diff --git a/.singularhistory b/.singularhistory
deleted file mode 100644
index a493264..0000000
--- a/.singularhistory
+++ /dev/null
@@ -1,442 +0,0 @@
-ring r = 0,(x,y),ds;
-ideal f = x,xy+y6+y9;
-kbase(std(f));
-ring s = 0,(x,y),dp;
-ideal f = x,xy+y6+y9
-;
-kbase(std(f));
-ideal f = x,xy+y6+y8+y9;
-kbase(std(f));
-setring r;
-f = imap(s,f);
-f;
-kbase(std(f));
-quit;
-LIB"AeCodPruebas.lib";
-ring r = 0,(x,y),ds;
-ideal f = x,y2,y3+x2y;
-def Q = MalgrRing(ideal(0),2,f);
-setring Q;
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-LIB"AeCodPruebas.lib";
-TargetIdeal(ideal(x,y));
-ring r = 0,(x,y),ds;
-ideal f = x,y2,y3+x2y;
-LIB"AeCodPruebas.lib";
-TargetIdeal(f, ideal(x,y));
-TargetIdeal(f, std(ideal(x,y)));
-LIB"AeCodPruebas.lib";
-TargetIdeal(f, std(ideal(x,y)));
-LIB"AeCodPruebas.lib";
-ring r = 0,(x,y),ds;
-ideal f = x,y2,y3+x2y;
-TargetIdeal(f, std(ideal(x,y)));
-ring r = 0,(x,y),ds;
-ideal f = x,y2,y3+x2y;
-LIB"AeCodPruebas.lib";
-TargetIdeal(f, std(ideal(x,y)));
-LIB"AeCodPruebas.lib";
-TargetIdeal(f, std(ideal(x,y)));
-LIB"AeCodPruebas.lib";
-TargetIdeal(f, std(ideal(x,y)));
-LIB"AeCodPruebas.lib";
-TargetIdeal(f, std(ideal(x,y)));
-LIB"AeCodPruebas.lib";
-TargetIdeal(f, std(ideal(x,y)));
-TargetIdeal(f, std(maxideal(3)));
-TargetIdeal(f, std(maxideal(5)));
-LIB"AeCodPruebas.lib";
-basering;
-AeNormal(f);
-LIB"AeCodPruebas.lib";
-AeNormal(f);
-;
-LIB"AeCodPruebas.lib";
-AeNormal(f);
-LIB"AeCodPruebas.lib";
-AeNormal(f);
-;
-LIB"AeCodPruebas.lib";
-AeNormal(f);
-ideal f = x+x4,y2,y3+x2y;
-LIB"AeCodPruebas.lib";
-ideal f = x+x4,y2,y3+x2y;
-AeNormal(f,maxideal(3));
-AeNormal(f,maxideal(4));
-AeNormal(f);
-LIB"AeCodPruebas.lib";
-AeNormal(f);
-AeNormal(f,maxideal(1));
-AeNormal(f,maxideal(2));
-AeNormal(f,maxideal(3));
-AeNormal(f,maxideal(4));
-AeNormal(f,maxideal(7));
-AeNormal(f,maxideal(4));
-AeNormal(f,maxideal(5));
-f;
-def Q = MalgrRing(ideal(0),2,f);
-setring Q;
-GF;
-Gens;
-setring r;
-ideal w = x+x4,y2;
-kbase(std(w));
-setring Q;
-GF;
-basering;
-GF;
-reduce(x2, GF);
-MalgrFormPoly(x2);
-MalgrFormPoly(x2, maxideal(4));
-MalgrFormPoly(x2, maxideal(2));
-MalgrFormPoly(x2, maxideal(5));
-MalgrFormPoly(x2, maxideal(6));
-GF;
-reduce(x2,GF);
-x2;
-X(3) - f[3];
-X(3) - mappingf[3];
-MalgrFormPoly(x2, maxideal(6));
-LIB"AeCodPruebas.lib";
-MalgrFormPoly(x2, maxideal(6));
-LIB"AeCodPruebas.lib";
-MalgrFormPoly(x2, maxideal(6));
-MalgrFormPoly(x2, ideal(x,y)^4);
-LIB"AeCodPruebas.lib";
-MalgrFormPoly(x2, ideal(x,y)^4);
-print(_);
-MalgrFormPoly(x3, ideal(x,y)^4);
-MalgrFormPoly(x3, ideal(x,y)^6);
-MalgrFormPoly(x3, ideal(x,y)^7);
-;
-GF;
-LIB"AeCodPruebas.lib";
-ring r = 0,(x,y),ds;
-ideal f = x,y2,y7+x2y;
-AeNormal(f);
-ideal f = x,y2,y5+x2y;
-AeNormal(f);
-ring r = 0,(t,x,y),ds;
-ideal f = t,x,y3+t2y,(x+y)^4+t3y;
-AeNormal(f);
-ideal f = t,x,y4+t3y,(x+y)^3+t3y;
-AeNormal(f);
-ideal f = t,x,y5+t4y,(x+y)^4+t3y;
-ideal f = t,x,y4+t3y,(x+y)^3+t2y;
-AeNormal(f);
-ideal f = t,x,y4+t3y,(x+y)^3+t2y;
-AeNormal(f);
-ideal f = t,x,y5+t4y,(x+y)^4+t3y;
-AeNormal(f);
-ideal f = t,x,y4+t3y,(x+y)^5+t4y;
-AeNormal(f);
-quit;
-ring r = 0,(x,y),ds;
-ideal f = x,y2,y3+x2y;
-AeNormal(f);
-LIB"AeCodPruebas.lib";
-AeNormal(f);
-LIB"AeCodPruebas.lib";
-AeNormal(f);
-ideal f = x+x4,y2,y3+x2y;
-AeNormal(f);
-AeNormal(f,maxideal(4));
-ideal f = x+x4,y2,y3+x2y;
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-LIB"AeCodPruebas.lib";
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-f;
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-f;
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(4));
-AeNormal(f,maxideal(6));
-AeNormal(f,maxideal(10));
-AeNormal(f,maxideal(20));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(10));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(10));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(10));
-dimX
-;
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(10));
-AeNormal(f,maxideal(10));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(10));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(10));
-AeNormal(f,maxideal(20));
-LIB"AeCodPruebas.lib";
-AeNormal(f,maxideal(20));
-f;
-ideal g = x,xy+y^6+y^9;
-AeNormal(g,maxideal(20));
-AeNormal(g,maxideal(10));
-AeNormal(g,maxideal(12));
-AeNormal(f,maxideal(12));
-AeNormal(f);
-AeNormal(g);
-AeNormal(g,maxideal(12));
-AeNormal(g,maxideal(20));
-AeNormal(g);
-AeNormal(g,maxideal(50));
-ring r = 0,(x,y),ds;
-ring R = 0,(X,Y),ds;
-setring r;
-map Rr = R,x2,y3;
-ideal J = maxideal(20);
-setring R;
-preimage(r,Rr,J);
-setring r;
-ideal J = maxideal(50);
-setring R;
-ideal J = maxideal(50);
-preimage(r,Rr,J);
-setring r;
-ideal J = maxideal(100);
-setring R;
-preimage(r,Rr,J);
-setring r;
-map f = R,x2+y3,y5+x7;
-J = maxideal(20);
-setring R;
-preimage(r,f,J);
-LIB"AeCodPruebas.lib";
-ring r = 0,(t,x,y),ds;
-ideal f = t,x,y3+t2y,(x+y)^4+t3y;
-AeNormal(f);
-ideal f = t,x,y3+t2y,(x+y)^4+t3y;
-f[4];
-LIB"AeCodPruebas.lib";
-ring r = 0,(t,x,y),ds;
-ideal f = t,x,y3+t2y,y4+(t3+x3)*y;
-AeNormal(f);
-ideal f = t,x,y3+t2y,(x+y)^4+t3y;
-f[4];
-f[4] = f[4] -x4;
-f;
-AeNormal(f);
-f[4]
-;
-f[4] = y3+(t3+x3)*y+xy3;
-AeNormal(f);
-f[4] = y3+(t3+x3)*y+xy3+x2y2;
-AeNormal(f);
-f[4] = y3+(t3+4x3)*y+4xy3+6x2y2;
-AeNormal(f);
-f;
-f[4] = y4+(t3+4x3)*y+4xy3+6x2y2;
-AeNormal(f);
-f[4] = y4+(t3+x3)*y+xy3+x2y2;
-AeNormal(f);
-f[4] = y4+t3y+x3y+xy3+x2y2;
-AeNormal(f);
-f[4] = y4+t3y+xy3+x2y2;
-AeNormal(f);f
-;
-f[4] = y4+t3y+xy3+x2y2+x3y;
-AeNormal(f);f
-;
-AeNormal(f);
-f[4] = y4+t3y+xy3+x2y2+x3y;
-AeNormal(f);
-f[4] = y4+t3y+xy3+x3y;
-AeNormal(f);
-f[4] = y4+t3y+xy3+x2y2+x3y;
-AeNormal(f);
-f[4] = y4+xy3+x2y2+x3y;
-AeNormal(f);
-f;
-AeNormal(f);
-f;
-f[4] = y4+x3y;
-AeNormal(f);
-f[4] = y4+x3y+xy3;
-AeNormal(f);
-f[4] = y4+x2y2+xy3;
-AeNormal(f);
-f[4] = y4+x3y+x2y2;
-AeNormal(f);f
-f;
-f = t,x,y4+t3y,y5+xy3+x2y3+x3y2+xy4;
-size(AeNormal(f));
-f = t,x,y4+t3y,y5+xy3+x2y3+x3y2+xy4+t4y;
-size(AeNormal(f));
-f = t,x,y4+t3y,(x+y)^5;
-size(AeNormal(f));
-f = t,x,y4+t3y,(x+y)^5+t4y;
-size(AeNormal(f));
-f[4];
-f[4]=x5+t4y+x4y+x3y2+x2y3+xy4+y5;
-size(AeNormal(f));
-f[4]=t4y+x4y+x3y2+x2y3+xy4+y5;
-size(AeNormal(f));
-f[4]=t4y+x3y2+x2y3+xy4+y5;
-size(AeNormal(f));
-f[4]=t4y+x4y+x3y2+x2y3+xy4+y5;
-size(AeNormal(f));
-f[4]=t4y+x4y+x3y2+x2y3+y5;
-size(AeNormal(f));
-f[4]=x4y+x3y2+x2y3+y5;
-size(AeNormal(f));
-f = t,x,y4+t3y,(x+y)^3,t2y;
-size(AeNormal(f));
-f = t,x,y4+t3y,(x+y)^3+t2y;
-size(AeNormal(f));
-f[4];
-f[4] = t2y+x2t+xy2+y3;
-size(AeNormal(f));
-f[4] = t2y+x2y+xy2+y3;
-size(AeNormal(f));
-f[4] = t2y+3x2y+3xy2+y3;
-size(AeNormal(f));
-f[4] =3x2y+3xy2+y3;
-size(AeNormal(f));
-f[4] = t3y + 3x2y+3xy2+y3;
-size(AeNormal(f));
-f[4] = t5y + 3x2y+3xy2+y3;
-size(AeNormal(f));
-f[4] = t10y + 3x2y+3xy2+y3;
-size(AeNormal(f));
-f[4] = 3y + 3x2y+3xy2+y3;
-size(AeNormal(f));
-f;
-size(AeNormal(f));
-f[4] =  + 3x2y+3xy2+y3;
-size(AeNormal(f));
-f[4] = y;
-size(AeNormal(f));
-size(AeNormal(f));
-f = t,x,y3+t2y,(x+y)^4;
-AeNormal(f);
-f = t,x,y3+t2y,(x+y)^4+t3y;
-AeNormal(f);
-f[4];
-f[4] = x4+t3y+4x3y+6x2y2+4xy3+y4
-;
-AeNormal(f);
-size(AeNormal(f));
-f[4] = x4+t3y+4x3y+6x2y2+4xy3+y4;
-size(AeNormal(f));
-f[4] = t3y+4x3y+6x2y2+4xy3+y4;
-size(AeNormal(f));
-f[4] = t3y+x3y+x2y2+xy3+y4;
-size(AeNormal(f));
-f[4] = x3y+x2y2+xy3+y4;
-size(AeNormal(f));
-f[4] = t3y+4x3y+6x2y2+4xy3+y4;
-size(AeNormal(f));
-f[4] = 4x3y+6x2y2+4xy3+y4;
-size(AeNormal(f));
-f[4] = x3y+x2y2+xy3+y4;
-size(AeNormal(f));
-f[4] = x2y2+xy3+y4;
-size(AeNormal(f));
-f[4] = x3y+x2y2+y4;
-size(AeNormal(f));
-f[3] = y4+t3y;
-size(AeNormal(f));
-f[4] = (x+y)^5+t4y;
-size(AeNormal(f));
-f[4];
-f[4] = x4y+x3y2+x2y3+y5;
-size(AeNormal(f));
-f[4]^2;
-f[4] = x4y+x3y2+x2y3+y5;
-size(AeNormal(f));
-f[4] = x4y+x3y2+y5;
-size(AeNormal(f));
-f[4] = x4y+2x3y2+y5;
-size(AeNormal(f));
-f[4] = x4y+3x3y2+y5;
-size(AeNormal(f));
-f[4] = 5x4y+3x3y2+y5;
-size(AeNormal(f));
-f;
-f = t,x,(x+y)^4+t2y,y3+t2y;
-AeNormal(f);
-f:
-;
-f = t,x,(x+y)^4+t3y,y3+t2y;
-AeNormal(f);
-f = t,x,(x+y)^4+t2y,y3+t2y;
-AeNormal(f);
-f = t,x,(x+y)^5+t2y,y3+t2y;
-AeNormal(f);
-f = t,x,(x+y)^5+t2y,y4+t2y;
-AeNormal(f);
-f;
-f = t,x,(x+y)^4+t3y,y3+t2y;
-AeNormal(f);
-f = t,x,(x+y)^4+t3y,y3;
-AeNormal(f);
-f = t,x,(x+y)^4+t3y,y3+t2y;
-f = t,x,(x+y)^4+t3y,y3+t2y;
-AeNormal(f);
-f[3];
-f = t,x,(x+y)^4+t3y,y3+t2y;
-f[3];
-f[3] = x4+x3y+x2y2+xy3+y4;
-AeNormal(f);
-f;
-LIB"AeCodPruebas.lib";
-ring r = 0,(t,x,y),ds;
-map f = t,x,y3+t2y,y4+x3y;
-ideal f = t,x,y3+t2y,y4+x3y;
-size(AeNormal(f));
-ideal f = t,x,y5+t4y,y6+x5y;
-size(AeNormal(f));
-ideal f = t,x,y5+t4y,y6+(x5+t4)*y;
-size(AeNormal(f));
-ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
-size(AeNormal(f));
-ideal f = t,x,y3+t2y,xy3+x2y2+x3y;
-size(AeNormal(f));
-ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
-size(AeNormal(f));
-ideal f = t,x,y3+t2y,y4+xy3+x3y;
-size(AeNormal(f));
-ideal f = t,x,y3+t2y,y4+xy3-x3y;
-size(AeNormal(f));
-ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
-ideal f = t,x,y3+t2y,y4+x2y2+x3y;
-ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
-ideal f = t,x,y3+t2y,y4+x2y2+x3y;
-size(AeNormal(f));
-ideal f = t,x,y4+t2y,y5+x2y2+x3y;
-size(AeNormal(f));
-ideal f = t,x,y4+t3y,y5+x4y+x3y2;
-size(AeNormal(f));
-ideal f = t,x,y4+t3y,y5+x4y+x3y2+x2y3;
-size(AeNormal(f));
-quit;
diff --git a/.singularhistory-82675.tmp b/.singularhistory-82675.tmp
deleted file mode 100644
index e69de29..0000000
diff --git a/comparison.md b/comparison.md
index 274ebea..4d17d2d 100644
--- a/comparison.md
+++ b/comparison.md
@@ -28,5 +28,6 @@ Time is expressed in seconds.
 | 2.       | 0.01 | 0.10 | 0.03 |
 | 3.       | 0.07 | 0.36 | 0.03 |
 | 4.       | 0.01 | 0.13 | 0.11 |
+| 5.       | ---- |         |
 | 6.       | 0.03 | 163.34 | 36659.08 |
 | 7.       | 0.03 | 0.60 | 83043.46 |