odd behaviour of normal(I) in 3-1-x in comparison to 3-0-4

[anonymous]

swallowtail/open swallowtail example, output of 3-0-4 ok
---------
INPUT: 
   LIB "sing.lib";
   LIB "primdec.lib";
   LIB "normal.lib";
   ring R=0,(t,u),dp;
   ring S2=0,(a,b,c,d),dp;
   setring R;
   ideal zero;
   ideal A=u-(1/2)*t2,ut-(1/3)*t3,ut2-(1/4)*t4,ut3-(1/5)*t5;
   map phi=(S2,A);
   setring(S2);
   ideal I2=preimage(R,phi,zero);
   list L=normal(I2);
   def R1=L[1];
   setring R1;
   normap;
   norid;

output of 3-0-4:
> normap;
normap[1]=-10/3*T(2)^2+1/6*T(1)
normap[2]=400/81*T(2)^3-5/9*T(1)*T(2)
normap[3]=-500/81*T(2)^4+50/27*T(1)*T(2)^2
normap[4]=-500/81*T(1)*T(2)^3
> norid;
norid[1]=0

output of 3-1-1:
> def R1=L[1][1];
// ** redefining R1 **
> setring R1;
> normap;
normap[1]=a
normap[2]=b
normap[3]=c
normap[4]=d
> norid;
norid[1]=T(5)+1
norid[2]=16*T(3)*c-3*T(4)*d-96*T(6)
norid[3]=18*T(1)*b-48*T(2)*c+5*T(3)*d
norid[4]=12*T(2)*b-T(4)*d-12*T(6)
norid[5]=8*T(3)*b-3*T(7)+d
norid[6]=-40*T(1)+15*T(4)*b+64*c
norid[7]=16*T(1)*a-3*T(4)*d-16*T(6)
norid[8]=16*T(2)*a-T(7)+3*d
norid[9]=-10*T(2)+5*T(4)*a+18*b
norid[10]=-72*T(1)*c+85*T(2)*d+240*T(6)*a-15*T(7)*b
norid[11]=-16*T(6)*c+T(7)*d+d^2
norid[12]=-20*T(1)*d-240*T(6)*b+15*T(7)*c+27*c*d
norid[13]=-8*T(1)*c+5*T(2)*d+3*b*d
norid[14]=-36*T(2)*c+5*T(3)*d+6*a*d
norid[15]=T(1)*d+T(3)*a*d-6*T(6)*b
norid[16]=-5*T(1)*d^2+108*T(6)*c^2-60*T(6)*b*d-3*T(7)*c*d
norid[17]=-8*T(1)*c*d+5*T(2)*d^2+48*T(6)*b*c-3*T(7)*b*d
norid[18]=144*T(1)*c^2-350*T(2)*c*d+25*T(3)*d^2+30*T(7)*b*c-30*T(7)*a*d
norid[19]=5*T(4)*d+10*T(6)+54*b^2-64*a*c
norid[20]=-276*T(2)*c*d+25*T(3)*d^2+864*T(6)*b^2-54*T(7)*a*d
norid[21]=576*T(2)*c^2-55*T(4)*d^2-960*T(6)*d+288*T(7)*b^2-288*T(7)*a*c
norid[22]=-24*T(4)*c-3*T(7)+48*a*b-23*d
norid[23]=-45*T(1)-5*T(3)*a+30*a^2+54*c
norid[24]=5184*T(2)*c^3-495*T(4)*c*d^2-8640*T(6)*c*d+480*T(7)*a*c^2-480*T(7)*a*b*d+200*T(7)*d^2
norid[25]=T(1)^2-T(2)*d
norid[26]=T(1)*T(2)-1/6*T(3)*d
norid[27]=T(2)^2-T(6)
norid[28]=T(1)*T(3)-6*T(6)
norid[29]=T(2)*T(3)-3/8*T(7)-27/40*d
norid[30]=T(3)^2-54/5*T(1)-6*T(3)*a
norid[31]=T(1)*T(4)+8/5*d
norid[32]=T(2)*T(4)+8/5*T(1)
norid[33]=T(3)*T(4)+48/5*T(2)
norid[34]=T(4)^2-64/45*T(3)+128/15*a
norid[35]=T(1)*T(5)+T(1)
norid[36]=T(2)*T(5)+T(2)
norid[37]=T(3)*T(5)+T(3)
norid[38]=T(4)*T(5)+T(4)
norid[39]=T(5)^2-1
norid[40]=T(1)*T(6)-1/16*T(7)*d-9/80*d^2
norid[41]=T(2)*T(6)-1/20*T(1)*d-1/16*T(7)*c-9/80*c*d
norid[42]=T(3)*T(6)-9/5*T(2)*d-6*T(6)*a
norid[43]=T(4)*T(6)+4/15*T(3)*d
norid[44]=T(5)*T(6)+T(6)
norid[45]=T(6)^2-1/20*T(3)*d^2-1/16*T(7)*a*d-9/80*a*d^2
norid[46]=T(1)*T(7)+T(1)*d-T(7)*c-9/5*c*d
norid[47]=T(2)*T(7)-3*T(2)*d-16*T(6)*a
norid[48]=T(3)*T(7)-3*T(3)*d-6*T(7)*a-54/5*a*d
norid[49]=T(4)*T(7)+48/5*T(1)*a+16*T(6)
norid[50]=T(5)*T(7)+T(7)
norid[51]=T(6)*T(7)-4/5*T(1)*a*d-3*T(6)*d-T(7)*a*c-9/5*a*c*d
norid[52]=T(7)^2-384/5*T(2)*a*d-256*T(6)*a^2-6/5*T(7)*d-27/5*d^2
norid[53]=324*b^2*c-384*a*c^2+60*a*b*d-25*d^2
norid[54]=81*b^3-96*a*b*c+15*a^2*d-5*c*d
norid[55]=12*a*b^2-12*a^2*c+4*c^2-5*b*d
norid[56]=60*a^2*c^2-60*a^2*b*d+108*c^3-135*b*c*d+25*a*d^2
norid[57]=60*a^2*b*c-60*a^3*d+108*b*c^2-135*b^2*d+20*a*c*d

[laplagne]

Eliminating redundant variables can sometimes be time consuming, that is why there is no simplification being done in the new version. (In the previous version, using chains of rings, it was crucial to simplify the rings in each step, but now it is not needed, it is only a matter of how should the output be presented.)

But this is something that was left pending. We wanted to add an option on how much simplification should the procedure perform in the output ring. (Sometimes also you don't want to eliminate the original variables, as it is done in the example given here.)

I will work on it soon.