LIB "integralbasis.lib";
ring R = 0, (x,y), dp;
int k = 3;
int d = 6;
// Polynomial of degree 6 in y with an ordinary multiple point
// at the origin of order k.
poly f = polyDK(d, k, 1231);
f;
==> -1/3x6-4/3x5y+x4y2+1/3x3y3-x2y4-4/3xy5+y6+1/3x5-x4y+x3y2+1/3x2y3-1/3xy4+4\
   /3y5+x4+4/3x3y-2/3x2y2+2/3xy3-y4+x3+2/3xy2+4/3y3
// The integral basis of R / <f>
list l = integralBasis(f, 2, "atOrigin");
l;
==> [1]:
==>    _[1]=x2
==>    _[2]=x2y
==>    _[3]=x2y2
==>    _[4]=-1413399/32768x8y2-1016807/12288x8y+19063/2048x7y2+1386535/32768x\
   8+15505/1536x7y-657/1024x6y2-151351/6144x7+2399/384x6y-65/32x5y2+36083/30\
   72x6-155/24x5y+15/16x4y2-191/96x5+7/6x4y-11/6x3y2+x2y3-5/48x4-x3y+4/3x2y2\
   +7/6x3-x2y+4/3x2
==>    _[5]=-1413399/32768x7y3-1016807/12288x7y2+19063/2048x6y3+1386535/32768\
   x7y+15505/1536x6y2-657/1024x5y3-151351/6144x6y+2399/384x5y2-65/32x4y3+360\
   83/3072x5y-155/24x4y2+15/16x3y3-191/96x4y+7/6x3y2-11/6x2y3+xy4-5/48x3y-x2\
   y2+4/3xy3+7/6x2y-xy2+4/3xy
==>    _[6]=-1413399/32768x6y4-1016807/12288x6y3+19063/2048x5y4+1386535/32768\
   x6y2+15505/1536x5y3-657/1024x4y4-151351/6144x5y2+2399/384x4y3-65/32x3y4+3\
   6083/3072x4y2-155/24x3y3+15/16x2y4-191/96x3y2+7/6x2y3-11/6xy4+y5-5/48x2y2\
   -xy3+4/3y4+7/6xy2-y3+4/3y2
==> [2]:
==>    x2