          ##### 7.5.4.0. minIntRoot
Procedure from library `dmod.lib` (see dmod_lib).

Usage:
minIntRoot(P, fact); P an ideal, fact an int

Return:
int

Purpose:
minimal integer root of a maximal ideal P

Note:
if fact==1, P is the result of some 'factorize' call,
else P is treated as the result of bernstein::gmssing.lib
in both cases without constants and multiplicities

Example:
 ```LIB "dmod.lib"; ring r = 0,(x,y),ds; poly f1 = x*y*(x+y); ideal I1 = bernstein(f1); // a local Bernstein poly I1; ==> I1=-4/3 ==> I1=-1 ==> I1=-2/3 minIntRoot(I1,0); ==> -1 poly f2 = x2-y3; ideal I2 = bernstein(f2); I2; ==> I2=-7/6 ==> I2=-1 ==> I2=-5/6 minIntRoot(I2,0); ==> -1 // now we illustrate the behaviour of factorize // together with a global ordering ring r2 = 0,x,dp; poly f3 = 9*(x+2/3)*(x+1)*(x+4/3); //global b-polynomial of f1=x*y*(x+y) ideal I3 = factorize(f3,1); I3; ==> I3=x+1 ==> I3=3x+2 ==> I3=3x+4 minIntRoot(I3,1); ==> -1 // and a more interesting situation ring s = 0,(x,y,z),ds; poly f = x3 + y3 + z3; ideal I = bernstein(f); I; ==> I=-2 ==> I=-5/3 ==> I=-4/3 ==> I=-1 minIntRoot(I,0); ==> -2 ```          User manual for Singular version 4.3.2, 2023, generated by texi2html.