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SINGULAR
code:
tau-constant strata of A3
************************************************************
** requires dynamic loading and ringlists (Singular 2.1) **
************************************************************
LIB "sing.lib";
LIB "partsb.lib";
ring rx=0,(x,y),ds;
poly f=x^4+y^2;
// determine basis of T1(f)
ideal jf=jacob(f),f;
ideal kb=kbase(std(jf));
kb;
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==>
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kb[1]=x2
kb[2]=x
kb[3]=1
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// define versal family
ring rt=0,(t(1..size(kb))),ds;
def rr=rt+rx;setring rr;
def f=imap(rx,f);
def kb=imap(rx,kb);
poly F=f;
for(int i=1;i<=size(kb);i++) { F=F+t(i)*kb[i]; }
F;
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==>
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y^2+x^4+t(1)*x^2+t(2)*x+t(3)
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// determine presentation of T1(F)
ideal jF=diff(F,x),diff(F,y),F;
list li=Ot_Presentation(jF,ideal(0),20,intvec(1,1,1,0,0));
matrix M=li[1];
// flattening stratification of M
flatteningStrat(M);
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==>
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[1]:
_[1]=256*t(3)^3-27*t(2)^4+144*t(1)*t(2)^2*t(3)-128*t(1)^2*t(3)^2-4*t(1)^3*t(2)^2+16*t(1)^4*t(3);
[2]:
_[1]=9*t(2)^2-8*t(1)*t(3)+2*t(1)^3
_[2]=12*t(2)*t(3)+t(1)^2*t(2)
_[3]=32*t(3)^2+3*t(1)*t(2)^2-8*t(1)^2*t(3)
[3]:
_[1]=t(1)
_[2]=t(2)
_[3]=t(3)
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--> Interpretation of the output.
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