Singular Manual: depthIdeal

| #### D.4.19.2 depthIdeal Procedure from library `mregular.lib` (see mregular_lib). 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. Example:
    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);

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