# Singular

#### D.15.31.2 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 ==> j[22]=xy3z18+1/4y5z18 ==> j[23]=xy4z17+1/5y4z19 ==> 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 ==> j[31]=xyz19+y3z19-37/26y4z19 ==> 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 ==> 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 ==> j[130]=xy8z3 ==> j[131]=xyz9-y7z5+1/2y5z7 ==> j[132]=x2z9-5/2y8z5 ==> j[133]=xy2z8-y8z4+1/2y6z6 ==> j[134]=xy3z7+1/2y7z5 ==> j[135]=xy4z6+1/2y8z4 ==> j[136]=xy5z5 ==> j[137]=xy6z4 ==> j[138]=xy7z3 ==> j[139]=y9z2 ==> j[140]=xy8z2 ==> j[141]=xyz8-y7z4+1/2y5z6 ==> j[142]=x2z8-5/2y8z4 ==> j[143]=xy2z7-y8z3+1/2y6z5 ==> j[144]=xy3z6+1/2y7z4 ==> j[145]=xy4z5+1/2y8z3 ==> j[146]=xy5z4 ==> j[147]=xy6z3 ==> j[148]=xy7z2 ==> j[149]=y9z+10y4z19 ==> j[150]=xy8z ==> j[151]=xyz7-y7z3+1/2y5z5 ==> j[152]=x2z7-5/2y8z3-13/3z21-10/3y3z19+185/39y4z19 ==> j[153]=xy2z6-y8z2+1/2y6z4 ==> j[154]=x2yz6 ==> j[155]=x3z6 ==> j[156]=xy3z5+1/2y7z3 ==> j[157]=xy4z4+1/2y8z2 ==> j[158]=xy5z3 ==> j[159]=xy6z2 ==> j[160]=xy7z-10y4z19 ==> j[161]=y9-13yz20 ==> j[162]=xy8 ==> j[163]=xyz6-y7z2+1/2y5z4 ==> j[164]=xy2z5-y8z+1/2y6z3-10y3z19+680/13y4z19 ==> j[165]=x2yz5 ==> j[166]=x3z5+13/3z21+10/3y3z19-185/39y4z19 ==> j[167]=xy3z4+1/2y7z2 ==> j[168]=xy4z3+1/2y8z+5y3z19-265/13y4z19 ==> j[169]=xy5z2 ==> j[170]=xy6z-10y3z19+35/13y4z19 ==> j[171]=xy7+13yz20 ==> 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 ==> j[175]=x3z4+x2z6-5/2y8z2 ==> j[176]=xy3z3+1/2y7z+5y2z19-5/3z21-65/3y3z19+370/39y4z19 ==> j[177]=x2y2z3-100/13y4z19 ==> j[178]=xy4z2+1/2y8+3/2x2z6-15/4y8z2-13/2z20+69/4yz20 ==> j[179]=xy5z-10y2z19+5/6z21+10/3y3z19-185/39y4z19 ==> j[180]=xy6-3x2z6+15/2y8z2+13z20+15yz20 ==> j[181]=x2yz3+10z21 ==> j[182]=x3z3+x2z5-5/2y8z-25y3z19+1925/13y4z19 ==> j[183]=xy3z2+1/2xyz4+1/4y5z2+5/4x2z6-25/8y8z2-15/2z20-15/2yz20 ==> j[184]=x2y2z2+10yz20 ==> j[185]=xy4z+1/2xy2z3+1/4y6z-15/2yz19-15/2y2z19-25/2y4z19 ==> j[186]=xy5-xyz4+y7-1/2y5z2-29/2x2z6+145/4y8z2+129/2z20+141/2yz20 ==> j[187]=x2y4+3x2z6-15/2y8z2-13z20-37/2yz20 ==> j[188]=x2yz2+10z20 ==> j[189]=x3z2+x2z4-5/2y8-15/2x2z6+75/4y8z2+65/2z20-585/4yz20 ==> j[190]=xy3z+1/2xyz3+1/4y5z+5/4x2z5-25/8y8z-15/2z19-15/2yz19-175/4y3z19+16\ 475/52y4z19 ==> j[191]=x2y2z+10yz19 ==> j[192]=x2y3+xyz4-y7+1/2y5z2+31/2x2z6-155/4y8z2-68z20-141/2yz20 ==> j[193]=x2yz+10z19 ==> j[194]=x3z+x2z3-5/2xy2z3-5/4y6z-45/2yz19+115/2y2z19+85/3z21-20/3y3z19+561\ 5/78y4z19 ==> j[195]=x2y2+4/3xy4+2/3xy2z2+1/3y6-xyz4+y7-1/2y5z2-31/2x2z6+155/4y8z2+68z2\ 0+553/6yz20 ==> 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 ==> j[29]=xyz15+y2z15+yz16+5yz21 ==> 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 ==> j[32]=y4z13-39/35y2z15-74/35yz16-39/35z17-114311/798yz21-126587/1596z22+7\ 0875/16yz22-7729425/224z23+14531794875/896z24 ==> j[33]=xy3z13-27/70y2z15+43/70yz16+43/70z17+118757/1596yz21+171239/3192z22\ -70875/32yz22+15954975/448z23-14531794875/896z24 ==> j[34]=xz15+yz15+z16+5z21-151575/8z24 ==> j[35]=xyz14+y2z14+yz15+5yz20+151575/16z24 ==> j[36]=xy2z13+y3z13+y2z14-5yz20-5z21-111675/16z24 ==> 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+39/7yz20+3056/133z21+2562435/2156yz21+58384395/431\ 2z22+4757545125/539z23-913076348631735/327712z24 ==> 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\ 8z23-77611672933260075/11142208z24 ==> j[40]=xy4z11-4/17y3z13+283/595y2z14+283/595yz15-172/595z16-1537461/4312y2\ z15-1537461/4312yz16-1537461/4312z17-4366/357yz20-232454/6783z21-64884199\ 5/146608yz21-6342681915/293216z22+39639375/2176yz22-31035888952875/234572\ 8z23+46566963638175885/11142208z24 ==> j[41]=y6z10+5/17y3z13+78/119y2z14+78/119yz15-76/119z16-3144177/4312y2z15-\ 3144177/4312yz16-3144177/4312z17-4825/119yz20-183885/2261z21-1696930965/1\ 46608yz21-13353125805/293216z22+118918125/2176yz22-65428421864625/2345728\ z23+199935960229764075/22284416z24 ==> j[42]=y7z9+232/187y3z13+348/187y2z14+161/187yz15+116/187z16+41553/88y2z15\ +41553/88yz16+41553/88z17+7785/187yz20+290710/3553z21+42390135/2992yz21+1\ 97137395/5984z22-2972953125/23936yz22+977771887875/47872z23-6387511968556\ 275/909568z24 ==> j[43]=xy6z9-287/187y3z13-3294/1309y2z14-1985/1309yz15+24/1309z16+138510/5\ 39y2z15+138510/539yz16+138510/539z17-1420/1309yz20+112120/24871z21-190092\ 825/73304yz21+1846696725/146608z22+832426875/11968yz22+8758799679375/1172\ 864z23-86883916940081475/44568832z24 ==> j[44]=xz14+yz14+z15+5z20-151575/8z23+647139375/64z24 ==> j[45]=xyz13+y2z13+yz14+5yz19+23925/8yz22+43875/4z23-647139375/128z24 ==> j[46]=xy2z12+y3z12+y2z13-5yz19-5z20-23925/8yz22-8475z23+319696875/128z24 ==> j[47]=xy3z11+y4z11+y3z12+5z20+16875/8yz22+13575/2z23-155975625/128z24 ==> 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+438615/25432z16-395/102yz19-7\ 45/102z20-1707075/6358yz20-13407525/50864z21-2959284375/50864yz21-2959284\ 375/101728z22+7017533609375/406912yz22+7015637765975/813824z23+3391275498\ 75/813824z24 ==> j[50]=xy5z9+y6z9-5/2y4z11-55/17y3z12-40/17y2z13-29/34yz14-2/17z15+438615/\ 12716y3z13+1315845/25432y2z14+1315845/25432yz15+438615/25432z16-1415/102y\ z19-1255/102z20-1707075/6358yz20-13407525/50864z21-2959284375/50864yz21-2\ 959284375/101728z22+7018189754975/406912yz22+7022473887575/813824z23-1707\ 20470125/813824z24 ==> j[51]=y7z8+7/2y6z9-35/4y4z11-2848/187y3z12-4617/374y2z13-3437/748yz14-115\ /187z15+58551255/279752y3z13+175653765/559504y2z14+175653765/559504yz15+5\ 8551255/559504z16-38545/748yz19-34055/748z20-107445825/69938yz20-17378354\ 25/1119008z21-443675323125/1119008yz21-443675323125/2238016z22+5625720982\ 51725/8952064yz22+562790878490325/17904128z23-4547863128375/17904128z24 ==> j[52]=xy6z8-5/2y6z9+35/4y4z11+2848/187y3z12+4617/374y2z13+3437/748yz14+11\ 5/187z15-58551255/279752y3z13-175653765/559504y2z14-175653765/559504yz15-\ 58551255/559504z16+38545/748yz19+37795/748z20+107445825/69938yz20+1737835\ 425/1119008z21+443675323125/1119008yz21+443675323125/2238016z22-562568321\ 599725/8952064yz22-562820420301525/17904128z23+2614689385875/17904128z24 ==> j[53]=y8z7-878/141y6z9+9877/517y4z11+915172/26367y3z12+253943/8789y2z13+9\ 4823/8789yz14+37210/26367z15-847642725/1643543y3z13-2534922297/3287086y2z\ 14-2534922297/3287086yz15-839636847/3287086z16+5435755695/3503192y2z15+54\ 35755695/3503192yz16+5435755695/3503192z17+1063395/8789yz19+5880395/52734\ z20+6007578570/1643543yz20+25156075905/6574172z21+1064589124796775/101242\ 2488yz21+1075884396851925/2024844976z22-2383632331137825/26296688yz22+103\ 195950091159325/1012422488z23-274018430271493924425/16198759808z24 ==> j[54]=xy7z7+769/282y6z9-21413/2068y4z11-30212/1551y3z12-17111/1034y2z13-1\ 2809/2068yz14-1235/1551z15+237013695/773432y3z13+707273613/1546864y2z14+7\ 07273613/1546864yz15+233246223/1546864z16-5435755695/3503192y2z15-5435755\ 695/3503192yz16-5435755695/3503192z17-133305/2068yz19-409355/6204z20-4097\ 17845/193358yz20-639413595/281248z21-156040912046925/238217056yz21-158698\ 623118725/476434112z22+688041879438525/24749824yz22-508310646770040175/38\ 11472896z23+64476566767453351725/3811472896z24 ==> j[55]=xz13+yz13+z14-20007/154y2z15-20007/154yz16-20007/154z17+5z19-100035\ /154yz21-1933395/308z22-4406592375/1232z23+576566423518975/561792z24 ==> j[56]=xyz12+y2z12+yz13+20007/308y2z15+20007/308yz16+20007/308z17+5yz18+20\ 42295/616yz21+5709015/1232z22+2581875/64yz22+17825173875/9856z23-57656547\ 5494975/1123584z24 ==> j[57]=xy2z11+y3z11+y2z12-13851/308y2z15-13851/308yz16-13851/308z17-5yz18-\ 5z19-1980735/616yz21-5038095/1232z22-2581875/64yz22-22282522875/9856z23+9\ 15874327042225/1123584z24 ==> j[58]=xy3z10+y4z10+y3z11+1539/44y2z15+1539/44yz16+1539/44z17+5z19+201015/\ 88yz21+594255/176z22+7745625/64yz22+3558400875/1408z23-77537732695475/802\ 56z24 ==> j[59]=xy4z9+y5z9+y4z10-7695/308y2z15-7695/308yz16-7695/308z17+5yz18-83347\ 5/616yz21-3235275/1232z22-12909375/64yz22-21828234375/9856z23+92636468662\ 2125/1123584z24 ==> j[60]=xy5z8+y6z8+y5z9+4617/308y2z15+4617/308yz16+4617/308z17-5yz18-5z19+2\ 82945/616yz21+2310765/1232z22+13820625/64yz22+15566792625/9856z23-6027924\ 06737525/1123584z24 ==> j[61]=xy6z7+y7z7+y6z8-1539/308y2z15-1539/308yz16-1539/308z17+5z19+244485/\ 616yz21-1432455/1232z22-10479375/64yz22-7060030875/9856z23+10437976377287\ 5/561792z24 ==> j[62]=y8z6+4y7z7+1096/141y6z8+438/47y5z9+3827/517y4z10+130/33y3z11+745/51\ 7y2z12+185/517yz13+74/1551z14-626565/48598y6z9+36597195/1069156y4z11+2938\ 45620/4543913y3z12+531935685/9087826y2z13+441719055/18175652yz14+30706050\ /4543913z15-824462422425/617972168y3z13+11079250419375/13595387696y2z14+1\ 1079250419375/13595387696yz15+29217423712725/13595387696z16+6498875861433\ 477/3622300528y2z15+6498875861433477/3622300528yz16+6498875861433477/3622\ 300528z17-115/47yz18-715/282z19+568770225/1652332yz19+75725325/150212z20+\ 83154721712625/3398846924yz20+2507243939897625/27190775392z21+23491579901\ 268980805/2093689705184yz21+16367386229217586595/523422426296z22-13196224\ 488747115125/19775109376yz22+1268637865899370688210625/8374758820736z23-1\ 7691473521227817276849545175/904473952639488z24 ==> j[63]=xy7z6-3y7z7-1096/141y6z8-438/47y5z9-3827/517y4z10-130/33y3z11-745/5\ 17y2z12-185/517yz13-74/1551z14+626565/48598y6z9-36597195/1069156y4z11-293\ 845620/4543913y3z12-531935685/9087826y2z13-441719055/18175652yz14-3070605\ 0/4543913z15+824462422425/617972168y3z13-11079250419375/13595387696y2z14-\ 11079250419375/13595387696yz15-29217423712725/13595387696z16-649889396117\ 5401/3622300528y2z15-6498893961175401/3622300528yz16-6498893961175401/362\ 2300528z17+350/47yz18+715/282z19-568770225/1652332yz19-75725325/150212z20\ -83154721712625/3398846924yz20-2507243939897625/27190775392z21-2349420352\ 2192320265/2093689705184yz21-32734262338246025995/1046844852592z22+131967\ 40688623697625/19775109376yz22-634320342549593324852625/4187379410368z23+\ 336141189847485260140967097625/17185005100150272z24 ==> j[64]=y9z5-52/5y7z7-6904/235y6z8-10137/235y5z9-20582/517y4z10-1327/55y3z1\ 1-25293/2585y2z12-7006/2585yz13-1072/2585z14+5639085/97196y6z9-329374755/\ 2138312y4z11-1284909129/4543913y3z12-4563044199/18175652y2z13-3526717563/\ 36351304yz14-238958289/9087826z15+7263199915155/1235944336y3z13-104892996\ 034485/27190775392y2z14-104892996034485/27190775392yz15-264683394167895/2\ 7190775392z16-292449214667345301/36223005280y2z15-292449214667345301/3622\ 3005280yz16-292449214667345301/36223005280z17+377/94yz18+689/47z19-491972\ 4405/3304664yz19-7499192895/3304664z20-465864054810075/3398846924yz20-232\ 72639204604175/54381550784z21-210513611918733814743/4187379410368yz21-588\ 763946311409477793/4187379410368z22+10568763114146744625/3595474432yz22-2\ 2836546608337302729045625/33499035282944z23+33613907149852300781381322425\ 5/3818890022255616z24 ==> j[65]=xy8z5+32/5y7z7+15232/705y6z8+7947/235y5z9+16755/517y4z10+3331/165y3\ z11+21568/2585y2z12+6081/2585yz13+2846/7755z14-4385955/97196y6z9+25618036\ 5/2138312y4z11+991063509/4543913y3z12+3499172829/18175652y2z13+2643279453\ /36351304yz14+177546189/9087826z15-510388642755/112358576y3z13+8273449519\ 5735/27190775392y2z14+82734495195735/27190775392yz15+206248546742445/2719\ 0775392z16+227460999045268251/36223005280y2z15+227460999045268251/3622300\ 5280yz16+227460999045268251/36223005280z17-617/94yz18-4829/282z19+3438349\ 05/300424yz19+5833235745/3304664z20+191354666548725/1699423462yz20+182581\ 51324808925/54381550784z21+163539441692436671493/4187379410368yz21+457825\ 644211426125893/4187379410368z22-89855404516525595625/39550218752yz22+177\ 62048053885050003338625/33499035282944z23-2352994088872107067347530909545\ /34370010200300544z24 ==> j[66]=y10z4+22y7z7+10142/141y6z8+5489/47y5z9+5475/47y4z10+226/3y3z11+1503\ /47y2z12+436/47yz13+212/141z14-970935/8836y6z9+54553185/194392y4z11+20150\ 2425/413083y3z12+709272945/1652332y2z13+491141745/3304664yz14+42414045/82\ 6166z15-13268790182475/1235944336y3z13+326186439486885/17303220704y2z14+3\ 26186439486885/17303220704yz15+511949502041535/17303220704z16+20533149915\ 4193607/9220401344y2z15+205331499154193607/9220401344yz16+205331499154193\ 607/9220401344z17+1015/94yz18-11195/282z19+9119149125/3304664yz19+1612626\ 9975/3304664z20+1722252380149575/4325805176yz20+40486832246297475/3460644\ 1408z21+86222628281316862035/666173997104yz21+3827600153784459109735/1065\ 8783953664z22-212431074992817667875/39550218752yz22+162431268984322756306\ 439625/85270271629312z23-5310151622816439181656857454575/2187182467291852\ 8z24 ==> j[67]=y11z3-44y7z7-21428/141y6z8-12122/47y5z9-12530/47y4z10-532/3y3z11-35\ 81/47y2z12-1058/47yz13-536/141z14+640905/8836y6z9-25563555/194392y4z11-35\ 2065/2209y3z12-1435545/8836y2z13-6018435/194392yz14-334095/4418z15+453354\ 657075/72702608y3z13-67922428047615/1017836512y2z14-67922428047615/101783\ 6512yz15-74269393246665/1017836512z16-893884195353597003/18440802688y2z15\ -893884195353597003/18440802688yz16-893884195353597003/18440802688z17-283\ 5/47yz18+22385/282z19-395171175/194392yz19-1172470725/194392z20-360596839\ 248225/508918256yz20-4892289394562775/2035673024z21-79258578474346178505/\ 313493645696yz21-861603516867110968945/1253974582784z22+72716568119281608\ 75/2326483456yz22-42411391510222913195424375/10031796662272z23+6799137804\ 17072973197368315825/1286577921936384z24 ==> j[68]=xy10z3+22y7z7+3762/47y6z8+6633/47y5z9+7055/47y4z10+102y3z11+2078/47\ y2z12+622/47yz13+108/47z14+165015/4418y6z9-14494815/97196y4z11-135666270/\ 413083y3z12-220413015/826166y2z13-194414175/1652332yz14+10030860/413083z1\ 5+695220126525/154493042y3z13+37658856241935/786510032y2z14+3765885624193\ 5/786510032yz15+375315091575885/8651610352z16+483221842054194717/18440802\ 688y2z15+483221842054194717/18440802688yz16+483221842054194717/1844080268\ 8z17+5125/94yz18-1865/47z19-1200619575/1652332yz19+1902866175/1652332z20+\ 2685641506920675/8651610352yz20+10670521865317425/8651610352z21+657636174\ 738694524465/5329391976832yz21+6992094684045264300435/21317567907328z22+5\ 553968548621501125/2471888672yz22+396131943695600228635027125/17054054325\ 8624z23-1041400629215382738611919651175/3645304112153088z24 ==> j[69]=xz12+yz12+z13+572/423y6z9-640/141y4z11-62420/7191y3z12-18392/2397y2\ z13-2504/799yz14-2480/7191z15+1900665/13583y3z13+361663461/2091782y2z14+3\ 61663461/2091782yz15+68961051/2091782z16-8853766965/1114652y2z15-88537669\ 65/1114652yz16-8853766965/1114652z17+5z18-212420/7191yz19-68020/2397z20-1\ 332663435/1045891yz20-8824397565/4183564z21-44412306927525/161067214yz21-\ 196723166744925/322134428z22+91232350818875/1303968yz22-85182191428382527\ 225/293786598336z23+2704144027538175568425/20616603392z24 ==> j[70]=xyz11+y2z11+yz12-286/423y6z9+320/141y4z11+31210/7191y3z12+9196/2397\ y2z13+1252/799yz14+1240/7191z15-15577245/149413y3z13-144213534/1045891y2z\ 14-144213534/1045891yz15-3197529/95081z16+8853766965/2229304y2z15+8853766\ 965/2229304yz16+8853766965/2229304z17+5yz17+106210/7191yz19+34010/2397z20\ +240968535/190162yz20+1567041480/1045891z21+327495838518225/1288537712yz2\ 1+936739277787825/2577075424z22-41631712161551725/1090117248yz22+16848071\ 2635652233925/1175146393344z23-2704164384351779233425/41233206784z24 ==> j[71]=xy2z10+y3z10+y2z11+286/423y6z9-320/141y4z11-31210/7191y3z12-9196/23\ 97y2z13-1252/799yz14-1240/7191z15+15577245/149413y3z13+23588253/149413y2z\ 14+23588253/149413yz15+8011008/149413z16-2186449605/318472y2z15-218644960\ 5/318472yz16-2186449605/318472z17-5yz17-5z18-106210/7191yz19-34010/2397z2\ 0-348801645/298826yz20-284992095/298826z21-49448618214075/184076816yz21-1\ 96416565735275/368153632z22+41631071717668525/1090117248yz22-245593810261\ 51879675/167878056192z23+309646295518591584225/5890458112z24 ==> j[72]=xy3z9+y4z9+y3z10-286/423y6z9+320/141y4z11+31210/7191y3z12+9196/2397\ y2z13+1252/799yz14+1240/7191z15-13527810/149413y3z13-154050822/1045891y2z\ 14-154050822/1045891yz15-59356152/1045891z16+9265418685/1114652y2z15+9265\ 418685/1114652yz16+9265418685/1114652z17+5z18+106210/7191yz19+34010/2397z\ 20+1234402740/1045891yz20+1383637755/2091782z21+105070137902325/322134428\ yz21+414705570236775/644268856z22-6168510692255975/136264656yz22+66200788\ 7526707950/4590415599z23-949601768600740724325/20616603392z24 ==> j[73]=xy4z8+y5z8+y4z9+286/423y6z9-320/141y4z11-31210/7191y3z12-9196/2397y\ 2z13-1252/799yz14-1240/7191z15+11478375/149413y3z13+142983873/1045891y2z1\ 4+142983873/1045891yz15+62635248/1045891z16-13234976775/2229304y2z15-1323\ 4976775/2229304yz16-13234976775/2229304z17+5yz17-106210/7191yz19-34010/23\ 97z20-2495999445/2091782yz20-31540410/95081z21-469793494110375/1288537712\ yz21-1411221542610375/2577075424z22+57065153864289475/1090117248yz22-1254\ 8681666592952425/391715464448z23+696060504549723377475/41233206784z24 ==> j[74]=xy5z7+y6z7+y5z8-286/423y6z9+320/141y4z11+31210/7191y3z12+9196/2397y\ 2z13+1252/799yz14+1240/7191z15-9428940/149413y3z13-131916924/1045891y2z14\ -131916924/1045891yz15-65914344/1045891z16+3678340815/2229304y2z15+367834\ 0815/2229304yz16+3678340815/2229304z17-5yz17-5z18+106210/7191yz19+34010/2\ 397z20+2601635235/2091782yz20+4140285/2091782z21+421375504864725/12885377\ 12yz21+812249983763325/2577075424z22-79973440545621125/1090117248yz22-167\ 063188394749078475/1175146393344z23+974495213822460648825/41233206784z24 ==> j[75]=xy6z6+y7z6+y6z7+286/423y6z9-320/141y4z11-31210/7191y3z12-9196/2397y\ 2z13-1252/799yz14-1240/7191z15+7379505/149413y3z13+120849975/1045891y2z14\ +120849975/1045891yz15+69193440/1045891z16+4568267565/1114652y2z15+456826\ 7565/1114652yz16+4568267565/1114652z17+5z18-106210/7191yz19-34010/2397z20\ -1392856425/1045891yz20+607166625/2091782z21-138961955560275/644268856yz2\ 1+3246371081325/1288537712z22+59036431911624575/545058624yz22+42739607320\ 93934325/10308301696z23-424081801037561315625/5154150848z24 ==> j[76]=xy7z5+y8z5+y7z6-286/423y6z9+320/141y4z11+31210/7191y3z12+9196/2397y\ 2z13+1252/799yz14+1240/7191z15-5330070/149413y3z13-109783026/1045891y2z14\ -109783026/1045891yz15-72472536/1045891z16-1123108335/101332y2z15-1123108\ 335/101332yz16-1123108335/101332z17+5yz17+106210/7191yz19+34010/2397z20+2\ 969790465/2091782yz20-570015855/1045891z21+373302122175/29284948yz21-2281\ 0656626775/58569896z22-50436732640756175/272529312yz22-545752583844195702\ 5/6676968144z23+608955833646803601675/3748473344z24 ==> j[77]=y9z4+9/2y8z5+38/5y7z6+28/5y6z7-6/5y5z8-13/2y4z9-32/5y3z10-33/10y2z1\ 1-11/10yz12-1/5z13-243/10y7z7-1701/20y6z8-1863/20y5z9-81/4y4z10+1539/20y3\ z11+1863/20y2z12+891/20yz13+81/10z14-1573/2115y6z9+352/141y4z11-157814630\ /79101y3z12-789848639/263670y2z13-263502293/87890yz14-158162263/158202z15\ +403948702323/13148344y3z13+8474527251387/184076816y2z14+8474527251387/18\ 4076816yz15+2819245418865/184076816z16-2277893907/253330y2z15-2277893907/\ 253330yz16-2277893907/253330z17-7yz17+13/4z18+486yz18+1701/4z19-231480772\ 3/158202yz19+5037026/26367z20+603143500229535/92038408yz20+11634440010787\ 95/368153632z21-134266161760124013/2577075424yz21-137028452905078101/5154\ 150848z22+1114271066009961257735/71947738368yz22+51874457100139726934015/\ 7050878360064z23+276524393448922094247795/1566861857792z24 ==> j[78]=xy8z4-7/2y8z5-38/5y7z6-28/5y6z7+6/5y5z8+13/2y4z9+32/5y3z10+33/10y2z\ 11+11/10yz12+1/5z13+243/10y7z7+1701/20y6z8+1863/20y5z9+81/4y4z10-1539/20y\ 3z11-1863/20y2z12-891/20yz13-81/10z14+1001/705y6z9-224/47y4z11+52490440/2\ 6367y3z12+262945693/87890y2z13+263364573/87890yz14+52711661/52734z15-4036\ 60006443/13148344y3z13-8457153221835/184076816y2z14-8457153221835/1840768\ 16yz15-2805913131633/184076816z16+317919689883/11146520y2z15+317919689883\ /11146520yz16+317919689883/11146520z17+2yz17-33/4z18-486yz18-1701/4z19+77\ 0823701/52734yz19-1803712/8789z20-603278818984755/92038408yz20-1163149571\ 242875/368153632z21+135044223950364363/2577075424yz21+141273988656213051/\ 5154150848z22-1090420035071554691885/71947738368yz22-41792722244763474154\ 565/7050878360064z23-685099534954253407593345/1566861857792z24 ==> j[79]=xy9z3+y10z3-9/2y8z5-38/5y7z6-28/5y6z7+6/5y5z8+13/2y4z9+32/5y3z10+33\ /10y2z11+11/10yz12+1/5z13+243/10y7z7+1701/20y6z8+1863/20y5z9+81/4y4z10-15\ 39/20y3z11-1863/20y2z12-891/20yz13-81/10z14+143/2115y6z9-32/141y4z11+1581\ 57940/79101y3z12+790860199/263670y2z13+263640013/87890yz14+158189543/1582\ 02z15-404057047923/13148344y3z13-8489953497915/184076816y2z14-84899534979\ 15/184076816yz15-2833154826993/184076816z16-232919344017/11146520y2z15-23\ 2919344017/11146520yz16-232919344017/11146520z17+7yz17+7/4z18-486yz18-170\ 1/4z19+2317144343/158202yz19-4662916/26367z20-603006984939855/92038408yz2\ 0-1163846020930875/368153632z21+132236704098135963/2577075424yz21+1303312\ 19207468751/5154150848z22-1159686946509974573885/71947738368yz22-68677251\ 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j[81]=xy10z2-9/2y10z3+165/4y8z5+88y7z6+77y6z7-275/4y4z9-149/2y3z10-161/4y\ 2z11-55/4yz12-5/2z13-1701/4y7z7-11907/8y6z8-13041/8y5z9-2835/8y4z10+10773\ /8y3z11+13041/8y2z12+6237/8yz13+567/4z14-2431/282y6z9+1360/47y4z11-921329\ 180/26367y3z12-1843856843/35156y2z13-1844874123/35156yz14-1845344615/1054\ 68z15+14155483898745/26296688y3z13+297092613853737/368153632y2z14+2970926\ 13853737/368153632yz15+98915839271307/368153632z16-270887899131/4458608y2\ z15-270887899131/4458608yz16-270887899131/4458608z17-95yz17+275/8z18+8505\ yz18+59535/8z19-27016215455/105468yz19+28572080/8789z20+21110683794699105\ /184076816yz20+40726306493438745/736307264z21-4698753505995194955/5154150\ 848yz21-4748618833102825785/10308301696z22+39114939183464627699725/143895\ 476736yz22+1893501137798116652057275/14101756720128z23+536564751106962074\ 4877275/3133723715584z24 ==> j[82]=xz11+yz11+z12+572/423y6z8+572/141y5z9+790/141y4z10+40/9y3z11+88/47y\ 2z12+46/141yz13+56/423z14-582770/6627y6z9+5608430/24299y4z11+540007510/12\ 39249y3z12+140696995/413083y2z13+45353685/413083yz14-8938535/1239249z15-1\ 27805831775/14044822y3z13-26678525255325/2162902588y2z14-26678525255325/2\ 162902588yz15-6996427161975/2162902588z16+965701597805963/1152550168y2z15\ +965701597805963/1152550168yz16+965707360556803/1152550168z17+910/141yz18\ +530/423z19+235982375/112659yz19+147407075/75106z20+41856813119250/540725\ 647yz20+466506627125625/4325805176z21+813428824867634820/41635874819yz21+\ 360803350499543037395/18985958917464z22-2044981435549759625/449434304yz22\ +379820494972020072979875/5329391976832z23-74930243087916747964230028075/\ 8201934252344448z24 ==> j[83]=xyz10+y2z10+yz11-44/3y7z7-22000/423y6z8-12694/141y5z9-4440/47y4z10-\ 572/9y3z11-1266/47y2z12-368/47yz13-592/423z14+291385/6627y6z9-2804215/242\ 99y4z11-354995030/1239249y3z12-112844135/413083y2z13-65172480/413083yz14-\ 38026370/1239249z15-4104216934875/154493042y3z13-87610866574725/216290258\ 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713/2305100336z17+3980/141yz18-10310/423z19-2165535925/2478498yz19-919789\ 925/826166z20+1387273664409075/1081451294yz20+2276001050636925/4325805176\ z21-50878211929841413645085/75943835669856yz21-16566371038690273007315/50\ 629223779904z22-11214474564379130063875/19775109376yz22-48611383464565202\ 15783625/21317567907328z23-114566709866068006344889739425/164038685046888\ 96z24 ==> j[85]=xy3z8+y4z8+y3z9-44/3y7z7-22000/423y6z8-12694/141y5z9-4440/47y4z10-5\ 72/9y3z11-1266/47y2z12-368/47yz13-592/423z14-794315/6627y6z9+19808935/485\ 98y4z11+898575340/1239249y3z12+246316000/413083y2z13+155880105/826166yz14\ -11090435/1239249z15-13583602174275/308986084y3z13-290354162377815/432580\ 5176y2z14-290354162377815/4325805176yz15-100183731937965/4325805176z16-86\ 5434793775917/1152550168y2z15-865434793775917/1152550168yz16-865429031025\ 077/1152550168z17-3980/141yz18+10310/423z19+5278324775/2478498yz19+879169\ 625/413083z20-659615379073650/540725647yz20-4122118457610525/8651610352z2\ 1+25548497753349154062865/37971917834928yz21+8279719802851236313835/25314\ 611889952z22+5512001817613562968375/9887554688yz22+2279386767016902381410\ 625/10658783953664z23+134353948523716011370456857925/16403868504688896z24 ==> j[86]=xy4z7+y5z7+y4z8+44/3y7z7+22000/423y6z8+12694/141y5z9+4440/47y4z10+5\ 72/9y3z11+1266/47y2z12+368/47yz13+592/423z14+820165/6627y6z9-10004695/242\ 99y4z11-924375050/1239249y3z12-252843830/413083y2z13-82764015/413083yz14+\ 12472705/1239249z15+6922621646775/154493042y3z13+149031192290445/21629025\ 88y2z14+149031192290445/2162902588yz15+52114489235595/2162902588z16+24823\ 81227491245/2305100336y2z15+2482392752992925/2305100336yz16+2482381227491\ 245/2305100336z17+3980/141yz18-10310/423z19-5645585125/2478498yz19-843374\ 425/413083z20+1297187944049925/1081451294yz20+2062173912456825/4325805176\ z21-50561824847932108997975/75943835669856yz21-16202257051507079051225/50\ 629223779904z22-10885418295936912302125/19775109376yz22-38727651899890821\ 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72/9y3z11+1266/47y2z12+368/47yz13+592/423z14+502210/6627y6z9-5655550/2429\ 9y4z11-532246295/1239249y3z12-135155360/413083y2z13-39011010/413083yz14+3\ 2866945/1239249z15+2824416045900/77246521y3z13+31908535379955/540725647y2\ z14+31908535379955/540725647yz15+12137623058655/540725647z16+305826537280\ 3955/1152550168y2z15+3058265372803955/1152550168yz16+3058271135554795/115\ 2550168z17+3980/141yz18-10310/423z19-1819427750/1239249yz19-607474925/826\ 166z20+607471821367650/540725647yz20+579107988351675/1081451294z21-222626\ 58475598588445775/37971917834928yz21-821349300336923555475/3164326486244z\ 22-4934719312810096564625/9887554688yz22-13859743719993905654625/66617399\ 7104z23-474598588592475460844829069175/16403868504688896z24 ==> j[89]=xy7z4+y8z4+y7z5-44/3y7z7-22000/423y6z8-12694/141y5z9-4440/47y4z10-5\ 72/9y3z11-1266/47y2z12-368/47yz13-592/423z14-360035/6627y6z9+670505/4418y\ 4z11+32395580/112659y3z12+7477640/37553y2z13+3556695/75106yz14-3842065/11\ 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550/413083z20-80051332955175/617972168yz20-220738142474775/308986084z21-2\ 3878555064365101845/380670855488yz21-17328862007227564772735/867929550512\ 64z22-1868878877799862375/308986084yz22-17995252524739734383894625/121814\ 67375616z23+424904594031505848545727956275/2343409786384128z24 ==> j[92]=y11z+11/2y10z2+35/2y9z3+75/2y8z4+45y7z5+21y6z6-21y5z7-45y4z8-75/2y3\ z9-35/2y2z10-11/2yz11-z12+242/3y7z7+117854/423y6z8+66671/141y5z9+68915/14\ 1y4z10+2926/9y3z11+6479/47y2z12+5819/141yz13+2948/423z14-14820025/17672y6\ z9+873381255/388784y4z11+3434435885/826166y3z12+10920930675/3304664y2z13+\ 6994380015/6609328yz14-22734095/1652332z15+146778297314625/2471888672y3z1\ 3+3946648865169015/34606441408y2z14+3946648865169015/34606441408yz15+1719\ 77518433115/3146040128z16+586848438081958029/36881605376y2z15+58684760824\ 5837069/36881605376yz16+586849267918078989/36881605376z17+16885/141yz18-5\ 9620/423z19+128385353575/6609328yz19+137287540725/6609328z20+127263206240\ 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j[99]=xy4z6+y5z6+y4z7-y10z3+55/6y8z5+88/3y7z6+154/3y6z7+176/3y5z8+275/6y4\ z9+73/3y3z10+49/6y2z11+11/6yz12+1/3z13-27183/2y7z7-26764501/564y6z8-15318\ 121/188y5z9-176093065/2068y4z10-7557373/132y3z11-50531529/2068y2z12-14830\ 573/2068yz13-3743269/3102z14+1405719171149/62983008y6z9-26098701044485/46\ 1875392y4z11-286531489029805/2944455624y3z12-336342178241569/3925940832y2\ z13-76335479575631/2617293888yz14-62885031805175/5888911248z15+2144197673\ 2934385/9887554688y3z13-6602383295616654047/1522683421952y2z14-6602375682\ 199544287/1522683421952yz15-9904447712488549337/1522683421952z16-78458368\ 51981512509823/1622790636544y2z15-7845836851981512509823/1622790636544yz1\ 6-7845836851981512509823/1622790636544z17-5yz17-95/12z18-2296555/94yz18+1\ 2055805/564z19-1200204388940305/2141422272yz19-726023508016505/713807424z\ 20-196100702405618841515/2284025132928yz20-43934311163922771200815/173585\ 910102528z21-13043238309443948468622285/468986493961216yz21-1445817020185\ 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4z9+73/3y3z10+49/6y2z11+11/6yz12+1/3z13-14055/2y7z7-13844125/564y6z8-7930\ 585/188y5z9-91182325/2068y4z10-3914125/132y3z11-26077665/2068y2z12-759890\ 5/2068yz13-1846525/3102z14-56738190001/62983008y6z9-788583031735/46187539\ 2y4z11+3705043629665/2944455624y3z12+33698825888021/3925940832y2z13+26934\ 521105179/2617293888yz14+48443172337795/5888911248z15-1674626841934085/98\ 87554688y3z13+6068824708329191147/1522683421952y2z14+6068817094912081387/\ 1522683421952yz15+6326709628569930477/1522683421952z16+438316603323713262\ 6075/1622790636544y2z15+4383166033237132626075/1622790636544yz16+43831660\ 33237132626075/1622790636544z17-5yz17-95/12z18-1228975/94yz18+6430475/564\ z19+229433021403845/2141422272yz19+177561956970445/713807424z20+437251626\ 0828943805/761341710976yz20+6733889229863237423305/57861970034176z21+6472\ 489146665446781282625/468986493961216yz21+68736014372542198909702625/1875\ 945975844864z22-235468550079971226057925/2847615750144yz22+67598204349319\ 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j[107]=xz9+yz9+z10-2y10z2-10y9z3-80/3y8z4-140/3y7z5-56y6z6-140/3y5z7-80/3\ y4z8-10y3z9-8/3y2z10-2/3yz11+4765/8y10z3-20835/16y8z5+7895y7z6+130465/4y6\ z7+114225/2y5z8+948125/16y4z9+314315/8y3z10+269835/16y2z11+78825/16yz12+6\ 155/8z13+10422463/144y7z7+30860986159/121824y6z8+11267616007/40608y5z9+24\ 51530645/40608y4z10-593889031/2592y3z11-3754807597/13536y2z12-5387471995/\ 40608yz13-1469311027/60912z14+1416414815/477144y6z9-8816857945/874764y4z1\ 1+66212212331860/11153241y3z12+530405865696055/59483952y2z13+177001804012\ 105/19827984yz14+531293352896875/178451856z15-451812888421348725/49437773\ 44y3z13-9467956171849602645/69212882816y2z14-9467956171849602645/69212882\ 816yz15-3142575733950720495/69212882816z16+4669864624952322557/4149180604\ 8y2z15+4669865039870383037/41491806048yz16+4669864694105332637/4149180604\ 8z17+36475/4yz17-677825/32z18-7346744615/5076yz18-154285681835/121824z19+\ 7773403307100775/178451856yz19-8644863356275/14870988z20-6754175699206002\ 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j[121]=x2yz6-y3z6-2y2z7-yz8+40y10z2+200y9z3+630y8z4+1320y7z5+1680y6z6+126\ 0y5z7+420y4z8-120y3z9-180y2z10-70yz11-50z12+3392/3y7z7+5062336/1269y6z8+2\ 917726/423y5z9+33733390/4653y4z10+1453558/297y3z11+3249508/1551y2z12+2849\ 128/4653yz13+1667198/13959z14+824859875/145794y6z9-21530818075/1069156y4z\ 11-503166594530/13631739y3z12-324495046255/9087826y2z13-282966185235/1817\ 5652yz14-60700373165/13631739z15+273674327539725/56179288y3z13+1075367159\ 69527575/13595387696y2z14+107536715969527575/13595387696yz15+413075287049\ 14125/13595387696z16+1390709606701412201/3622300528y2z15+1390704716595699\ 401/3622300528yz16+1390706346630937001/3622300528z17+929435/423yz18-20988\ 05/1269z19-60756900425/450636yz19-365571595775/1652332z20+153631004775148\ 125/849711731yz20+2397615030608356125/27190775392z21-10677692774577796473\ 522745/119340313195488yz21-8543001261389272550615555/179010469793232z22-1\ 533912321925569677241875/19775109376yz22+15562075862209915374841875/83747\ 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0/81yz17+162175/162z18+548903525/141yz18-3026775025/846z19+27820127662598\ 75825/28909200672yz19+631251774268012825/9636400224z20+834549760512521153\ 551225/10278113098176yz20+14530392406701081768114725/781136595461376z21-1\ 43805121095377365823474118475/4455371692631552yz21-1168361866569917419774\ 687429825/53464460311578624z22-58813484594869708628716919721625/219124031\ 9735808yz22-5298255598048491212044632289975509125/103934910845708845056z2\ 3+13773306630404801119508893030689754375/2887080856825245696z24 ```