# Singular

#### D.4.21.7 intersectZ

Procedure from library `primdecint.lib` (see primdecint_lib).

Return:
the intersection of the input ideals

Note:
this is an alternative to intersect(I,J) over integers, is faster for some examples and should be kept for debug purposes.

Example:
 ```LIB "primdecint.lib"; ring R=integer,(a,b,c,d),dp; ideal I1=9,a,b; ideal I2=3,c; ideal I3=11,2a,7b; ideal I4=13a2,17b4; ideal I5=9c5,6d5; ideal I6=17,a15,b15,c15,d15; ideal I=intersectZ(I1,I2); I; ==> I[1]=9 ==> I[2]=3b ==> I[3]=3a ==> I[4]=bc ==> I[5]=ac I=intersectZ(I,I3); I; ==> I[1]=99 ==> I[2]=3b ==> I[3]=3a ==> I[4]=bc ==> I[5]=ac I=intersectZ(I,I4); I; ==> I[1]=39a2 ==> I[2]=13a2c ==> I[3]=51b4 ==> I[4]=17b4c ==> I[5]=3a2b4 ==> I[6]=a2b4c I=intersectZ(I,I5); I; ==> I[1]=78a2d5 ==> I[2]=117a2c5 ==> I[3]=102b4d5 ==> I[4]=153b4c5 ==> I[5]=6a2b4d5 ==> I[6]=9a2b4c5 ==> I[7]=39a2c5d5 ==> I[8]=51b4c5d5 ==> I[9]=3a2b4c5d5 I=intersectZ(I,I6); I; ==> I[1]=1326a2d5 ==> I[2]=1989a2c5 ==> I[3]=102b4d5 ==> I[4]=153b4c5 ==> I[5]=663a2c5d5 ==> I[6]=51b4c5d5 ==> I[7]=78a2d15 ==> I[8]=117a2c15 ==> I[9]=78a15d5 ==> I[10]=117a15c5 ==> I[11]=6a2b4d15 ==> I[12]=9a2b4c15 ==> I[13]=39a2c5d15 ==> I[14]=39a2c15d5 ==> I[15]=6a2b15d5 ==> I[16]=9a2b15c5 ==> I[17]=6a15b4d5 ==> I[18]=9a15b4c5 ==> I[19]=39a15c5d5 ==> I[20]=3a2b4c5d15 ==> I[21]=3a2b4c15d5 ==> I[22]=3a2b15c5d5 ==> I[23]=3a15b4c5d5 ```