1/3;
ring R1 = 0, (x,y,z), lp; // Q[x,y,z], ordine lessicografico
1/3;
1/3
num a = 1/3;
number a = 1/3;
help ring;
// ** Displaying help in browser 'firefox-www'.
// ** Use 'system("--browser", <browser>);' to change browser,
// ** where <browser> can be: "firefox-www", "konqueror-www", "lynx-www", "dummy", "emacs".
running `firefox http://www.singular.uni-kl.de/Manual/4-0-2/ &`

;
poly f1 = x^2+y+z-1;
poly f2 = x+y^2+z-1;
poly f3 = x+y+z^2-1;
ideal I = f1, f2, f3;;
ideal I = f1, f2, f3;
// ** redefining I **
I;
I[1]=x2+y+z-1
I[2]=x+y2+z-1
I[3]=x+y+z2-1
std(I);
_[1]=z6-4z4+4z3-z2
_[2]=2yz2+z4-z2
_[3]=y2-y-z2+z
_[4]=x+y+z2-1
GI = _;
ideal GI = _;
GI;
GI[1]=z6-4z4+4z3-z2
GI[2]=2yz2+z4-z2
GI[3]=y2-y-z2+z
GI[4]=x+y+z2-1
// [CLO, pag. 90]
;
ring R = 0, (x,y), Dp;
poly f1 = x^3 - 2*x*y;
poly f2 = x^2*y - 2*y^2 + x;
ideal I = f1, f2;
groebner(I);
_[1]=2y2-x
_[2]=xy
_[3]=x2
std(I);
_[1]=2y2-x
_[2]=xy
_[3]=x2
option(option(redSB);
 error at token `;`
option(redSB);
ring R2 = 0, (x,y), lp;
ideal I = x^10 + y^8*z^2, x*y + y^2 + z^2;
ring R2 = 0, (x,y,z), lp;
// ** redefining R2 **
ideal I = x^10 + y^8*z^2, x*y + y^2 + z^2;
std(I);
_[1]=y20+11y18z2+45y16z4+120y14z6+210y12z8+252y10z10+210y8z12+120y6z14+45y4z16+10y2z18+z20
_[2]=xz18-y19-11y17z2-45y15z4-120y13z6-210y11z8-252y9z10-210y7z12-120y5z14-45y3z16-9yz18
_[3]=xy+y2+z2
_[4]=x2z16+y18+11y16z2+45y14z4+120y12z6+210y10z8+252y8z10+210y6z12+120y4z14+44y2z16+8z18
_[5]=x3z14+7xz16-y17-11y15z2-45y13z4-120y11z6-210y9z8-252y7z10-210y5z12-119y3z14-35yz16
_[6]=x4z12+6x2z14+y16+11y14z2+45y12z4+120y10z6+210y8z8+252y6z10+209y4z12+110y2z14+27z16
_[7]=x5z10+5x3z12+20xz14-y15-11y13z2-45y11z4-120y9z6-210y7z8-251y5z10-200y3z12-75yz14
_[8]=x6z8+4x4z10+14x2z12+y14+11y12z2+45y10z4+120y8z6+209y6z8+242y4z10+165y2z12+48z14
_[9]=x7z6+3x5z8+9x3z10+28xz12-y13-11y11z2-45y9z4-119y7z6-200y5z8-207y3z10-90yz12
_[10]=x8z4+2x6z6+5x4z8+14x2z10+y12+11y10z2+44y8z4+110y6z6+165y4z8+132y2z10+42z12
_[11]=x9z2+x7z4+2x5z6+5x3z8+14xz10-y11-10y9z2-35y7z4-75y5z6-90y3z8-42yz10
_[12]=x10+y8z2
ring R3 = 0, (x,y,z), dp;
I;
ideal I = imap(R2,I);
std(I);
_[1]=xy+y2+z2
_[2]=x10+y8z2
_[3]=y11-x9z2+10y9z2-x7z4+35y7z4-2x5z6+75y5z6-5x3z8+90y3z8-14xz10+42yz10
x*y^2*z^3  >    x*y*z^4;
1
x*y^2*z^3  >    x^2*y*z^4;
0
x*y^2*z^3  ==    x^2*y*z^4;
0
x*y^2*z^3  !=    x^2*y*z^4;
1
x*y^2*z^3  <>    x^2*y*z^4;
1
x*y^2*z^3  ><    x^2*y*z^4;
   skipping text from ` `
LIB "surf.lib";
// ** loaded /usr/bin/../share/singular/LIB/surf.lib (4.0.0.0,Jun_2013)
ring R = 0,(x,y),dp;
// ** redefining R **
ideal J = x^3-y^2;
plot(J);
Close window to exit from `singularsurf`.
0
ring R = 0,(x,y,z),dp;
// ** redefining R **
// superficie romana di Steiner 1844
ideal J = x^2*y^2+x^2*z^2+y^2*z^2-17*x*y*z;
surfer(J);
Close window to exit from `surfer`.
0
monitor("");