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5.1.95 preimage
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Syntax: preimage (ring_name,map_name,ideal_name)preimage (ring_name,ideal_expression,ideal_name)-
Type: ideal
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Purpose: returns the preimage of an ideal under a given map.
The second argument has to be a map from the basering to the given ring (or an ideal defining such a map), and the ideal has to be an ideal in the given ring.-
Note: To compute the kernel of a map, the preimage of zero has to be determined. Hence there is no special command for computing the kernel of a map in SINGULAR.
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Example: ring r1=32003,(x,y,z,w),lp; ring r=32003,(x,y,z),dp; ideal i=x,y,z; ideal i1=x,y; ideal i0=0; map f=r1,i; setring r1; ideal i1=preimage(r,f,i1); i1; → i1[1]=w → i1[2]=y → i1[3]=x // the kernel of f preimage(r,f,i0); → _[1]=w