# Singular

#### D.14.4.7 boolean_ideal

Procedure from library `polybori.lib` (see polybori_lib).

Usage:
boolean_ideal(Is[, rb]); Is Ideal, rb boolean ring

Return:
default: ideal Is in the representation of the boolean ring rb==boolean_poly_ring(basering); optional input: rb boolean ring

Example:
 ```LIB "polybori.lib"; ring r0=2,x(1..4),lp; poly f1=x(1)^2+2*x(2)*(x(3))-x(4)^3; poly f2=x(1)^2-x(3)*x(1); poly f3=x(2)+5-2*x(1); poly f4=x(1)*x(2)-x(3); ideal I=f1,f2,f3,f4; boolean_ideal(I); ==> _[1] = x(1) + x(4) ==> _[2] = x(1)*x(3) + x(1) ==> _[3] = x(2) + 1 ==> _[4] = x(1)*x(2) + x(3) ==> ring r1=0,x,Dp; poly f1=x3+2*x+1; poly f2=x10-x5+2x; poly f3=19; ideal I=f1,f2,f3; boolean_ideal(I); ==> _[1] = x + 1 ==> _[2] = 0 ==> _[3] = 1 ==> ring r2=32003,(x,y,z),Dp; bring bbr2=r2; poly f1=xyz+20*x^2*y-3*xz+15; poly f2=32002*xy+z2; poly f3=19; ideal I=f1,f2,f3; boolean_ideal(I); ==> _[1] = x*y*z + x*z + 1 ==> _[2] = x*y + z ==> _[3] = 1 ==> boolean_ideal(I,bbr2); ==> _[1] = x*y*z + x*z + 1 ==> _[2] = x*y + z ==> _[3] = 1 ==> ```
See also: boolean_std.