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/*======================================================================
AFUPMPR(M,I,B,J,L; Js,j)
Algebraic number field univariate polynomial minimal polynomial of a real root.
Inputs
M : in Z[x], the minimal polynomial of an algebraic number alpha.
I : an acceptable isolating interval for alpha.
B : in Q(alpha)[x]. B has a unique root beta of odd multiplicity
in J.
J : a Binary rational interval which is either left-open and right-closed
or a one-point interval.
L : is a nonempty list (L1,...,Lt) of positive irreducible elements of
Z[x]. Exactly one Li has beta as a root.
Outputs
Js : a Binary rational interval. Js is a subinterval of J which is an
isolating interval for beta as a root of Lj. Js is either left-open
and right-closed or a one-point interval.
j : a BETA-digit. Lj is the unique element of L having beta as a root.
======================================================================*/
#include "qepcad.h"
void AFUPMPR(Word M, Word I, Word B, Word J, Word L, Word *Js_, Word *j_)
{
Word Js,L1,Lp,a,b,c,j,jp,s,t,v,vp;
/* hide L1,Lp,j,jp,s,t,v,vp; */
Step1: /* Initialize. */
j = 0;
FIRST2(J,&a,&b);
t = AFUPSR(M,I,B,b);
if (t == 0)
goto Step4;
Step2: /* Test for real roots of each Li in current interval. */
v = 0;
jp = 0;
Lp = L;
Js = LIST2(a,b);
do
{
ADV(Lp,&L1,&Lp);
jp = jp + 1;
vp = IUPVOI(L1,Js);
if (vp > 1)
goto Step3;
if (vp == 1)
if (v == 1)
goto Step3;
else
{
v = 1;
j = jp;
}
}
while (!(Lp == NIL));
goto Return;
Step3: /* Bisect current interval. */
c = RIB(a,b);
s = AFUPSR(M,I,B,c);
if (s == 0)
{
b = c;
goto Step4;
}
else
if (s * t < 0)
a = c;
else
{
b = c;
t = s;
}
goto Step2;
Step4: /* B has root at right end point of current interval. */
j = 0;
Js = LIST2(b,b);
Lp = L;
do
{
ADV(Lp,&L1,&Lp);
j = j + 1;
if (PDEG(L1) == 1)
if (IUPBES(L1,b) == 0)
goto Return;
}
while (1);
Return: /* Prepare for return. */
*Js_ = Js;
*j_ = j;
return;
}
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