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D.15.33.2 modBorder

Procedure from library rstandard.lib (see rstandard_lib).

Usage:
modBorder(I,i); I is an ideal, i an integer.

Return:
ideal, a border basis for I using modular methods.

Purpose:
Computes a border basis for the ideal given by the generators in I using modular techniques.
If second argument is 0 then the result is not verified.

Example:
 
LIB "rstandard.lib";
ring R=0,(x,y,z),ds;
poly f=x3y+x5+x3y2+2x2y3+x2yz2+xy5+x12+y16+z20;
ideal i= jacob(f);
i=i,f;
ideal j=modBorder(i,1);  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]=y6z17-14/5y4z19
==> j[10]=xy5z17
==> j[11]=y7z16-1/2y5z18
==> j[12]=xy6z16
==> j[13]=y8z15-2/5y4z19
==> j[14]=y9z14
==> j[15]=xy8z14
==> j[16]=z22
==> j[17]=yz21+10/13y4z19
==> j[18]=xz21
==> j[19]=y2z20
==> j[20]=xyz20
==> j[21]=xy2z19+y4z19-1/3y5z19
==> j[22]=xy3z18+1/4y5z18
==> j[23]=xy4z17+1/4y6z17-1/2y4z19+37/52y5z19
==> j[24]=xy5z16
==> j[25]=y7z15-1/2y5z17+y3z19-37/26y4z19
==> j[26]=xy6z15
==> j[27]=xy7z14
==> j[28]=y9z13
==> j[29]=xy8z13
==> j[30]=xz20+17/12z22
==> j[31]=xyz19+y3z19+17/12yz21-1/3y4z19+37/78y5z19
==> j[32]=xy2z18-y8z14+1/2y6z16
==> j[33]=xy3z17+1/4y5z17-1/2y3z19+37/52y4z19
==> j[34]=xy4z16+1/2y8z14
==> j[35]=xy5z15
==> j[36]=xy6z14
==> j[37]=xy7z13
==> j[38]=y9z12
==> j[39]=xy8z12
==> j[40]=xz19+y2z19+17/12z21-1/3y3z19+37/78y4z19
==> j[41]=xyz18-y7z14+1/2y5z16
==> j[42]=x2z18-5/2y8z14
==> j[43]=xy2z17-y8z13+1/2y6z15
==> j[44]=xy3z16+1/2y7z14
==> j[45]=xy4z15+1/2y8z13
==> j[46]=xy5z14
==> j[47]=xy6z13
==> j[48]=xy7z12
==> j[49]=y9z11
==> j[50]=xy8z11
==> j[51]=xyz17-y7z13+1/2y5z15
==> j[52]=x2z17-5/2y8z13
==> j[53]=xy2z16-y8z12+1/2y6z14
==> j[54]=xy3z15+1/2y7z13
==> j[55]=xy4z14+1/2y8z12
==> j[56]=xy5z13
==> j[57]=xy6z12
==> j[58]=xy7z11
==> j[59]=y9z10
==> j[60]=xy8z10
==> j[61]=xyz16-y7z12+1/2y5z14
==> j[62]=x2z16-5/2y8z12
==> j[63]=xy2z15-y8z11+1/2y6z13
==> j[64]=xy3z14+1/2y7z12
==> j[65]=xy4z13+1/2y8z11
==> j[66]=xy5z12
==> j[67]=xy6z11
==> j[68]=xy7z10
==> j[69]=y9z9
==> j[70]=xy8z9
==> j[71]=xyz15-y7z11+1/2y5z13
==> j[72]=x2z15-5/2y8z11
==> j[73]=xy2z14-y8z10+1/2y6z12
==> j[74]=xy3z13+1/2y7z11
==> j[75]=xy4z12+1/2y8z10
==> j[76]=xy5z11
==> j[77]=xy6z10
==> j[78]=xy7z9
==> j[79]=y9z8
==> j[80]=xy8z8
==> j[81]=xyz14-y7z10+1/2y5z12
==> j[82]=x2z14-5/2y8z10
==> j[83]=xy2z13-y8z9+1/2y6z11
==> j[84]=xy3z12+1/2y7z10
==> j[85]=xy4z11+1/2y8z9
==> j[86]=xy5z10
==> j[87]=xy6z9
==> j[88]=xy7z8
==> j[89]=y9z7
==> j[90]=xy8z7
==> j[91]=xyz13-y7z9+1/2y5z11
==> j[92]=x2z13-5/2y8z9
==> j[93]=xy2z12-y8z8+1/2y6z10
==> j[94]=xy3z11+1/2y7z9
==> j[95]=xy4z10+1/2y8z8
==> j[96]=xy5z9
==> j[97]=xy6z8
==> j[98]=xy7z7
==> j[99]=y9z6
==> j[100]=xy8z6
==> j[101]=xyz12-y7z8+1/2y5z10
==> j[102]=x2z12-5/2y8z8
==> j[103]=xy2z11-y8z7+1/2y6z9
==> j[104]=xy3z10+1/2y7z8
==> j[105]=xy4z9+1/2y8z7
==> j[106]=xy5z8
==> j[107]=xy6z7
==> j[108]=xy7z6
==> j[109]=y9z5
==> j[110]=xy8z5
==> j[111]=xyz11-y7z7+1/2y5z9
==> j[112]=x2z11-5/2y8z7
==> j[113]=xy2z10-y8z6+1/2y6z8
==> j[114]=xy3z9+1/2y7z7
==> j[115]=xy4z8+1/2y8z6
==> j[116]=xy5z7
==> j[117]=xy6z6
==> j[118]=xy7z5
==> j[119]=y9z4
==> j[120]=xy8z4
==> j[121]=xyz10-y7z6+1/2y5z8
==> j[122]=x2z10-5/2y8z6-13/3z24
==> j[123]=xy2z9-y8z5+1/2y6z7
==> j[124]=xy3z8+1/2y7z6
==> j[125]=xy4z7+1/2y8z5
==> j[126]=xy5z6
==> j[127]=xy6z5
==> j[128]=xy7z4
==> j[129]=y9z3-13yz23
==> j[130]=xy8z3
==> j[131]=xyz9-y7z5+1/2y5z7
==> j[132]=x2z9-5/2y8z5-13/3z23-10/3y3z21
==> j[133]=xy2z8-y8z4+1/2y6z6
==> j[134]=xy3z7+1/2y7z5
==> j[135]=xy4z6+1/2y8z4
==> j[136]=xy5z5-13y3z21+13/2yz23
==> j[137]=xy6z4+13/2y2z22
==> j[138]=xy7z3
==> j[139]=y9z2-13yz22
==> j[140]=xy8z2
==> j[141]=xyz8-y7z4+1/2y5z6-10y2z22-5/6z24
==> j[142]=x2z8-5/2y8z4-13/3z22-10/3y3z20+185/39y4z20
==> j[143]=xy2z7-y8z3+1/2y6z5-10y3z21-99/2yz23
==> j[144]=xy3z6+1/2y7z4-99/2y2z22
==> j[145]=xy4z5+1/2y8z3-99/2y3z21
==> j[146]=xy5z4+13/2yz22-99/2y4z20
==> j[147]=xy6z3-10y3z21-287/6yz23
==> j[148]=xy7z2-10y4z20-287/6y2z22
==> j[149]=y9z-13yz21
==> j[150]=xy8z-10y5z19-287/6y3z21
==> j[151]=xyz7-y7z3+1/2y5z5-10y2z21-5/6z23+155/3y3z21
==> j[152]=x2z7-5/2y8z3-13/3z21-10/3y3z19+185/39y4z19
==> j[153]=xy2z6-y8z2+1/2y6z4-10y3z20-99/2yz22+185/13y4z20
==> j[154]=x2yz6-13/4yz22+99/4y4z20-197/6y2z22+85/72z24
==> j[155]=x3z6+13/3z22+10/3y3z20-185/39y4z20-39y2z22
==> j[156]=xy3z5+1/2y7z3-99/2y2z21+195/2yz23
==> j[157]=xy4z4+1/2y8z2-99/2y3z20+195/2y2z22
==> j[158]=xy5z3-10y2z21+5/6z23+10/3y3z21+141/2yz23
==> j[159]=xy6z2-10y3z20-287/6yz22-1330/39y4z20+141/2y2z22
==> j[160]=xy7z-10y4z19-287/6y2z21-1330/39y5z19+141/2y3z21
==> j[161]=y9-13yz20
==> j[162]=xy8+13y2z20+15y3z20+141/2y4z20+351/4y2z22
==> j[163]=xyz6-y7z2+1/2y5z4-10y2z20-5/6z22+155/3y3z20-1505/78y4z20
==> j[164]=xy2z5-y8z+1/2y6z3-10y3z19-99/2yz21+185/13y4z19
==> j[165]=x2yz5-5/6xz21-10y8z15+5y6z17-10y4z19-257/6y2z21-5/12z23-155/6y7z17\
   -1330/39y5z19+413/6y3z21-141/4yz23
==> j[166]=x3z5+13/3z21+10/3y3z19-185/39y4z19-39y2z21-30y5z19-377/2y3z21-198y\
   z23
==> j[167]=xy3z4+1/2y7z2-99/2y2z20+195/2yz22+30z24
==> j[168]=xy4z3+1/2y8z+5y3z19+69/4yz21-185/26y4z19-15/2y2z21-325/8yz23
==> j[169]=xy5z2-10y2z20+5/6z22+10/3y3z20+141/2yz22+1930/39y4z20
==> j[170]=xy6z-10y3z19-287/6yz21-1330/39y4z19+141/2y2z21+5365/78y5z19
==> j[171]=xy7+13yz20+15y2z20+141/2y3z20-5/2xz22+351/4yz22-30y8z16+15y6z18+17\
   7/4y4z20+2245/8y2z22
==> j[172]=xyz5-y7z+1/2y5z3-10y2z19-5/6z21+155/3y3z19-1505/78y4z19
==> j[173]=xy2z4-y8+1/2y6z2-3x2z6+15/2y8z2+13z20-99/2yz20
==> j[174]=x2yz4+4/3y9+5/3x2z8-10y9z2-25/6y8z4-2x2z10-25/6y9z4+5y8z6+8x2z12+5\
   0/3y9z6-20y8z8+10/3x2z14+125/18y9z8-25/3y8z10-40/3x2z16-250/9y9z10+100/3y\
   8z12-50/9x2z18-625/54y9z12-52/3yz20+125/9y8z14+200/9x2z20+218/3y2z20+5/9z\
   22+1250/27y9z14-310/9y3z20-10yz22-500/9y8z16+1505/117y4z20+250/27x2z22-94\
   /3z24
==> j[175]=x3z4+x2z6-5/2y8z2-15/2x2z8+75/4y8z4+122x2z10-75/8y9z4-305y8z6+15/2\
   x2z14+125/8y9z8-75/4y8z10-25/2x2z18-625/24y9z12+125/4y8z14+65/2z22-585/4y\
   z22+125/6x2z22+115/2y2z22-1501/3z24
==> j[176]=xy3z3+1/2y7z+5/4x2z7-25/8y8z3+5y2z19-85/12z21-155/6y3z19-15/2yz21+\
   1505/156y4z19-175/4y3z21
==> j[177]=x2y2z3-2/3y9z-49/3x2z9+5y9z3+245/6y8z5+5y9z5-4x2z13-25/3y9z7+10y8z\
   9-4x2z15-25/3y9z9+10y8z11+20/3x2z17+125/9y9z11-50/3y8z13+20/3x2z19+125/9y\
   9z13+56/3yz21-50/3y8z15-100/9x2z21-109/3y2z21+647/9z23-625/27y9z15+620/9y\
   3z21+454/3yz23
==> j[178]=xy4z2+1/2y8+3/2x2z6-15/4y8z2-25/8y9z2+5/2x2z12+125/24y9z6-25/4y8z8\
   -25/6x2z16-625/72y9z10+125/12y8z12-13/2z20+69/4yz20+125/18x2z20-15/2y2z20\
   +3125/216y9z14-625/36y8z16-175/4y4z20-25/2z24
==> j[179]=xy5z-29/2x2z7+145/4y8z3-10y2z19+191/3z21+155/3y3z19+141/2yz21-1505\
   /78y4z19
==> j[180]=xy6-3x2z6+15/2y8z2+145/4y9z2-29x2z12-725/12y9z6+145/2y8z8+145/3x2z\
   16+3625/36y9z10-725/6y8z12+13z20+15yz20-725/9x2z20+141/2y2z20-18125/108y9\
   z14+3625/18y8z16+145z24
==> j[181]=x2yz3-2x2z9-5/6y11z-15/4y9z3+5y8z5+25/4y11z3-25/2y9z5-725/12y10z5-\
   5/2y9z7-525/8x2z15-125/12y11z7+125/6y9z9+4075/36y10z9+2625/16y8z11-350/3y\
   9z11+995/8x2z19+10z21+625/36y11z11-625/18y9z13-22625/108y10z13-4975/16y8z\
   15+290/3x2z21+26/3z23+2525/6y9z15+35/2y3z21+25/18xz23-6661/12yz23
==> j[182]=x3z3+x2z5-5/2y8z-15/2x2z7+75/4y8z3+122x2z9-75/8y9z3-305y8z5+15/2x2\
   z13+125/8y9z7-75/4y8z9-25/2x2z17-625/24y9z11+125/4y8z13+65/2z21-585/4yz21\
   +125/6x2z21+115/2y2z21-1501/3z23+3125/72y9z15-1240/3y3z21-694yz23
==> j[183]=xy3z2+1/2xyz4+1/4y5z2+5/4x2z6-25/8y8z2-15/2z20-15/2yz20-175/4y3z20\
   +16475/52y4z20
==> j[184]=x2y2z2-2/3y9-49/3x2z8+5y9z2+245/6y8z4+5y9z4-4x2z12-25/3y9z6+10y8z8\
   -4x2z14-25/3y9z8+10y8z10+20/3x2z16+125/9y9z10-50/3y8z12+20/3x2z18+125/9y9\
   z12+56/3yz20-50/3y8z14-100/9x2z20-109/3y2z20+647/9z22-625/27y9z14+620/9y3\
   z20+454/3yz22+250/9y8z16+3815/117y4z20-100/9x2z22-6401/12y2z22+20z24
==> j[185]=xy4z+1/2xy2z3+1/4y6z-25/8y9z+5/2x2z11+125/24y9z5-25/4y8z7-25/6x2z1\
   5-625/72y9z9+125/12y8z11-15/2yz19+125/18x2z19-15/2y2z19+3125/216y9z13-625\
   /36y8z15-175/4y4z19-25/2z23+16475/52y5z19
==> j[186]=xy5-xyz4+y7-1/2y5z2-29/2x2z6+145/4y8z2+129/2z20+141/2yz20
==> j[187]=x2y4+3x2z6-2/3xyz6-1/3y9+2/3y7z2-1/3y5z4-y10-15/2y8z2-67/6x2z8-25/\
   6y11-145/4y9z2+145/3y10z2+335/12y8z4-41/3xyz10+5y11z2+115/24y9z4+41/3y7z6\
   -41/6y5z8+1069/12x2z12+1/4xyz12+125/18y11z4+701/12y9z6-1/4y7z8+1/8y5z10-8\
   00/9y10z6-5345/24y8z8-5x2z14+205/9xyz14-25/3y11z6+6385/72y9z8-205/9y7z10+\
   205/18y5z12+10y10z8+25/2y8z10-5705/36x2z16+153/4xyz16-625/54y11z8-3505/36\
   y9z10-153/4y7z12+153/8y5z14+4375/27y10z10+28525/72y8z12-57x2z18-1025/27xy\
   z18-13z20+125/9y11z10-70325/216y9z12+1025/27y7z14-1025/54y5z16-85/6yz20-1\
   00/3y10z12+285/2y8z14+30325/108x2z20-4855/36xyz20-69y2z20+99/2z22+3125/16\
   2y11z12+19685/108y9z14+4855/36y7z16-4855/72y5z18+611/6y3z20+119/4yz22-237\
   50/81y10z14-151625/216y8z16-2017/4y4z20+1955/9x2z22+5773/81xyz22-55/6y2z2\
   2-145z24
==> j[188]=x2yz2+xyz6-y7z2+1/2y5z4-2x2z8-25/6y9z2+5y8z4-5/3xyz10+5/3y7z6-5/6y\
   5z8+10/3x2z12+125/18y9z6-25/3y8z8+25/9xyz14-25/9y7z10+25/18y5z12-50/9x2z1\
   6-625/54y9z10+125/9y8z12-125/27xyz18+10z20+125/27y7z14-125/54y5z16+250/27\
   x2z20-10y2z20+47/6z22+3125/162y9z14+175/3y3z20-6401/12yz22-625/27y8z16-62\
   50/13y4z20+625/81xyz22-50/3z24
==> j[189]=x3z2+x2z4-5/2y8-15/2x2z6+8xyz6-8y7z2+4y5z4+75/4y8z2+122x2z8-75/8y9\
   z2-305y8z4-15/4xyz10+15/4y7z6-15/8y5z8+15/2x2z12+125/8y9z6-75/4y8z8+25/4x\
   yz14-25/4y7z10+25/8y5z12-25/2x2z16-625/24y9z10+125/4y8z12-125/12xyz18+65/\
   2z20+125/12y7z14-125/24y5z16-585/4yz20+125/6x2z20-45/2y2z20-507z22+3125/7\
   2y9z14-694yz22-625/12y8z16-525/4y4z20+625/36xyz22-75/2z24
==> j[190]=xy3z+1/2xyz3+1/4y5z+5/4x2z5-25/8y8z-15/2z19-15/2yz19-175/4y3z19+16\
   475/52y4z19
==> j[191]=x2y2z-xyz5+y7z-1/2y5z3+xy2z5-y8z+1/2y6z3-37/2x2z7+185/4y8z3+5y9z3+\
   2xyz11-2y7z7+y5z9-4x2z13-25/3y9z7+10y8z9-10/3xyz15+10/3y7z11-5/3y5z13+20/\
   3x2z17+125/9y9z11+10yz19-50/3y8z13+50/9xyz19+10y2z19+81z21-50/9y7z15+25/9\
   y5z17+581/6yz21+175/3y4z19-100/9x2z21-6401/12y2z21-625/27y9z15-16475/39y5\
   z19-175/6y3z21
==> j[192]=x2y3+xyz4-y7+1/2y5z2-xy2z4+y8-1/2y6z2+37/2x2z6-1/2xyz6-y9+1/2y7z2-\
   1/4y5z4-25/6y10-185/4y8z2-5/4x2z8+185/4y9z2-5/3xy2z8+5y10z2+115/24y8z4-5/\
   6y6z6+37/2xyz10-37/2y7z6+37/4y5z8+2xy2z10+125/18y10z4-2y8z6+y6z8-37x2z12-\
   1025/12y9z6+25/9xy2z12-25/3y10z6+1615/18y8z8+25/18y6z10-205/6xyz14+10y9z8\
   +205/6y7z10-205/12y5z12-10/3xy2z14-625/54y10z8+10/3y8z10-5/3y6z12+205/3x2\
   z16+4xyz16+625/4y9z10-4y7z12+2y5z14-125/27xy2z16+125/9y10z10-8975/54y8z12\
   -125/54y6z14-8x2z18+125/2xyz18-81z20-100/3y9z12-125/2y7z14+125/4y5z16+50/\
   9xy2z18-8yz20+3125/162y10z12+130/9y8z14+25/9y6z16-125x2z20-40/3xyz20+581/\
   6y2z20+15/2z22-30625/108y9z14+40/3y7z16-20/3y5z18+625/81xy2z20-2017/4y3z2\
   0-55/6yz22-625/27y10z14+49375/162y8z16+625/162y6z18-3125/13y4z20+80/3x2z2\
   2-6125/54xyz22+185z24
==> j[193]=x2yz+xyz5-y7z+1/2y5z3-2x2z7-25/6y9z+5y8z3-5/3xyz9+5/3y7z5-5/6y5z7+\
   10/3x2z11+125/18y9z5-25/3y8z7+25/9xyz13-25/9y7z9+25/18y5z11-50/9x2z15-625\
   /54y9z9+125/9y8z11-125/27xyz17+10z19+125/27y7z13-125/54y5z15+250/27x2z19-\
   10y2z19+47/6z21+3125/162y9z13+175/3y3z19-6401/12yz21-625/27y8z15-6250/13y\
   4z19+625/81xyz21-50/3z23-625/81y7z17+897775/2106y5z19
==> j[194]=x3z+x2z3-5/2xy2z3-5/4y6z+8xyz5-8y7z+4y5z3+122x2z7-75/8y9z-305y8z3-\
   15/4xyz9+15/4y7z5-15/8y5z7+15/2x2z11+125/8y9z5-75/4y8z7+25/4xyz13-25/4y7z\
   9+25/8y5z11-25/2x2z15-625/24y9z9+125/4y8z11-125/12xyz17+125/12y7z13-125/2\
   4y5z15-45/2yz19+125/6x2z19-45/2y2z19-507z21+3125/72y9z13-694yz21-625/12y8\
   z15-525/4y4z19+625/36xyz21-75/2z23-625/36y7z17+897775/936y5z19
==> j[195]=x2y2+4/3xy4+2/3xy2z2+1/3y6-xyz4+y7-1/2y5z2+xy2z4-y8+1/2y6z2-37/2x2\
   z6-25/6y9+185/4y8z2-5/3xyz8+5y9z2+5/3y7z4-5/6y5z6+10/3x2z10+2xyz10+125/18\
   y9z4-2y7z6+y5z8-25/3y8z6-4x2z12+25/9xyz12-25/3y9z6-25/9y7z8+25/18y5z10+10\
   y8z8-50/9x2z14-10/3xyz14-625/54y9z8+10/3y7z10-5/3y5z12+125/9y8z10+20/3x2z\
   16-125/27xyz16+125/9y9z10+125/27y7z12-125/54y5z14-50/3y8z12+250/27x2z18+5\
   0/9xyz18+81z20+3125/162y9z12-50/9y7z14+25/9y5z16+581/6yz20-625/27y8z14-10\
   0/9x2z20+625/81xyz20-6401/12y2z20-50/3z22-625/27y9z14-625/81y7z16+625/162\
   y5z18-175/6y3z20+250/9y8z16+16475/78y4z20-1250/81x2z22-250/27xyz22+50/3y2\
   z22+125/18z24
==> j[196]=x2y+4/3xy3+2/3xyz2-4/3xy4+1/3y5-2/3xy2z2-1/3y6+5/3x2z4+xyz4-y7+1/2\
   y5z2-25/6y8-2x2z6+5y8z2+47/6z20-6401/12yz20
==> j[197]=x3+x2z2-3xy4-4xy2z2-2y6+8xyz4-8y7+4y5z2+122x2z6-305y8z2-507z20-694\
   yz20
ring S=0,(x,y,z),ds;
ideal i=
3x2+6xy+3y2+6xz+6yz+3z2+3x2yz+4xy2z+y3z+4xyz2+2y2z2+yz3+10x9,
3x2+6xy+3y2+6xz+6yz+3z2+x3z+4x2yz+3xy2z+2x2z2+4xyz2+xz3+10y9,
3x2+6xy+3y2+6xz+6yz+3z2+x3y+2x2y2+xy3+4x2yz+4xy2z+3xyz2+10z9;
ideal j=modBorder(i,0);  j;
==> j[1]=z25
==> j[2]=yz24
==> j[3]=xz24
==> j[4]=yz23+1/2z24
==> j[5]=xz23+1/2z24
==> j[6]=y2z22+1/2z24
==> j[7]=xyz22-z24
==> j[8]=xz22+yz22+z23
==> j[9]=y2z21+yz22+z23
==> j[10]=xyz21-z23
==> j[11]=xz21+yz21+z22
==> j[12]=y2z20+yz21+z22
==> j[13]=xyz20-z22
==> j[14]=xz20+yz20+z21
==> j[15]=y2z19+yz20+z21
==> j[16]=xyz19-z21
==> j[17]=xz19+yz19+z20
==> j[18]=y2z18+yz19+z20
==> j[19]=xyz18-z20
==> j[20]=xz18+yz18+z19+5z24
==> j[21]=y2z17+yz18+z19-22805/228z24
==> j[22]=xyz17-z19+22235/228z24
==> j[23]=xz17+yz17+z18+5z23
==> j[24]=y2z16+yz17+z18+5yz22-22235/228z23+3371625/32z24
==> j[25]=xyz16-z18+22235/228z23-3371625/32z24
==> j[26]=y3z15-z18+13985/228yz22+40345/228z23-10114875/64z24
==> j[27]=xy2z15-yz17-16265/228yz22-9625/114z23+3371625/64z24
==> j[28]=xz16+yz16+z17+5z22-151575/8z25
==> j[29]=xyz15+y2z15+yz16+5yz21+151575/16z25
==> j[30]=y3z14+3/2y2z15+3/2yz16+1/2z17+15695/228yz21+13985/456z22-70875/32yz\
   22-70875/64z23
==> j[31]=xy2z14-1/2y2z15-3/2yz16-1/2z17-16835/228yz21-16265/456z22+70875/32y\
   z22+70875/64z23-23925/8yz24-8475z25
==> j[32]=y4z13-39/35y2z15-74/35yz16-39/35z17-114311/798yz21-126587/1596z22+7\
   0875/16yz22-7729425/224z23+14531794875/896z24+913078227343185/327712z25
==> j[33]=xy3z13-27/70y2z15+43/70yz16+43/70z17+118757/1596yz21+171239/3192z22\
   -70875/32yz22+15954975/448z23-14531794875/896z24+16875/8yz24-913076002997\
   985/327712z25
==> j[34]=xz15+yz15+z16+5z21-151575/8z24+647139375/64z25
==> j[35]=xyz14+y2z14+yz15+5yz20+23925/8yz23+43875/4z24+2581875/64yz24-161139\
   375/32z25
==> j[36]=xy2z13+y3z13+y2z14-5yz20-5z21-23925/8yz23-8475z24-2581875/64yz24+39\
   639375/16z25
==> j[37]=y4z12+2y3z13+66/35y2z14+31/35yz15-4/35z16-512487/2156y2z15-512487/2\
   156yz16-512487/2156z17-39/7yz20-2391/133z21-2562435/2156yz21-58384395/431\
   2z22-4757545125/539z23+913078227343185/327712z24
==> j[38]=xy3z12-y3z13-66/35y2z14-31/35yz15+4/35z16+512487/2156y2z15+512487/2\
   156yz16+512487/2156z17+1539/44y2z17+1539/44yz18+1539/44z19+1783836285795/\
   644268856y2z18+1783836285795/644268856yz19+1783836285795/644268856z20+885\
   28073007357027521/319763518609920y2z19+88529854546960711361/3197635186099\
   20yz20+1682172986755908082259/6075506853588480z21+35894522440957194368147\
   4561/9379729879224320y2z20+358945235557507070337397761/9379729879224320yz\
   21+358945351410929611106101761/9379729879224320z22-1183993296337111535446\
   2745569439/25753497978028068864y2z21-11839932963371115354462745569439/257\
   53497978028068864yz22-11839705647176760874321489377439/257534979780280688\
   64z23-25394944049750339148383370647597115091/5281441520340736269066240y2z\
   22-25394944037686146339164130862070407891/5281441520340736269066240yz23-4\
   82783526661007808169289544029214466729/100347388886473989112258560z24+607\
   90404318157439245757104439304404653/63296100216538326466560y2z23+42553283\
   0286858967288136190312178704571/443072701515768285265920yz24+425532831227\
   231009038234810860446064571/443072701515768285265920z25
==> j[39]=y5z11-30/17y3z13-281/119y2z14-162/119yz15+48/119z16+2562435/4312y2z\
   15+2562435/4312yz16+2562435/4312z17+8140/357yz20+354395/6783z21+823087575\
   /146608yz21+10312820775/293216z22-39639375/2176yz22+51740725336875/234572\
   8z23-7018033348175/406912yz23-5284127548508836025/757670144z24+8284893637\
   5/813824z25
==> j[40]=xy4z11-4/17y3z13+283/595y2z14+283/595yz15-172/595z16-1537461/4312y2\
   z15-1537461/4312yz16-1537461/4312z17-7695/308y2z17-7695/308yz18-7695/308z\
   19+138651579236117/11596839408y2z18+138651579236117/11596839408yz19+13865\
   1579236117/11596839408z20-343468221441132532501/159881759304960y2z19-1144\
   90058915261848327/53293919768320yz20-6526000311455684714639/3037753426794\
   240z21-5144593677760691566678033087/56278379275345920y2z20-51445939268315\
   19109391261887/56278379275345920yz21-5144594895142616274904637887/5627837\
   9275345920z22+3627895608407012040531635398575479/2832884777583087575040y2\
   z21+3627895660012610400093952514775479/2832884777583087575040yz22+3627858\
   127037742731089486684995479/2832884777583087575040z23+5538435103581237420\
   32370152966770159009/58095856723748098959728640y2z22+55384451226191142955\
   1086613084685031009/58095856723748098959728640yz23+1052764945097768538735\
   9478070358328244371/1103821277751213880234844160z24-236037126307610312471\
   2816769832032738977363/2352882197311798007869009920y2z23-2360371263410045\
   541420064114319234558146963/2352882197311798007869009920yz24-236037127126\
   9986214398575515181159354596963/2352882197311798007869009920z25
==> j[41]=y6z10+5/17y3z13+78/119y2z14+78/119yz15-76/119z16-3144177/4312y2z15-\
   3144177/4312yz16-3144177/4312z17-224784485505/27415696y2z16-224784485505/\
   27415696yz17-224784485505/27415696z18+905/102y2z19-22615/714yz20-982945/1\
   3566z21+1707075/6358y2z20-28178653005/2492336yz21-225664791885/4984672z22\
   +2959284375/50864y2z21+15755169377925/219325568yz22-11858851351097775/438\
   651136z23-7018033348175/406912y2z22+7017602247725/203456yz23+135295933123\
   426897775/16668743168z24+82848936375/813824yz24+84313420234986172275/8773\
   02272z25
==> j[42]=y7z9+232/187y3z13+348/187y2z14+161/187yz15+116/187z16+41553/88y2z15\
   +41553/88yz16+41553/88z17+224784485505/7833056y2z16+224784485505/7833056y\
   z17+224784485505/7833056z18-6335/204y2z19+23735/2244yz20+2164505/42636z21\
   -11949525/12716y2z20+61166745/4624yz21+3255739515/101728z22-20714990625/1\
   01728y2z21-5776123043025/31332224yz22+1091771632434825/62664448z23+491262\
   33437225/813824y2z22-518138647897925/8952064yz23-19039203360789066725/476\
   2498048z24-579942554625/1627648yz24-84313483905069969525/250657792z25
==> j[43]=xy6z9-287/187y3z13-3294/1309y2z14-1985/1309yz15+24/1309z16+138510/5\
   39y2z15+138510/539yz16+138510/539z17-5619530958681/274156960y2z16-5619530\
   958681/274156960yz17-5619530958681/274156960z18+55065933/94864y2z17+55065\
   933/94864yz18+55065933/94864z19+1268013093957594703/5102609339520y2z18+12\
   68013093957594703/5102609339520yz19+1268013093957594703/5102609339520z20-\
   4537974201958376765953/351739870470912y2z19-4537974583524928384513/351739\
   870470912yz20-86221479709574111036947/6683057538947328z21-297252011976731\
   66779851603019/96477221614878720y2z20-208076410135013504827501893133/6753\
   40551304151040yz21-208076399877019597114435653133/675340551304151040z22-1\
   31859364273680068362180579743515393/11331539110332350300160y2z21-13185936\
   4646862678804442455900758273/11331539110332350300160yz22-1318592569999424\
   03127829899163670273/11331539110332350300160z23-1132107079505260599785528\
   92632146127077/116191713447496197919457280y2z22-1132029776525334720573375\
   93911177938277/116191713447496197919457280yz23-21600015997868917857896158\
   50450350085263/2207642555502427760469688320z24-81403629820334085979337820\
   95154151224812785/2300595926260424718805254144y2z23-814036298669015297322\
   8924552632882455671377/2300595926260424718805254144yz24-81398101811343657\
   15309302705435233582313377/2300595926260424718805254144z25
==> j[44]=xz14+yz14+z15-20007/154y2z16-20007/154yz17-20007/154z18+72345504375\
   /23009602y2z17+72345504375/23009602yz18+72345504375/23009602z19+194626974\
   83358541/166543499276y2z18+19462697483358541/166543499276yz19+19463530200\
   854921/166543499276z20-1747325581279081740960867/167495176414720y2z19-174\
   7325581279081740960867/167495176414720yz20-1747325581279081740960867/1674\
   95176414720z21-181748927068776708548241721/6331317668476416y2z20-18174892\
   7068776708548241721/6331317668476416yz21-181748927068776708548241721/6331\
   317668476416z22+255497944379/45964872y2z21+17374293731923/3539295144yz22-\
   2543721707927/3539295144z23-43686743935217021/54606267936y2z22-3297778642\
   574360617/4204682631072yz23-19692354431253709867/4204682631072z24+1001031\
   91994170219675/2803121754048y2z23+7834337759610606883655/215840375061696y\
   z24+11334182244432728476300915/8201934252344448z25
==> j[45]=xyz13+y2z13+yz14+20007/308y2z16+20007/308yz17+20007/308z18-72345504\
   375/46019204y2z17-72345504375/46019204yz18-72345504375/46019204z19-194676\
   90543982939/333086998552y2z18-19466025108990179/333086998552yz19-19467690\
   543982939/333086998552z20+1747276344437119215326307/334990352829440y2z19+\
   1747276344437119215326307/334990352829440yz20+1747276344437119215326307/3\
   34990352829440z21+183080762531831017440391873/12662635336952832y2z20+1830\
   80762531831017440391873/12662635336952832yz21+183080762531831017440391873\
   /12662635336952832z22-6185472721236701869599132467/42208784456509440y2z21\
   -6185472581297108604003439667/42208784456509440yz22-618547252564369570565\
   4943667/42208784456509440z23+76656603485035046536374408146149/18234194885\
   21207808y2z22+4509211973191901828994228968597/107259969913012224yz23+4509\
   212180138292893641357016597/107259969913012224z24-99929992243390916119/56\
   06243508096y2z23-43726908580850044633313/2050483563086112yz24-56799728170\
   53308831033027/8201934252344448z25
==> j[46]=xy2z12+y3z12+y2z13-13851/308y2z16-13851/308yz17-13851/308z18-212902\
   959195/161067214y2z17-212902959195/161067214yz18-212902959195/161067214z1\
   9+998616846966128/849711731y2z18+998612598407473/849711731yz19+9986125984\
   07473/849711731z20-11056693532676714362632239/426351358146560y2z19-110566\
   93532676714362632239/426351358146560yz20-11056693532676714362632239/42635\
   1358146560z21-1335011246738121686684859577609/8332014051714963456y2z20-13\
   35011246738121686684859577609/8332014051714963456yz21-1335011246738121686\
   684859577609/8332014051714963456z22+956015234389850766925480194315737/228\
   4360519178519147520y2z21+956015227044537726414012461096537/22843605191785\
   19147520yz22+956015225048271781640819947136537/2284360519178519147520z23-\
   856169566423088808268130771154685/2735129232781811712y2z22-85616956655150\
   5671736662432527485/2735129232781811712yz23-85616957225411306700516482891\
   9485/2735129232781811712z24-2616454780091430342757593925861/1770675949597\
   040640y2z23-546835687388858541347039408042549/370071273465781493760yz24-5\
   46630752046795669658612653842549/370071273465781493760z25
==> j[47]=xy3z11+y4z11+y3z12+1539/44y2z16+1539/44yz17+1539/44z18+178383628579\
   5/644268856y2z17+1783836285795/644268856yz18+1783836285795/644268856z19+8\
   8528073007357027521/319763518609920y2z18+88528073007357027521/31976351860\
   9920yz19+88529671824950077121/319763518609920z20+358945224409571943681474\
   561/9379729879224320y2z19+358945224409571943681474561/9379729879224320yz2\
   0+358945224409571943681474561/9379729879224320z21-11839932963371115354462\
   745569439/25753497978028068864y2z20-11839932963371115354462745569439/2575\
   3497978028068864yz21-11839932963371115354462745569439/2575349797802806886\
   4z22-25394944049750339148383370647597115091/5281441520340736269066240y2z2\
   1-25394944037686146339164130862070407891/5281441520340736269066240yz22-25\
   394944031917821928666982968199623891/5281441520340736269066240z23+6079040\
   4318157439245757104439304404653/63296100216538326466560y2z22+425532830286\
   858967288136190312178704571/443072701515768285265920yz23+4255328312272310\
   09038234810860446064571/443072701515768285265920z24+318610916119077870956\
   8694408032348196203/295381801010512190177280y2z23+60536074012662401656392\
   016857729607149937/5612254219199731613368320yz24+605360700973121863328297\
   12722491635745937/5612254219199731613368320z25
==> j[48]=y5z10+5/2y4z11+55/17y3z12+40/17y2z13+29/34yz14+2/17z15-438615/12716\
   y3z13-1315845/25432y2z14-1315845/25432yz15-438615/25432z16+905/102yz19+74\
   5/102z20+1707075/6358yz20+13407525/50864z21+2959284375/50864yz21+29592843\
   75/101728z22-7018033348175/406912yz22-7019757749975/813824z23+82848936375\
   /813824z24
==> j[49]=xy4z10-3/2y4z11-55/17y3z12-40/17y2z13-29/34yz14-2/17z15+438615/1271\
   6y3z13+1315845/25432y2z14+1315845/25432yz15+438615/25432z16-1425/4y3z15-3\
   44565/616y2z16-344565/616yz17-125115/616z18+326291051227861/1420021152y3z\
   16+29488177944937/82686912y2z17+29488177944937/82686912yz18+1765208046099\
   8593/139162072896z19-2919587284209915419/311457972672y3z17-25915504302827\
   67405131/159881759304960y2z18-2591551049432717654731/159881759304960yz19-\
   69755114392691981339/10205218679040z20+62690113280941969250008817/3261587\
   8898211840y3z18-1802121862501495957160131373/20356009525125120y2z19-18021\
   21867966930836069059373/20356009525125120yz20-370879876197150176879180759\
   27/410028191863234560z21+2048528851575268972865362037/304958467698280704y\
   3z19+62159480857280354403330148735107703/48159041218912488775680y2z20+621\
   59478055371377639633181799107703/48159041218912488775680yz21+618359757800\
   85099545286767294224663/48159041218912488775680z22+4851369465814122351289\
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==> j[56]=xyz12+y2z12+yz13+3325/14382y4z12+3325/7191y3z13+1045/2397y2z14+2945\
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==> j[57]=xy2z11+y3z11+y2z12-3325/14382y4z12-3325/7191y3z13-1045/2397y2z14-29\
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==> j[90]=xy8z3+y9z3+y8z4+44/3y7z7+22000/423y6z8+12694/141y5z9+4440/47y4z10+5\
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==> j[91]=xy9z2+y10z2+y9z3-44/3y7z7-22000/423y6z8-12694/141y5z9-4440/47y4z10-\
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==> j[92]=y11z+11/2y10z2+35/2y9z3+75/2y8z4+45y7z5+21y6z6-21y5z7-45y4z8-75/2y3\
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==> j[93]=xy10z-9/2y10z2-35/2y9z3-75/2y8z4-45y7z5-21y6z6+21y5z7+45y4z8+75/2y3\
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==> j[160]=x2+2xy+y2+2xz+2yz+z2-2/3xy2z-2/3y3z-2/3xyz2-4/3y2z2-2/3yz3-1/3xy2z\
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   5/3102y4z10+1845502865/198y3z11+4126709415/1034y2z12+3701280965/3102yz13+\
   947136845/4653z14-4520669493739885/850270608y6z9+85503196850075525/623531\
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   0/81yz17+162175/162z18+548903525/141yz18-3026775025/846z19+27820127662598\
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   551225/10278113098176yz20+14530392406701081768114725/781136595461376z21-1\
   43805121095377365823474118475/4455371692631552yz21-1168361866569917419774\
   687429825/53464460311578624z22-58813484594869708628716919721625/219124031\
   9735808yz22-5298255598048491212044632289975509125/103934910845708845056z2\
   3+13773306630404801119508893030689754375/2887080856825245696z24
See also: borderBasis.