D.4.21.2 depthIdeal

Usage:

depthIdeal (i[,e]); i ideal, e integer

Return:

an integer, the depth of S/i where S=K[x(0)..x(n)] is the basering. (returns -1 if i is not homogeneous or if i=(1))

Assume:

i is a proper homogeneous ideal.
e=0: (default)
If K is an infinite field, makes random changes of coordinates. If K is a finite field, works over a transcendental extension. e=1: Makes random changes of coordinates even when K is finite. It works if it terminates, but may result in an infinite loop. After 30 loops, a warning message is displayed and -1 is returned.

Note:

If printlevel > 0 (default = 0), dim(S/i) is also displayed.

LIB "mregular.lib";
ring r=0,(x,y,z,t,w),dp;
ideal i=y2t,x2y-x2z+yt2,x2y2,xyztw,x3z2,y5+xz3w-x2zw2,x7-yt2w4;
depthIdeal(i);
==> 1
depthIdeal(lead(std(i)));
==> 0
// Additional information is displayed if you change printlevel (=1);