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SINGULAR
example: Saturation
LIB "elim.lib";
LIB "primdec.lib";
ring r=0,(x,y,z),dp;
ideal I1=x5z3,xyz,yz4;
primdecGTZ(I1); // the 4 components (2 embedded)
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==>
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[1]: [2]: [3]: [4]:
[1]: [1]: [1]: [1]:
_[1]=z _[1]=y _[1]=z3 _[1]=z4
_[2]=x5 _[2]=y _[2]=x
[2]: [2]: [2]: [2]:
_[1]=z _[1]=y _[1]=z _[1]=z
_[2]=x _[2]=y _[2]=x
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We compute the saturation of I1
w.r.t. <z> and
the corresponding saturation exponent:
ideal I2=z;
sat(I1,I2);
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==>
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[1]:
_[1]=y
_[2]=x5
[2]:
4
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We see that three components (1 isolated and 2
embedded) are removed.
A second example: to compute the projective subscheme defined by a
homogeneous ideal, we compute the saturation w.r.t. the
irrelevant ideal.
ideal I=(x2z+y3)*maxideal(2);
sat(I,maxideal(1));
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==>
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[1]:
_[1]=y3+x2z
[2]:
2
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