z4-8619y8z6-5822x2z12-5637y13z2-\
11833y11z4-9967y9z6-264y14z2-9917y12z4+12161y10z6+14555y8z8-13880x2z14+14\
591y15z2-5675y13z4-8406y11z6+10124y9z8-10457y16z2+15719y14z4-4323y12z6+32\
79y10z8+2697y8z10+6281x2z16+8776y17z2+5145y15z4-5985y13z6+50y11z8-4282y9z\
10+9503y18z2+4394y16z4-9043y14z6+5084y12z8+3105y10z10+299y8z12+10960x2z18\
-13210y19z2-4125y17z4+1974y15z6+7328y13z8-13910y11z10+11824y9z12-13674y20\
z2+7780y18z4+2272y16z6-1343y14z8-15971y12z10+7831y10z12+4603y8z14-10272x2\
z20-15969z22-4709y21z2-6855y19z4-1496y17z6+8726y15z8+11676y13z10-3641y11z\
12+4924y9z14+10407xz22-2337yz22+15313y22z2-7295y20z4+12017y18z6-50y16z8-6\
442y14z10+2847y12z12-11415y10z14-6323y8z16-13833y4z20-4325x2z22-5195y2z22\
-14309z24
==> j[176]=xy3z3-16001y7z-11717x2z7-14240y9z+9170y10z+13291y8z3-5278x2z9+1551\
7y11z+13192y9z3+8707y12z+7781y10z3+13195y8z5-14852x2z11+8017y13z+689y11z3\
+6241y9z5-15238y14z+9766y12z3-12488y10z5+5127y8z7+8570x2z13-9502y15z-1479\
y13z3+13107y11z5-9787y9z7-15063y16z-3405y14z3+5579y12z5+3180y10z7+10578y8\
z9+9088x2z15+627y17z+10809y15z3-7213y13z5+7343y11z7+12581y9z9+1967y18z+12\
235y16z3-8688y14z5-2388y12z7-2569y10z9+9283y8z11+12165x2z17+8357y19z+1358\
6y17z3+2149y15z5-11072y13z7-1283y11z9+8280y9z11-5xz19-12702y20z+14882y18z\
3+8068y16z5+917y14z7-11430y12z9+1253y10z11-14411y8z13+11741x2z19-15908z21\
+297y21z-9237y19z3+14838y17z5+10918y15z7-7418y13z9-6211y11z11+14264y9z13-\
3634y3z19+7194xz21+13675yz21+5967y22z+1679y20z3+7488y18z5+9502y16z7-8747y\
14z9+15500y12z11+760y10z13-13351y8z15+4974y4z19+14443x2z21-8674y2z21-1876\
z23-6499y23z+5569y21z3-15539y19z5-6179y17z7+12873y15z9+7159y13z11-6648y11\
z13+7479y9z15+8626y5z19+13001y3z21-11683xz23-12890yz23
==> j[177]=x2y2z3+10yz21
==> j[178]=xy4z2-16001y8-16000x2z6+14860y9-5626y10+7997y8z2-10745x2z8+14619y1\
1-1351y9z2-3086y12+1816y10z2+10861y8z4+159x2z10+9013y13-14928y11z2+3103y9\
z4+10663y14-4475y12z2+14430y10z4+15604y8z6+14211x2z12+2545y15-6596y13z2-7\
503y11z4-13633y9z6+11570y16-9658y14z2+1736y12z4+4255y10z6+12477y8z8-13785\
x2z14-1084y17+11974y15z2-8969y13z4-2998y11z6+36y9z8+3454y18-11078y16z2+12\
734y14z4+8958y12z6-10880y10z8-13542y8z10-2333x2z16+2474y19-11844y17z2+533\
1y15z4+7274y13z6-8280y11z8+14685y9z10+11478y20-168y18z2+2721y16z4-843y14z\
6-3955y12z8+1252y10z10-10169y8z12+4608x2z18+15995z20+11357y21+11957y19z2+\
8087y17z4-9648y15z6-11775y13z8-15652y11z10-7410y9z12-10294xz20+6856yz20-1\
4711y22+13977y20z2+1815y18z4-11694y16z6-963y14z8+282y12z10+10478y10z12-11\
520y8z14-8409x2z20-15322y2z20+1878z22+4033y23-3233y21z2+811y19z4-4136y17z\
6-7728y15z8+7209y13z10+2425y11z12+6719y9z14+10006y3z20+12326xz22+12745yz2\
2+4241y24-5998y22z2+11772y20z4+6797y18z6+3565y16z8+12779y14z10-1394y12z12\
-8805y10z14+5021y8z16-12532y4z20+9864x2z22+3859y2z22+596z24
==> j[179]=xy5z+9716x2z7+7120y9z+2442y10z+7713y8z3+7898x2z9+13844y11z-12120y9\
z3+5228y12z+8977y10z3+12258y8z5-10693x2z11-15643y13z+1025y11z3+745y9z5+70\
72y14z-937y12z3+398y10z5+10731y8z7-4056x2z13-4367y15z+15093y13z3-4658y11z\
5+13044y9z7+8597y16z-4491y14z3-7051y12z5-3033y10z7+10140y8z9-14652x2z15-4\
362y17z+11162y15z3+7973y13z5+2821y11z7+13171y9z9-447y18z+14572y16z3+8896y\
14z5-13990y12z7-2271y10z9+4627y8z11-11025x2z17+5421y19z-12471y17z3+5923y1\
5z5+15345y13z7+15252y11z9+11868y9z11-15999xz19+10920y20z+15196y18z3-6362y\
16z5-13453y14z7-14581y12z9-5586y10z11+11561y8z13-5614x2z19+15994y2z19-342\
8z21+5151y21z-1239y19z3+10752y17z5-9383y15z7-4005y13z9-405y11z11+7749y9z1\
3-8477y7z15-11763y5z17-14192y3z19-3597xz21+9164yz21-4014y22z+13075y20z3+1\
4515y18z5+1127y16z7+774y14z9+5708y12z11+2922y10z13+14035y8z15-2487y4z19-8\
028x2z21+4337y2z21+10152z23+4046y23z+15539y21z3-3255y19z5+6920y17z7-13034\
y15z9-787y13z11+10352y11z13+5627y9z15+11368y5z19-10018y3z21+4927xz23-4590\
yz23
==> j[180]=xy6-3x2z6-9143y9+7510y10-15994y8z2-6233x2z8+12557y11-12352y9z2-696\
4y12-4592y10z2-419y8z4-3339x2z10+14149y13+4200y11z2+10153y9z4-1400y14-100\
50y12z2-6096y10z4-7654y8z6-2557x2z12-9777y15+12468y13z2-214y11z4-14715y9z\
6-9951y16+15265y14z2+12170y12z4+8500y10z6-9609y8z8-10223x2z14+5082y17+114\
0y15z2+15772y13z4+14693y11z6-2771y9z8-5477y18+10392y16z2-10449y14z4+6939y\
12z6-7962y10z8+9556y8z10+6319x2z16-2866y19-9916y17z2+15018y15z4-13849y13z\
6+8794y11z8-8972y9z10+9140y20-12450y18z2-14444y16z4-10127y14z6+14913y12z8\
+6683y10z10+204y8z12-9131x2z18+13z20+9369y21+11837y19z2+5132y17z4-2751y15\
z6-7281y13z8-12754y11z10-5688y9z12+13712xz20-9138yz20-8389y22+13062y20z2+\
15165y18z4+4938y16z6-11134y14z8-6219y12z10+1571y10z12+6826y8z14+10594x2z2\
0+9805y2z20+8335z22-761y23-9884y21z2+7833y19z4+14716y17z6-4971y15z8-3428y\
13z10-2523y11z12-13805y9z14-1435y3z20-802xz22+5863yz22+2186y24-10771y22z2\
+6593y20z4+2258y18z6-5077y16z8-9856y14z10-10155y12z12+3565y10z14+5518y8z1\
6-8266y4z20-1304x2z22+3576y2z22-3501z24
==> j[181]=x2yz3+10z21
==> j[182]=x3z3+x2z5+15999y8z+15994x2z7-8477y9z-11523y10z-7982y8z3-2953x2z9-1\
4969y11z+9602y9z3-4512y12z+10793y10z3-8619y8z5-5822x2z11-5637y13z-11833y1\
1z3-9967y9z5-264y14z-9917y12z3+12161y10z5+14555y8z7-13880x2z13+14591y15z-\
5675y13z3-8406y11z5+10124y9z7-10457y16z+15719y14z3-4323y12z5+3279y10z7+26\
97y8z9+6281x2z15+8776y17z+5145y15z3-5985y13z5+50y11z7-4282y9z9+9503y18z+4\
394y16z3-9043y14z5+5084y12z7+3105y10z9+299y8z11+10960x2z17-13210y19z-4125\
y17z3+1974y15z5+7328y13z7-13910y11z9+11824y9z11-13674y20z+7780y18z3+2272y\
16z5-1343y14z7-15971y12z9+7831y10z11+4603y8z13-10272x2z19-15969z21-4709y2\
1z-6855y19z3-1496y17z5+8726y15z7+11676y13z9-3641y11z11+4924y9z13+10407xz2\
1-2337yz21+15313y22z-7295y20z3+12017y18z5-50y16z7-6442y14z9+2847y12z11-11\
415y10z13-6323y8z15-13833y4z19-4325x2z21-5195y2z21-14309z23-10942y23z+125\
75y21z3-10278y19z5+14005y17z7-14264y15z9+2990y13z11-13452y11z13-10873y9z1\
5+4287y5z19+15247y3z21-11859xz23-13913yz23
==> j[183]=xy3z2-16001xyz4+8001y5z2+8002x2z6+11998y8z2-7982x2z8-10773y9z2-330\
8y10z2-12048y8z4-11143x2z10-15931y11z2+3060y9z4-8284y12z2+1787y10z4+11856\
y8z6+12704x2z12-2048y13z2-13215y11z4-14818y9z6+8034y14z2+8613y12z4-5332y1\
0z6+243y8z8+8422x2z14+12171y15z2-4138y13z4-5075y11z6+5660y9z8-717y16z2+14\
899y14z4-5394y12z6-5119y10z8+10948y8z10+10787x2z16-1460y17z2+9848y15z4+63\
50y13z6+10482y11z8-3449y9z10-6378y18z2-8066y16z4-11260y14z6-15472y12z8-12\
237y10z10-10966y8z12+15283x2z18+15994z20+735y19z2-12424y17z4-565y15z6+655\
5y13z8+8604y11z10+3178y9z12+15994yz20+13704y20z2+4428y18z4-15410y16z6+681\
1y14z8+12474y12z10+2820y10z12+9797y8z14+9014x2z20-8082z22-4460y21z2+4047y\
19z4-2202y17z6+7319y15z8+1852y13z10-6826y11z12+12571y9z14-8107y3z20+5923x\
z22-10459yz22-10546y22z2+11103y20z4+1650y18z6+12017y16z8-14408y14z10+2257\
y12z12-13187y10z14+9468y8z16-4590y4z20-7356x2z22+14075y2z22+13364z24
==> j[184]=x2y2z2+10yz20
==> j[185]=xy4z-16001xy2z3+8001y6z+3991y9z-15964y10z+1262x2z9+15889y11z-12591\
y9z3-5349y12z-12033y10z3-3155y8z5-14070x2z11+12439y13z+3991y11z3+849y9z5-\
139y14z-1830y12z3-6927y10z5+3172y8z7-7573x2z13+7374y15z+5160y13z3+3664y11\
z5-11333y9z7+644y16z-8078y14z3-9259y12z5+3611y10z7+2931y8z9+3208x2z15-108\
58y17z+12913y15z3-9002y13z5+13109y11z7-962y9z9-11523y18z+11739y16z3-2560y\
14z5-9761y12z7-13883y10z9-8020y8z11-1355x2z17+1378y19z+12511y17z3-7326y15\
z5-15492y13z7-7521y11z9+826y9z11+15994yz19-287y20z-10950y18z3+9541y16z5+4\
41y14z7-7753y12z9+5749y10z11-12614y8z13-3870x2z19+15994y2z19+11522y21z-82\
92y19z3-2163y17z5-12669y15z7-5253y13z9-8695y11z11+251y9z13+8032xz21-231y2\
2z+269y20z3+9257y18z5-9630y16z7+13650y14z9-3769y12z11+9559y10z13+9675y8z1\
5-8107y4z19-358x2z21+7757y2z21+3241z23+11735y23z+14495y21z3-12029y19z5-64\
08y17z7-11365y15z9+2532y13z11+8679y11z13+7013y9z15+8832y5z19+15593y3z21-1\
051xz23-2027yz23
==> j[186]=xy5-xyz4+y7+16001y5z2+15987x2z6-6855y9+491y10+8037y8z2-6761x2z8+12\
938y11-401y9z2+13512y12-15111y10z2+901y8z4-12870x2z10+13694y13-14081y11z2\
+1737y9z4-4653y14+754y12z2-10239y10z4+172y8z6-9543x2z12-9925y15+12511y13z\
2-6238y11z4-6113y9z6-8232y16+15683y14z2-13769y12z4-9942y10z6+7856y8z8+254\
1x2z14+185y17+7013y15z2-7429y13z4+13417y11z6+2219y9z8+13492y18-13758y16z2\
-4173y14z4-12954y12z6+12747y10z8+9649y8z10+2110x2z16-13360y19+74y17z2+213\
8y15z4+1687y13z6-5124y11z8-771y9z10-1252y20-8958y18z2+8087y16z4-2612y14z6\
-5455y12z8+14817y10z10-5275y8z12+5974x2z18-15937z20+12029y21+11677y19z2-1\
2477y17z4-7727y15z6+7062y13z8-3035y11z10-11195y9z12+2272xz20+9178yz20-895\
5y22-9252y20z2-6898y18z4-1086y16z6+11662y14z8+8940y12z10-9189y10z12-14935\
y8z14-1706x2z20-9765y2z20-9397z22+4144y23+2870y21z2+10141y19z4+4533y17z6-\
11931y15z8+4519y13z10+330y11z12+8617y9z14+6160y3z20-15601xz22+13898yz22+3\
973y24-13753y22z2+9784y20z4-2090y18z6+14813y16z8+6622y14z10-2561y12z12-14\
281y10z14+4265y8z16-14152y4z20-6465x2z22+13131y2z22+10319z24
==> j[187]=x2y4+3x2z6-14859xyz6+2285y9+14859y7z2+8572y5z4-163y10+15994y8z2-54\
04x2z8+4644xyz8-5573y11-374y9z2-4644y7z4+2322y5z6-2619y12-3959y10z2+13510\
y8z4-852x2z10-5454xyz10+6306y13+9037y11z2+7490y9z4+5454y7z6-2727y5z8+9610\
y14-6468y12z2-9744y10z4+2130y8z6+3563x2z12-3743xyz12-671y15-9910y13z2-581\
y11z4-6236y9z6+3743y7z8+14130y5z10+13774y16-15415y14z2+142y12z4+15227y10z\
6+7094y8z8-2314x2z14+15754xyz14+14126y17+7266y15z2+9346y13z4-9212y11z6+15\
657y9z8-15754y7z10+7877y5z12-5005y18+13666y16z2-841y14z4+6274y12z6-9730y1\
0z8+5785y8z10+15354x2z16-10487xyz16-5851y19-11641y17z2-2596y15z4+13317y13\
z6-9972y11z8-11609y9z10+10487y7z12+10758y5z14+848y20+3428y18z2+4521y16z4+\
2809y14z6-7804y12z8+13794y10z10-6382y8z12+10273x2z18-5627xyz18-13z20-1599\
y21-4122y19z2+6700y17z4+3981y15z6+8879y13z8-9378y11z10+9988y9z12+5627y7z1\
4+13188y5z16-13722yz20+3829y22+10232y20z2+13008y18z4-1972y16z6+12781y14z8\
+14884y12z10+8720y10z12-9681y8z14+5240x2z20-14110xyz20+3255y2z20+15990z22\
-8727y23+12184y21z2-6077y19z4-4294y17z6+9399y15z8+250y13z10-8194y11z12+71\
12y9z14+14110y7z16-7055y5z18-6027y3z20-3493yz22-13623y24-11534y22z2-12450\
y20z4-14456y18z6-12913y16z8+12256y14z10-11585y12z12+10888y10z14-13100y8z1\
6-4063y4z20-1659x2z22-4730xyz22+7837y2z22-1381z24
==> j[188]=x2yz2+10z20
==> j[189]=x3z2+x2z4+15999y8+15994x2z6+10852xyz6-10294y9-10852y7z2+5426y5z4-3\
873y10-7982y8z2-10630x2z8+8235xyz8-9089y11+10899y9z2-8235y7z4-11884y5z6+1\
5430y12+8983y10z2-5428y8z4-13226x2z10-4468xyz10-13062y13-1805y11z2+8404y9\
z4+4468y7z6-2234y5z8+10691y14-13479y12z2+7261y10z4+1062y8z6-3218x2z12+945\
7xyz12-12725y15-13315y13z2+14095y11z4+11150y9z6-9457y7z8-11273y5z10+6156y\
16+1575y14z2+9545y12z4-5484y10z6+8045y8z8-5475x2z14+1191xyz14+5420y17-289\
5y15z2+15489y13z4+5597y11z6+4928y9z8-1191y7z10-15406y5z12+14733y18+12909y\
16z2+11749y14z4-3189y12z6+4260y10z8-2314y8z10-14702x2z16-7418xyz16-12370y\
19-3359y17z2+10498y15z4+903y13z6-1662y11z8-11876y9z10+7418y7z12-3709y5z14\
+6616y20-2823y18z2-4506y16z4-6282y14z6+14670y12z8-7896y10z10+4752y8z12+24\
9x2z18-538xyz18-15969z20+7221y21-3571y19z2+6805y17z4-3538y15z6-8594y13z8+\
1262y11z10-4337y9z12+538y7z14-269y5z16-2337yz20+9549y22-8681y20z2-7886y18\
z4-9329y16z6+9118y14z8+1548y12z10-15807y10z12+15379y8z14+537x2z20-190xyz2\
0+12649y2z20-9801z22+11838y23-8226y21z2+1154y19z4+13586y17z6+13150y15z8+1\
843y13z10-11237y11z12-7612y9z14+190y7z16-95y5z18-15081y3z20-8717yz22+1079\
8y24+2788y22z2-2826y20z4+13398y18z6+2722y16z8+8381y14z10+6334y12z12+11601\
y10z14+14659y8z16-7797y4z20-11086x2z22-15472xyz22-10371y2z22-14252z24
==> j[190]=xy3z-16001xyz3+8001y5z+8002x2z5+11998y8z-7982x2z7+2608xyz7-10773y9\
z-2608y7z3+1304y5z5-3308y10z-12048y8z3-14481x2z9-14996xyz9-15931y11z-63y9\
z3+14996y7z5-7498y5z7-8284y12z+15552y10z3-11802y8z5-6848x2z11-8996xyz11-2\
048y13z-14300y11z3+13418y9z5+8996y7z7-4498y5z9+8034y14z+5158y12z3+8726y10\
z5-14883y8z7-3473x2z13-7346xyz13+12171y15z+7111y13z3-630y11z5+3959y9z7+73\
46y7z9-3673y5z11-717y16z+855y14z3-5504y12z5-413y10z7-7319y8z9-8775x2z15-1\
1409xyz15-1460y17z-367y15z3-9953y13z5+15807y11z7-7684y9z9+11409y7z11+1029\
7y5z13-6378y18z-6823y16z3-14284y14z5-5099y12z7+9265y10z9+5936y8z11+9855x2\
z17+4244xyz17+15994z19+735y19z+13453y17z3+1692y15z5-7559y13z7-12792y11z9+\
4334y9z11-4244y7z13+2122y5z15+15994yz19+13704y20z-14484y18z3+2146y16z5-13\
655y14z7-142y12z9+5277y10z11-8636y8z13-3367x2z19+820xyz19-8082z21-4460y21\
z+2021y19z3+8441y17z5-11696y15z7+4942y13z9-11701y11z11+11052y9z13-820y7z1\
5+410y5z17-8107y3z19-10459yz21-10546y22z-13478y20z3+12620y18z5-15162y16z7\
-13580y14z9+5494y12z11+328y10z13-7584y8z15-4590y4z19-3700x2z21+13047xyz21\
+14075y2z21-1404z23-905y23z-9934y21z3-12201y19z5-9760y17z7-4355y15z9-2776\
y13z11+7481y11z13+7360y9z15-13047y7z17-7094y5z19-13331y3z21-10548yz23
==> j[191]=x2y2z+10yz19
==> j[192]=x2y3+xyz4-y7-16001y5z2-4568xy2z4+4568y8-2284y6z2-2282x2z6-10457xyz\
6+11089y9+10457y7z2+10773y5z4+8652xy2z6-2808y10-2947y8z2+4326y6z4-10141x2\
z8+776xyz8+3553y11-4377y9z2-776y7z4+388y5z6+11249xy2z8-11720y12+10339y10z\
2-1898y8z4-10377y6z6+14134x2z10-10296xyz10-11716y13+4192y11z2+13917y9z4+1\
0296y7z6-5148y5z8+5840xy2z10-5761y14-15106y12z2+6380y10z4-9172y8z6+2920y6\
z8+6263x2z12+4288xyz12-9366y15+8072y13z2+10382y11z4-9257y9z6-4288y7z8+214\
4y5z10+10510xy2z12-15709y16+10786y14z2-10608y12z4-7464y10z6-10166y8z8+525\
5y6z10+10720x2z14+13091xyz14-11913y17+7752y15z2-12830y13z4+6281y11z6-1169\
4y9z8-13091y7z10-9456y5z12-12809xy2z14-10799y18-14588y16z2-12547y14z4-119\
01y12z6+6904y10z8-13991y8z10+9597y6z12-15277x2z16-1988xyz16+9895y19-5343y\
17z2-15191y15z4+1700y13z6-10298y11z8-10468y9z10+1988y7z12-994y5z14+10109x\
y2z16+7690y20-12913y18z2-287y16z4+11986y14z6+13625y12z8+5750y10z10+12082y\
8z12-10947y6z14-4970x2z18-6736xyz18+4554z20+1248y21+11100y19z2+2603y17z4-\
7082y15z6-311y13z8+13841y11z10-14179y9z12+6736y7z14-3368y5z16-3008xy2z18+\
1881yz20+15210y22+5862y20z2+10714y18z4-2396y16z6-12948y14z8-9640y12z10-30\
96y10z12+15433y8z14-1504y6z16+1438x2z20+8105xyz20+13609y2z20-3160z22+9898\
y23-8997y21z2-13013y19z4-5694y17z6+9220y15z8+1412y13z10+3020y11z12-8663y9\
z14-8105y7z16-11949y5z18+6314xy2z20+15859y3z20+1175yz22+13156y24-1849y22z\
2-10163y20z4-2279y18z6+5936y16z8+6581y14z10+11856y12z12+10570y10z14-9909y\
8z16+3157y6z18-10199y4z20+2997x2z22-13405xyz22-13576y2z22-3353z24
==> j[193]=x2yz+10z19
==> j[194]=x3z+x2z3+15999xy2z3-8002y6z+15999xyz5-15999y7z-8002y5z3+5xy2z5-5y8\
z-15999y6z3-8007x2z7+4021xyz7+12058y9z-4021y7z3-13991y5z5-135xy2z7-8302y1\
0z+4151y8z3+15934y6z5-5949x2z9-8292xyz9+1165y11z-8677y9z3+8292y7z5-4146y5\
z7+766xy2z9-7588y12z+15588y10z3-1895y8z5+383y6z7+11273x2z11+13677xyz11-15\
016y13z-15056y11z3-7290y9z5-13677y7z7-9163y5z9-10319xy2z11-1276y14z-14211\
y12z3+2083y10z5-1862y8z7+10842y6z9-13812x2z13-6478xyz13-2299y15z+13722y13\
z3-1866y11z5+14979y9z7+6478y7z9-3239y5z11+5194xy2z13+1378y16z-5180y14z3-1\
3861y12z5-15571y10z7-2667y8z9+2597y6z11+15808x2z15+569xyz15-12472y17z-132\
52y15z3+7151y13z5+15046y11z7+15520y9z9-569y7z11-15717y5z13+6864xy2z15-134\
50y18z+10173y16z3+10777y14z5-11869y12z7-4936y10z9-14381y8z11+3432y6z13-14\
579x2z17-4667xyz17-11993y19z-255y17z3+6391y15z5-13325y13z7-12712y11z9+427\
3y9z11+4667y7z13+13668y5z15+7222xy2z17+15979yz19-6582y20z+13351y18z3+8106\
y16z5+5620y14z7+2185y12z9-1027y10z11+13224y8z13+3611y6z15+4334x2z19+3693x\
yz19-15919y2z19-15944z21-12443y21z+13280y19z3+1720y17z5+5137y15z7+2614y13\
z9-15155y11z11+10714y9z13-3693y7z15-14155y5z17+1447xy2z19-165y3z19+15924y\
z21-5962y22z-2789y20z3-2147y18z5+5902y16z7+9573y14z9+1559y12z11+14140y10z\
13-12282y8z15-15278y6z17+8862y4z19-6754x2z21+7032xyz21-6627y2z21-12248z23\
-14748y23z+2698y21z3-11852y19z5-7708y17z7+3507y15z9-3873y13z11+14043y11z1\
3+12229y9z15-7032y7z17+5638y5z19+8324xy2z21+9379y3z21+6091yz23
==> j[195]=x2y2+10669xy4-10667xy2z2+10668y6-xyz4+y7+16001y5z2+4568xy2z4-4568y\
8+2284y6z2+2282x2z6+7793xyz6+10248y9-7793y7z2-12105y5z4+9624xy2z6-3294y10\
-15329y8z2+4812y6z4+3481x2z8-1471xyz8-823y11+2987y9z2+1471y7z4+15266y5z6+\
11917xy2z8+14852y12-7616y10z2-4618y8z4-10043y6z6+130x2z10+4241xyz10+9325y\
13+13443y11z2-14834y9z4-4241y7z6-13881y5z8-14268xy2z10-13116y14-4929y12z2\
-13910y10z4+13943y8z6-7134y6z8-5399x2z12-5620xyz12-1156y15-9122y13z2-1438\
y11z4-11556y9z6+5620y7z8-2810y5z10+9940xy2z12-10005y16+12622y14z2+15271y1\
2z4+13754y10z6-12444y8z8+4970y6z10-14050x2z14-14983xyz14-8023y17+1910y15z\
2+1287y13z4-13593y11z6+5219y9z8+14983y7z10+8510y5z12+5708xy2z14+10019y18+\
8998y16z2-7852y14z4-13719y12z6+14948y10z8-2586y8z10+2854y6z12+10547x2z16+\
1513xyz16-2871y19+4754y17z2-314y15z4-7032y13z6+2154y11z8-7581y9z10-1513y7\
z12-15245y5z14+2481xy2z16-6496y20+6110y18z2-9090y16z4+11089y14z6-4262y12z\
8+14170y10z10-12847y8z12-14761y6z14-12219x2z18-5810xyz18-4554z20-7053y21-\
8727y19z2-118y17z4-13641y15z6-2114y13z8+14470y11z10-5831y9z12+5810y7z14-2\
905y5z16+15840xy2z18-1881yz20-7881y22+12015y20z2-10653y18z4+13503y16z6+81\
36y14z8+4934y12z10+15074y10z12-1294y8z14+7920y6z16-800x2z20-11226xyz20-14\
443y2z20-10235z22+15457y23-13668y21z2-8384y19z4-607y17z6+13436y15z8+14157\
y13z10+11178y11z12-8124y9z14+11226y7z16-5613y5z18-10544xy2z20-640y3z20+10\
068yz22+9801y24-4968y22z2-699y20z4+733y18z6+5345y16z8+2468y14z10+2127y12z\
12+7945y10z14+12544y8z16-5272y6z18+432y4z20-10817x2z22+11518xyz22+6413y2z\
22+13778z24
==> j[196]=x2y+10669xy3-10667xyz2-10669xy4+10668y5+10667xy2z2-10668y6-10666x2\
z4+xyz4-y7-16001y5z2+760xy2z4-6098y8+380y6z2-2282x2z6+10483xyz6+15653y9-1\
0483y7z2-10760y5z4-8234xy2z6+6024y10+13939y8z2-4117y6z4+10206x2z8-6069xyz\
8+3955y11-264y9z2+6069y7z4+12967y5z6-4995xy2z8+14760y12-6752y10z2+11483y8\
z4+13504y6z6+13023x2z10+4238xyz10+3801y13-1475y11z2+15961y9z4-4238y7z6+21\
19y5z8-12540xy2z10+2594y14+3879y12z2+6052y10z4-4016y8z6-6270y6z8+10595x2z\
12-2325xyz12+7445y15+527y13z2+2880y11z4+14424y9z6+2325y7z8+14839y5z10-849\
7xy2z12-9931y16-2960y14z2+666y12z4+10706y10z6-1989y8z8+11753y6z10+10189x2\
z14+15856xyz14+7243y17-7500y15z2-695y13z4+15939y11z6-7984y9z8-15856y7z10+\
7928y5z12-1459xy2z14-2995y18-9587y16z2-742y14z4+1511y12z6-13150y10z8-8012\
y8z10+15272y6z12+7637x2z16-10181xyz16+4065y19-11557y17z2+937y15z4-6119y13\
z6+13680y11z8+14623y9z10+10181y7z12+10911y5z14+5518xy2z16+691y20-3737y18z\
2-1215y16z4+7551y14z6-11739y12z8-1193y10z10-8609y8z12+2759y6z14-9455x2z18\
+5288xyz18+4554z20+14382y21-5399y19z2+13476y17z4-6234y15z6-6884y13z8-7554\
y11z10-7945y9z12-5288y7z14+2644y5z16-7515xy2z18+1047yz20+1233y22-2677y20z\
2-3736y18z4+3747y16z6+7967y14z8+616y12z10-8879y10z12+15151y8z14+12244y6z1\
6-505x2z20-12029xyz20-2341y2z20+13521z22+7500y23+6851y21z2+4984y19z4-8732\
y17z6-9765y15z8-4488y13z10+12354y11z12-9232y9z14+12029y7z16+9987y5z18+208\
3xy2z20-9127y3z20+14772yz22-12343y24-13064y22z2-6084y20z4+252y18z6+15502y\
16z8-9188y14z10+10961y12z12+1455y10z14+15181y8z16-14960y6z18+13035y4z20-1\
2963x2z22-9931xyz22-15900y2z22+10519z24
==> j[197]=x3+x2z2-3xy4-4xy2z2+14xy5-2y6-6xyz4-36xy6+6y7-3y5z2+14xy2z4+10861x\
y7-14y8+7y6z2-15x2z6+5388xyz6-1508xy8+10801y9-5388y7z2+2694y5z4+15553xy2z\
6-2437xy9-922y10+486y8z2-8225y6z4+13470x2z8-14484xyz8+5775xy10-6245y11-13\
204y9z2+14484y7z4-7242y5z6-2154xy2z8-441xy11+13166y12-6852y10z2+482y8z4-1\
077y6z6-4207x2z10+14853xyz10+13193xy12+2118y13+4856y11z2-4807y9z4-14853y7\
z6-8575y5z8-14706xy2z10+2178xy13+13668y14+716y12z2+8351y10z4+9222y8z6-735\
3y6z8-10872x2z12+917xyz12+4365xy14-15507y15+552y13z2-846y11z4-10772y9z6-9\
17y7z8-15543y5z10-11222xy2z12+8398xy15-15571y16+3088y14z2+3802y12z4+8267y\
10z6+6399y8z8-5611y6z10-13709x2z14+10046xyz14+556xy16-11561y17-10894y15z2\
+4737y13z4+11759y11z6-12717y9z8-10046y7z10+5023y5z12+10017xy2z14+11378xy1\
7+14478y18-14088y16z2-15308y14z4+15681y12z6+15086y10z8+8254y8z10-10993y6z\
12-6888x2z16+1933xyz16+2633xy18+9709y19+14973y17z2+2174y15z4-7561y13z6+78\
27y11z8-15082y9z10-1933y7z12-15035y5z14-10741xy2z16+4827xy19-15012y20-436\
8y18z2+9086y16z4+7002y14z6-4027y12z8+15666y10z10-4042y8z12+10631y6z14-111\
69x2z18-3942xyz18+110z20+13423xy20+12191y21-2405y19z2-5129y17z4+8466y15z6\
-6233y13z8+5407y11z10+12644y9z12+3942y7z14-1971y5z16-14669xy2z18-160yz20-\
8104xy21-5338y22-14650y20z2-10783y18z4+7722y16z6-960y14z8+13323y12z10+352\
7y10z12-5413y8z14+8667y6z16-9819x2z20-15602xyz20+2695y2z20+15289z22+4685x\
y22+10477y23-9747y21z2+4355y19z4+15885y17z6-15871y15z8-5550y13z10+5111y11\
z12-3816y9z14+15602y7z16-7801y5z18+1669xy2z20+15138y3z20+7015yz22-15447xy\
23-1627y24-14810y22z2+3804y20z4-8592y18z6-15632y16z8+4483y14z10-13523y12z\
12-11734y10z14+6877y8z16-15167y6z18+4074y4z20-7327x2z22-11644xyz22-4052y2\
z22-7711z24
|
See also:
modBorder.
|
Online Manual
