C-CAL,1969

01.01 C TO FIND REAL ROOTS OF A P(X)=0.
01.02 C NEWTON-RAPHSON METHOD.
01.10 A !!?DEGREE?,!,"COEFF.";S K=0;F I=0,DE;A C(I)
01.20 A !?LL UL?;F X=LL,UL;D 2
01.30 T !!,%2,K," REAL ROOT(S) IN ["LL,","UL,"]";G 1.1

02.10 S P=0;F I=0,DE;S P=P*X+C(I)
02.20 D 3

03.05 S Y=X-1;S Q=0;F I=0,DE;S Q=Q*Y+C(I)
03.10 I [P*Q]3.2,3.3;R
03.20 D 4
03.25 R
03.30 I [P]3.4,3.5
03.40 R
03.50 T %2,!"ROOT ="Y+1;S K=K+1;R

04.10 S AP=(2*Y+1)/2
04.20 S P=0;F I=0,DE;S P=P*AP+C(I)
04.30 F J=0,DE;S B(J)=C(J)*(DE-J)
04.40 S P'=0;F J=0,DE-1;S P'=P'*AP+B(J)
04.50 S RO=AP-P/P';I (RO-AP)4.6,4.7
04.60 S AP=RO;G 4.2
04.70 T %6.03,!"ROOT ="RO;S K=K+1;R
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