Laguerre15m_or.h

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#Sum of the multiplicities of all roots in a circle
cohn_schur := proc(po,ce,ra)
local p1,de,deg,ep,ld,lc,di,c0,p2,coun,k,b;
if ce=0 and ra=1 then
    p1:=po
else
    p1:=sort(expand(eval(po,z=ra*z+ce)))
fi;
 
if degree(p1)<0 then
    coun:=1
else
ld:=ldegree(p1);
coun:=ld;
if ld<infinity and ld>0 then
    p1:=quo(p1,z^ld,z)
fi;
de:=degree(p1);
while de>1 do
lc:=lcoeff(p1);
c0:=coeff(p1,z,0);
di:=Re(lc)^2+Im(lc)^2-Re(c0)^2-Im(c0)^2;
p2:=add(conjugate(coeff(p1,z,de-j))*z^j,j=0..de);
if di>0 then
p1:=quo(expand(conjugate(lc)*p1-c0*p2),z,z);
coun:=coun+1;
userinfo(3,spa,‘NoName‘,‘Case I‘,‘Degree‘,degree(p1),‘Count‘,coun)
elif di<0 then
p1:=expand(conjugate(c0)*p1-lc*p2);
userinfo(3,spa,‘NoName‘,‘Case II‘,‘Degree‘,degree(p1),‘Count‘,coun)
else
ep:=lc/conjugate(c0);
k:=0;
while k<=de and coeff(p1,z,k)=ep*conjugate(coeff(p1,z,de-k)) do
k:=k+1
od;
if k<=de then
b:=(coeff(p1,z,de-k)-ep*conjugate(coeff(p1,z,k)))/lc;
p1:=sort(expand((z^k+2*b/evalf(abs(b)))*p1));
deg:=degree(p1);
p2:=add(conjugate(coeff(p1,z,deg-j))*z^j,j=0..deg);
lc:=lcoeff(p1);
c0:=coeff(p1,z,0);
p1:=expand(conjugate(c0)*p1-lc*p2);
deg:=degree(p1);
p2:=add(conjugate(coeff(p1,z,deg-j))*z^j,j=0..deg);
lc:=lcoeff(p1);
c0:=coeff(p1,z,0);
p1:=quo(expand(conjugate(lc)*p1-c0*p2),z,z);
coun:=coun+1;
userinfo(3,spa,‘NoName‘,‘Case III‘,‘Degree‘,degree(p1),‘Count‘,coun)
else
p1:=add((de-j)*coeff(p1,z,de-j)*z^j,j=0..de-1);
userinfo(3,spa,‘NoName‘,‘Case IV‘,‘Degree‘,degree(p1),‘Count‘,coun)
fi
fi;
de:=degree(p1)
od;
if degree(p1)=1 then
lc:=lcoeff(p1);
c0:=coeff(p1,z,0);
if (Re(c0)^2+Im(c0)^2)<(Re(lc)^2+Im(lc)^2) then
coun:=coun+1;
userinfo(3,spa,‘NoName‘,‘Case I‘,‘Degree‘,0,‘Count‘,coun)
fi
fi
fi;
userinfo(1,spa,‘NoName‘,‘cohn_schur‘,coun);
coun
end: #cohn_schur