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D.4.25.3 realrad
Procedure from library realrad.lib (see realrad_lib).
- Usage:
- realrad(id), id an ideal of arbitrary dimension
- Return:
- the real radical of id
- Exampe:
- example realrad; shows an example
Example:
| | LIB "realrad.lib";
ring r1=0,(x,y,z),lp;
//dimension 0
ideal i0=(x2+1)*(x3-2),(y3-2)*(y2+y+1),z3+2;
//dimension 1
ideal i1=(y3+3y2+y+1)*(y2+4y+4)*(x2+1),(x2+y)*(x2-y2)*(x2+2xy+y2)*(y2+y+1);
ideal i=intersect(i0,i1);
realrad(i);
==> _[1]=2x4y+5x4-2x2y3-3x2y2+5x2y-2y4-5y3
==> _[2]=-3x4+4x2y4+20x2y3+31x2y2+9x2y+8x2+4y5-4y4z2+4y4z+20y4-20y3z2+20y3z+3\
1y3-28y2z2+28y2z+12y2-12yz2+12yz+8y-8z2+8z
==> _[3]=y4z3+2y4+5y3z3+10y3+7y2z3+14y2+3yz3+6y+2z3+4
==> _[4]=59y5z2+38y5z-74y5+333y4z2+116y4z-488y4+603y3z2-104y3z-1108y3+443y2z2\
-404y2z-1048y2+232yz2-146yz-502y+76z2-148z-236
==> _[5]=59xy4z2+38xy4z-74xy4+295xy3z2+190xy3z-370xy3+413xy2z2+266xy2z-518xy2\
+177xyz2+114xyz-222xy+118xz2+76xz-148x+38y4z2-74y4z-118y4+190y3z2-370y3z-\
590y3+266y2z2-518y2z-826y2+114yz2-222yz-354y+76z2-148z-236
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