Singular

7.5.7.0. makeMalgrange

Usage:

makeMalgrange(F [,ORD]); F an ideal, ORD an optional string

Return:

ring (Weyl algebra) containing an ideal IF

Purpose:

create the ideal by Malgrange associated with F = F[1],...,F[P].

Note:

Activate the output ring with the setring command. In this ring, the ideal IF is the ideal by Malgrange corresponding to F.
The value of ORD must be an arbitrary ordering in K<_t,_x,_Dt,_Dx> written in the string form. By default ORD = 'dp'.

Display:

If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.

LIB "dmodvar.lib";
ring R = 0,(x,y,z),Dp;
ideal I = x^2+y^3, z;
def W = makeMalgrange(I);
setring W;
W;
==> // coefficients: QQ
==> // number of vars : 10
==> //        block   1 : ordering dp
==> //                  : names    t(1) t(2) x y z Dt(1) Dt(2) Dx Dy Dz
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    Dt(1)t(1)=t(1)*Dt(1)+1
==> //    Dt(2)t(2)=t(2)*Dt(2)+1
==> //    Dxx=x*Dx+1
==> //    Dyy=y*Dy+1
==> //    Dzz=z*Dz+1
IF;
==> IF[1]=-y^3-x^2+t(1)
==> IF[2]=t(2)-z
==> IF[3]=2*x*Dt(1)+Dx
==> IF[4]=3*y^2*Dt(1)+Dy
==> IF[5]=Dt(2)+Dz