Singular

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
==> j[18]=xz21
==> j[19]=y2z20
==> j[20]=xyz20
==> j[21]=xy2z19+y4z19
==> j[22]=xy3z18+8001y5z18
==> j[23]=xy4z17-12801y4z19
==> j[24]=xy5z16
==> j[25]=y7z15+16001y5z17+y3z19+6153y4z19
==> j[26]=xy6z15
==> j[27]=xy7z14
==> j[28]=y9z13
==> j[29]=xy8z13
==> j[30]=xz20
==> j[31]=xyz19+y3z19+6153y4z19
==> j[32]=xy2z18-y8z14-16001y6z16
==> j[33]=xy3z17+8001y5z17+16001y3z19+12925y4z19
==> j[34]=xy4z16-16001y8z14
==> j[35]=xy5z15
==> j[36]=xy6z14
==> j[37]=xy7z13
==> j[38]=y9z12
==> j[39]=xy8z12
==> j[40]=xz19+y2z19+13336z21-10668y3z19-2051y4z19
==> 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
==> 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
==> j[130]=xy8z3
==> j[131]=xyz9-y7z5-16001y5z7
==> j[132]=x2z9+15999y8z5
==> j[133]=xy2z8-y8z4-16001y6z6
==> j[134]=xy3z7-16001y7z5
==> j[135]=xy4z6-16001y8z4
==> j[136]=xy5z5
==> j[137]=xy6z4
==> j[138]=xy7z3
==> j[139]=y9z2
==> j[140]=xy8z2
==> j[141]=xyz8-y7z4-16001y5z6
==> j[142]=x2z8+15999y8z4
==> j[143]=xy2z7-y8z3-16001y6z5
==> j[144]=xy3z6-16001y7z4
==> j[145]=xy4z5-16001y8z3
==> j[146]=xy5z4
==> j[147]=xy6z3
==> j[148]=xy7z2
==> j[149]=y9z+10y4z19
==> j[150]=xy8z
==> j[151]=xyz7-y7z3-16001y5z5
==> j[152]=x2z7+15999y8z3-10672z21-10671y3z19+11493y4z19
==> j[153]=xy2z6-y8z2-16001y6z4
==> j[154]=x2yz6
==> j[155]=x3z6
==> j[156]=xy3z5-16001y7z3
==> j[157]=xy4z4-16001y8z2
==> j[158]=xy5z3
==> j[159]=xy6z2
==> j[160]=xy7z-10y4z19
==> j[161]=y9-13yz20
==> j[162]=xy8
==> j[163]=xyz6-y7z2-16001y5z4
==> j[164]=xy2z5-y8z-16001y6z3-10y3z19-7333y4z19
==> j[165]=x2yz5
==> j[166]=x3z5+10672z21+10671y3z19-11493y4z19
==> j[167]=xy3z4-16001y7z2
==> j[168]=xy4z3-16001y8z+5y3z19-14791y4z19
==> j[169]=xy5z2
==> j[170]=xy6z-10y3z19+7388y4z19
==> j[171]=xy7+13yz20
==> j[172]=xyz5-y7z-16001y5z3-10y2z19+5333z21-10616y3z19+391y4z19
==> j[173]=xy2z4-y8-16001y6z2-3x2z6-15994y8z2+13z20+15952yz20
==> j[174]=x2yz4
==> j[175]=x3z4+x2z6+15999y8z2
==> j[176]=xy3z3-16001y7z+5y2z19+10666z21+10646y3z19-9017y4z19
==> j[177]=x2y2z3-7393y4z19
==> j[178]=xy4z2-16001y8-16000x2z6+7997y8z2+15995z20+8018yz20
==> j[179]=xy5z-10y2z19-5333z21+10671y3z19-11493y4z19
==> j[180]=xy6-3x2z6-15994y8z2+13z20+15yz20
==> j[181]=x2yz3+10z21
==> j[182]=x3z3+x2z5+15999y8z-25y3z19-9699y4z19
==> j[183]=xy3z2-16001xyz4+8001y5z2+8002x2z6+11998y8z2+15994z20+15994yz20
==> j[184]=x2y2z2+10yz20
==> j[185]=xy4z-16001xy2z3+8001y6z+15994yz19+15994y2z19+15989y4z19
==> j[186]=xy5-xyz4+y7+16001y5z2+15987x2z6+8037y8z2-15937z20-15931yz20
==> j[187]=x2y4+3x2z6+15994y8z2-13z20+15983yz20
==> j[188]=x2yz2+10z20
==> j[189]=x3z2+x2z4+15999y8+15994x2z6-7982y8z2-15969z20-8147yz20
==> j[190]=xy3z-16001xyz3+8001y5z+8002x2z5+11998y8z+15994z19+15994yz19+7957y3\
   z19+14472y4z19
==> j[191]=x2y2z+10yz19
==> j[192]=x2y3+xyz4-y7-16001y5z2-15986x2z6+7962y8z2-68z20+15931yz20
==> j[193]=x2yz+10z19
==> j[194]=x3z+x2z3+15999xy2z3-8002y6z+15979yz19-15944y2z19+10696z21+10661y3z\
   19+7047y4z19
==> j[195]=x2y2+10669xy4-10667xy2z2+10668y6-xyz4+y7+16001y5z2+15986x2z6-7962y\
   8z2+68z20+5426yz20
==> j[196]=x2y+10669xy3-10667xyz2-10669xy4+10668y5+10667xy2z2-10668y6-10666x2\
   z4+xyz4-y7-16001y5z2-5338y8-2x2z6+5y8z2-5326z20-13868yz20
==> j[197]=x3+x2z2-3xy4-4xy2z2-2y6+8xyz4-8y7+4y5z2+122x2z6-305y8z2-507z20-694\
   yz20