Singular

LIB "difform.lib";
///////////////////////////////////////////////////////////////
// Example for a differential algebra over a polynomial ring //
///////////////////////////////////////////////////////////////
ring R = 0,(a,b,c),ds;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms da, db, dc are available.
setring Omega_R;
// The differential algebra is given by:
basering;
==> // coefficients: QQ
==> // number of vars : 6
==> //        block   1 : ordering dp
==> //                  : names    Da Db Dc
==> //        block   2 : ordering ds
==> //                  : names    a b c
==> //        block   3 : ordering C
==> // noncommutative relations:
==> //    DbDa=-Da*Db
==> //    DcDa=-Da*Dc
==> //    DcDb=-Db*Dc
==> // quotient ring from ideal
==> _[1]=Da^2
==> _[2]=Db^2
==> _[3]=Dc^2
kill R,Omega_R,da,db,dc;
/////////////////////////////////////////////////////////////
// Example for a differential algebra over a quotient ring //
/////////////////////////////////////////////////////////////
ring R = 0,(x,y,z),lp;
ideal I = x+y+z,xyz;
qring S = std(I);
diffAlgebra();
==> // The differential algebra Omega_S was constructed and the differential \
   forms dx, dy, dz are available.
setring Omega_S;
// The differential algebra is given by:
basering;
==> // coefficients: QQ
==> // number of vars : 6
==> //        block   1 : ordering dp
==> //                  : names    Dx Dy Dz
==> //        block   2 : ordering lp
==> //                  : names    x y z
==> //        block   3 : ordering C
==> // noncommutative relations:
==> //    DyDx=-Dx*Dy
==> //    DzDx=-Dx*Dz
==> //    DzDy=-Dy*Dz
==> // quotient ring from ideal
==> _[1]=y^2*z+y*z^2
==> _[2]=x+y+z
==> _[3]=Dz*y^4+3*Dz*y^3*z+2*Dz*y^2*z^2
==> _[4]=Dy*z^3+2*Dz*y^3+5*Dz*y^2*z+2*Dz*y*z^2
==> _[5]=2*Dy*y*z+Dy*z^2+Dz*y^2+2*Dz*y*z
==> _[6]=Dx+Dy+Dz
==> _[7]=Dy*Dz*y^2+2*Dy*Dz*y*z
==> _[8]=Dz^2
==> _[9]=Dy^2
==> _[10]=Dx^2
kill Omega_S,dx,dy,dz;