GCL (GNU Common Lisp) Version(2.2.2) Sat Oct 31 16:13:00 PST 1998 Licensed under GNU Public Library License Contains Enhancements by W. Schelter Maxima 5.2 Sat Oct 31 16:12:50 PST 1998 (with enhancements by W. Schelter). (C1) display2d:false; (D1) FALSE (C2) batch("quintic.mac"); batching #/home/doyle/max/quintic/quintic.mac (C3) "load utility routines" (D3) "load utility routines" (C4) HESSIAN2(F):=BLOCK([F11,F12,F22],F11:DIFF(F,Z1,2),F22:DIFF(F,Z2,2), F12:DIFF(F,Z1,1,Z2,1), RATSIMP(DETERMINANT(MATRIX([F11,F12],[F12,F22])))) (C5) AUGMENTEDHESSIAN2(F,G):=BLOCK([F11,F12,F22,G1,G2],F11:DIFF(F,Z1,2), F22:DIFF(F,Z2,2),F12:DIFF(F,Z1,1,Z2,1),G1:DIFF(G,Z1), G2:DIFF(G,Z2), RATSIMP(DETERMINANT( MATRIX([F11,F12,G1],[F12,F22,G2],[G1,G2,0])))) (C6) JACOBIAN2(F,G):=BLOCK([F1,F2,G1,G2],F1:DIFF(F,Z1),F2:DIFF(F,Z2), G1:DIFF(G,Z1),G2:DIFF(G,Z2), RATSIMP(DETERMINANT(MATRIX([F1,F2],[G1,G2])))) (C7) CROSS2(F):=RATSIMP([-F[2],F[1]]) (C8) D2(F):=RATSIMP([DIFF(F,Z1),DIFF(F,Z2)]) (C9) NEWTON2(F):=RATSIMP(CROSS2(D2(F))) (C10) CRITICAL2(F):=JACOBIAN2(F[1],F[2]) (C11) PROMOTE2(EXPR,HVAR):=BLOCK([PRET], IF HVAR[1] = Z1 OR HVAR[1] = Z2 OR HVAR[2] = Z1 OR HVAR[2] = Z2 THEN ERROR("can't promote z1 or z2"),PRET:EXPR, PRET:SUBST(SAVEZ1,Z1,PRET),PRET:SUBST(SAVEZ2,Z2,PRET), PRET:SUBST(Z1,HVAR[1],PRET),PRET:SUBST(Z2,HVAR[2],PRET),PRET) (C12) DEMOTE2(EXPR,HVAR):=BLOCK([PRET], IF HVAR[1] = Z1 OR HVAR[1] = Z2 OR HVAR[2] = Z1 OR HVAR[2] = Z2 THEN ERROR("can't demote z1 or z2"),PRET:EXPR, PRET:SUBST(HVAR[1],Z1,PRET),PRET:SUBST(HVAR[2],Z2,PRET), PRET:SUBST(Z1,SAVEZ1,PRET),PRET:SUBST(Z2,SAVEZ2,PRET),PRET) (C13) DOIT2(HVAR,'DOITFUN,[DOITEXPR]):=BLOCK([DOITRET],DOITRET:DOITEXPR, DOITRET:PROMOTE2(DOITRET,HVAR),DOITRET:APPLY(DOITFUN,DOITRET), DOITRET:DEMOTE2(DOITRET,HVAR),DOITRET) (C14) HOMOG2(HVAR,VAR,DEG,EXPR):=RATSIMP( HVAR[2]^DEG*SUBST(HVAR[1]/HVAR[2],VAR,EXPR)) (C15) NHOMOG2(HVAR,VAR,EXPR):=RATSIMP(SUBLIS([HVAR[1] = VAR,HVAR[2] = 1], EXPR)) (C16) DISCRIMINANT(POLY,VAR):=BLOCK([DEG,LEAD],DEG:HIPOW(POLY,VAR), LEAD:RATCOEF(POLY,VAR,DEG), POLY\_DISCRIMINANT(POLY,VAR)/LEAD^(2*DEG-2)) (C17) PRUNE(EXPR,VAR,DEG):=BLOCK([RATWEIGHTS,RATWTLVL],RATWEIGHT(VAR,1), RATWTLVL:DEG,RATSIMP(EXPR)) (C18) RATCOEFF2(EXPR,VAR1,DEG1,VAR2,DEG2):=RATCOEF(RATCOEF(EXPR,VAR1,DEG1), VAR2,DEG2) (C19) "load general definitions" (D19) "load general definitions" (C20) POWERDISP:TRUE (C21) ALGEBRAIC:TRUE (C22) TELLRAT(EE^4+EE^3+EE^2+EE+1) (C23) DW('DWFN,[DWARGS]):=APPLY(DOIT2,APPEND([[W1,W2],DWFN],DWARGS)) (C24) HZ(DEG,EXPR):=HOMOG2([Z1,Z2],Z,DEG,EXPR) (C25) NHZ(EXPR):=NHOMOG2([Z1,Z2],Z,EXPR) (C26) HW(DEG,EXPR):=HOMOG2([W1,W2],W,DEG,EXPR) (C27) NHW(EXPR):=NHOMOG2([W1,W2],W,EXPR) (C28) FRAC(EXPR):=RATSIMP(EXPR[1]/EXPR[2]) (C29) NFRAC(EXPR):=[NUM(EXPR),DENOM(EXPR)] (C30) COMPOSE(F,G,HVAR):=SUBLIS([HVAR[1] = G[1],HVAR[2] = G[2]],F) (C31) COMPZ(F,G):=COMPOSE(F,G,[Z1,Z2]) (C32) COMPW(F,G):=COMPOSE(F,G,[W1,W2]) (C33) LOOKATPOLE(FORM):=RATSIMP(COMPW(COMPZ(FORM,[Z2,Z1]),[W2,W1])) (C34) LOOKATONE(FORM):=RATSIMP(COMPW(COMPZ(FORM,[Z1+Z2,Z2]),[W1+W2,W2])) (C35) "compute and store icosahedral forms" (D35) "compute and store icosahedral forms" (C36) F12:RATSIMP(Z1*Z2*(Z1^10+11*Z1^5*Z2^5-Z2^10)) (D36) Z1^11*Z2+11*Z1^6*Z2^6-Z1*Z2^11 (C37) H20:RATSIMP(1/121*HESSIAN2(F12)) (D37) -Z1^20+228*Z1^15*Z2^5-494*Z1^10*Z2^10-228*Z1^5*Z2^15-Z2^20 (C38) T30:RATSIMP(1/20*JACOBIAN2(F12,H20)) (D38) Z1^30+522*Z1^25*Z2^5-10005*Z1^20*Z2^10-10005*Z1^10*Z2^20-522*Z1^5*Z2^25 +Z2^30 (C39) IF RATSIMP(T30^2+H20^3+(-1728)*F12^5) # 0 THEN ERROR("basic identity failed") (C40) PHI31\_10:RATSIMP((-T30)*[Z1,Z2]) (D40) [-Z1^31-522*Z1^26*Z2^5+10005*Z1^21*Z2^10+10005*Z1^11*Z2^20 +522*Z1^6*Z2^25-Z1*Z2^30, -Z1^30*Z2-522*Z1^25*Z2^6+10005*Z1^20*Z2^11+10005*Z1^10*Z2^21 +522*Z1^5*Z2^26-Z2^31] (C41) PHI31\_01:RATSIMP(H20*NEWTON2(F12)) (D41) [Z1^31-162*Z1^26*Z2^5-14565*Z1^21*Z2^10+35340*Z1^16*Z2^15 +9615*Z1^11*Z2^20-2442*Z1^6*Z2^25-11*Z1*Z2^30, -11*Z1^30*Z2+2442*Z1^25*Z2^6+9615*Z1^20*Z2^11-35340*Z1^15*Z2^16 -14565*Z1^10*Z2^21+162*Z1^5*Z2^26+Z2^31] (C42) PHI31:W1*PHI31\_10+W2*PHI31\_01 (D42) [W2*(Z1^31-162*Z1^26*Z2^5-14565*Z1^21*Z2^10+35340*Z1^16*Z2^15 +9615*Z1^11*Z2^20-2442*Z1^6*Z2^25-11*Z1*Z2^30) +W1*(-Z1^31-522*Z1^26*Z2^5+10005*Z1^21*Z2^10+10005*Z1^11*Z2^20 +522*Z1^6*Z2^25-Z1*Z2^30), W1*(-Z1^30*Z2-522*Z1^25*Z2^6+10005*Z1^20*Z2^11+10005*Z1^10*Z2^21 +522*Z1^5*Z2^26-Z2^31) +W2*(-11*Z1^30*Z2+2442*Z1^25*Z2^6+9615*Z1^20*Z2^11-35340*Z1^15*Z2^16 -14565*Z1^10*Z2^21+162*Z1^5*Z2^26+Z2^31)] (C43) T6:RATSIMP(Z1^6+2*Z1^5*Z2+(-5)*Z1^4*Z2^2+(-5)*Z1^2*Z2^4+(-2)*Z1*Z2^5 +Z2^6) (D43) Z1^6+2*Z1^5*Z2-5*Z1^4*Z2^2-5*Z1^2*Z2^4-2*Z1*Z2^5+Z2^6 (C44) W8:RATSIMP(1/400*HESSIAN2(T6)) (D44) -Z1^8+Z1^7*Z2-7*Z1^6*Z2^2-7*Z1^5*Z2^3+7*Z1^3*Z2^5-7*Z1^2*Z2^6-Z1*Z2^7 -Z2^8 (C45) CHI12:RATSIMP(H20/W8) (D45) Z1^12+Z1^11*Z2-6*Z1^10*Z2^2-20*Z1^9*Z2^3+15*Z1^8*Z2^4-24*Z1^7*Z2^5 +11*Z1^6*Z2^6+24*Z1^5*Z2^7+15*Z1^4*Z2^8+20*Z1^3*Z2^9-6*Z1^2*Z2^10 -Z1*Z2^11+Z2^12 (C46) "compute sums of products of forms in z and w" (D46) "compute sums of products of forms in z and w" (C47) FOR I THRU 5 DO DEFINE(T[I](Z1,Z2),RATSIMP(COMPZ(T6,[EE^(3*I)*Z1,EE^(2*I)*Z2]))) (C48) FOR I THRU 5 DO DEFINE(CHI[I](Z1,Z2), RATSIMP(COMPZ(CHI12,[EE^(3*I)*Z1,EE^(2*I)*Z2]))) (C49) TCHI:RATSIMP(SUM(T[I](Z1,Z2)*CHI[I](W1,W2),I,1,5)) (D49) (75*W1^8*W2^4+100*W1^3*W2^9)*Z1^6+(-200*W1^9*W2^3+150*W1^4*W2^8)*Z1^5*Z2 +(150*W1^10*W2^2-600*W1^5*W2^7 -25*W2^12) *Z1^4*Z2^2 +(-25*W1^12+600*W1^7*W2^5 +150*W1^2*W2^10) *Z1^2*Z2^4 +(-150*W1^8*W2^4-200*W1^3*W2^9)*Z1*Z2^5 +(-100*W1^9*W2^3+75*W1^4*W2^8)*Z2^6 (C50) TT:RATSIMP(SUM(T[I](Z1,Z2)*T[I](W1,W2),I,1,5)) (D50) (10*W1^5*W2+5*W2^6)*Z1^6+(10*W1^6-20*W1*W2^5)*Z1^5*Z2 +125*W1^2*W2^4*Z1^4*Z2^2+125*W1^4*W2^2*Z1^2*Z2^4 +(-20*W1^5*W2-10*W2^6)*Z1*Z2^5 +(5*W1^6-10*W1*W2^5)*Z2^6 (C51) TTX2:RATSIMP(SUM(T[I](Z1,Z2)*T[I](W1,W2)^2,I,1,5)) (D51) (75*W1^8*W2^4+100*W1^3*W2^9)*Z1^6+(-200*W1^9*W2^3+150*W1^4*W2^8)*Z1^5*Z2 +(150*W1^10*W2^2-600*W1^5*W2^7 -25*W2^12) *Z1^4*Z2^2 +(-25*W1^12+600*W1^7*W2^5 +150*W1^2*W2^10) *Z1^2*Z2^4 +(-150*W1^8*W2^4-200*W1^3*W2^9)*Z1*Z2^5 +(-100*W1^9*W2^3+75*W1^4*W2^8)*Z2^6 (C52) "prepare to reexpress forms in terms of Z" (D52) "prepare to reexpress forms in terms of Z" (C53) ZEXPRESS(FORM,DEG):=EXPRESS(FORM,DEG,(-Z1+Z2)/1728,Z2,F12^5,T30^2,5) (C54) REXPRESS(FORM,DEG):=EXPRESS(FORM,DEG,R,1,T6^2,F12,1) (C55) EXPRESS(FORM,DEG,VAR1,VAR2,FORM1,FORM2,GAP):=BLOCK( [TEMPLATE,EQNS,UNKNS,SOLS,G,I],LOCAL(A), TEMPLATE:SUM(A[I]*FORM1^I*FORM2^(DEG-I),I,0,DEG), FORM:PRUNE(EV(FORM,Z2 = 1),Z1,GAP*DEG), TEMPLATE:PRUNE(EV(TEMPLATE,Z2 = 1),Z1,GAP*DEG), EQNS:MAKELIST(RATCOEF(FORM,Z1,GAP*I) = RATCOEF(TEMPLATE,Z1,GAP*I),I,0,DEG), UNKNS:MAKELIST(A[I],I,0,DEG),SOLS:SOLVE(EQNS,UNKNS), G:SUM(A[I]*VAR1^I*VAR2^(DEG-I),I,0,DEG),RATSIMP(EV(G,SOLS))) (C56) "reexpress fhat,..." (D56) "reexpress fhat,..." (C57) F5Z:ZEXPRESS(F12^5,1) (D57) (-Z1+Z2)/1728 (C58) H3Z:ZEXPRESS(H20^3,1) (D58) -Z1 (C59) T2Z:ZEXPRESS(T30^2,1) (D59) Z2 (C60) FHATCHECK:RATSIMP(HZ(6, HW(12, 91125*Z^6+((-133650)*W^2+61560*W-193536)*Z^5 +((-66825)*W^4+142560*W^3+133056*W^2 +(-61440)*W+102400) *Z^4 +(5940*W^6+4752*W^5+63360*W^4 +(-140800)*W^3) *Z^3 +((-1485)*W^8+3168*W^7+(-10560)*W^6) *Z^2+(440*W^9-66*W^10)*Z+W^12))) (C61) FHAT:COMPZ(F12,PHI31)*F12^4 (C62) FHAT:ZEXPRESS(FHAT,7) (C63) FHAT:RATSIMP(FHAT/F5Z) (D63) 91125*W2^12*Z1^6+(-133650*W1^2*W2^10+61560*W1*W2^11-193536*W2^12) *Z1^5*Z2 +(-66825*W1^4*W2^8+142560*W1^3*W2^9+133056*W1^2*W2^10 -61440*W1*W2^11+102400*W2^12) *Z1^4*Z2^2 +(5940*W1^6*W2^6+4752*W1^5*W2^7+63360*W1^4*W2^8 -140800*W1^3*W2^9) *Z1^3*Z2^3 +(-1485*W1^8*W2^4+3168*W1^7*W2^5-10560*W1^6*W2^6) *Z1^2*Z2^4+(-66*W1^10*W2^2+440*W1^9*W2^3)*Z1*Z2^5 +W1^12*Z2^6 (C64) IF RATSIMP(FHAT-FHATCHECK # 0) THEN ERROR("fhat is wrong") (C65) HHAT:RATSIMP(1/(11^2*12^2*H3Z*T2Z)*DW(HESSIAN2,FHAT)) (C66) THAT:RATSIMP(1/(240*T2Z)*DW(JACOBIAN2,FHAT,HHAT)) (C67) IF RATSIMP(T2Z*THAT^2+H3Z*HHAT^3+(-1728)*F5Z*FHAT^5) # 0 THEN ERROR("hat identity failed") (C68) "reexpress tchihat,..." (D68) "reexpress tchihat,..." (C69) TCHIHATCHECK:RATSIMP(HZ(7, HW(12, RATSIMP( 100*Z*(Z-1) *((1215*W-648)*Z^4 +((-540)*W^3-216*W^2+(-1152)*W+640)*Z^3 +(378*W^5-504*W^4+960*W^3)*Z^2 +(36*W^7-168*W^6)*Z-W^9))))) (D69) (121500*W1*W2^11-64800*W2^12)*Z1^6*Z2 +(-54000*W1^3*W2^9-21600*W1^2*W2^10-236700*W1*W2^11+128800*W2^12) *Z1^5*Z2^2 +(37800*W1^5*W2^7-50400*W1^4*W2^8+150000*W1^3*W2^9+21600*W1^2*W2^10 +115200*W1*W2^11-64000*W2^12) *Z1^4*Z2^3 +(3600*W1^7*W2^5-16800*W1^6*W2^6-37800*W1^5*W2^7+50400*W1^4*W2^8 -96000*W1^3*W2^9) *Z1^3*Z2^4+(-100*W1^9*W2^3-3600*W1^7*W2^5+16800*W1^6*W2^6)*Z1^2*Z2^5 +100*W1^9*W2^3*Z1*Z2^6 (C70) TCHIHAT:COMPW(TCHI,PHI31)*F12*T30 (C71) TCHIHAT:ZEXPRESS(TCHIHAT,7) (C72) IF RATSIMP(TCHIHAT-TCHIHATCHECK # 0) THEN ERROR("tchihat is wrong") (C73) TTHAT:COMPW(TT,PHI31)*F12^4 (C74) TTHAT:ZEXPRESS(TTHAT,4) (C75) TTX2HAT:COMPW(TTX2,PHI31)*F12*T30 (C76) TTX2HAT:ZEXPRESS(TTX2HAT,7) (C77) IF RATSIMP(TCHIHAT-TTX2HAT # 0) THEN ERROR("tchihat and ttx2hat don't agree") (C78) "prepare to compute magic polynomials" (D78) "prepare to compute magic polynomials" (C79) ACOEFF(I,J):=CONCAT(A\_,I,"_",J) (C80) ATERM(I,J):=ACOEFF(I,J)*Z^I*W^J (C81) KILLSOFF(ZAP,GAP,I,J):=IF ZAP-J > GAP*I THEN TRUE ELSE FALSE (C82) LIVECOEFF(I,J):=IF KILLSOFF(ZAPROOT,GAPROOT,I,J) OR KILLSOFF(ZAPPOLE,GAPPOLE,DEGZ-I,DEGW-J) THEN FALSE ELSE TRUE (C83) UNKNCOEFFS(DEGZ,DEGW,ZAPROOT,GAPROOT,ZAPPOLE,GAPPOLE):=BLOCK([I,J,L:[]], FOR I FROM 0 THRU DEGZ DO (FOR J FROM 0 THRU DEGW DO (IF LIVECOEFF(I,J) THEN L:APPEND(L,[ACOEFF(I,J)]))), L) (C84) UNKNFORM(DEGZ,DEGW,ZAPROOT,GAPROOT,ZAPPOLE,GAPPOLE):=BLOCK([I,J,SUM:0], FOR I FROM 0 THRU DEGZ DO (FOR J FROM 0 THRU DEGW DO (IF LIVECOEFF(I,J) THEN SUM:SUM+ATERM(I,J))),RAT(SUM)) (C85) MAGI(DEGZ,DEGW,ZAPROOT,GAPROOT,ZAPPOLE,GAPPOLE,ZAPONE,GAPONE):=BLOCK( [FORM,UNKNS,EQS,SOLS,I,J], FORM:UNKNFORM(DEGZ,DEGW,ZAPROOT,GAPROOT,ZAPPOLE,GAPPOLE), UNKNS:UNKNCOEFFS(DEGZ,DEGW,ZAPROOT,GAPROOT,ZAPPOLE,GAPPOLE), ONEFORM:RATSIMP(SUBST([Z = 1+Z,W = 1+W],FORM)),EQS:[], FOR I FROM 0 THRU DEGZ DO (FOR J FROM 0 THRU DEGW DO (IF KILLSOFF(ZAPONE,GAPONE,I,J) THEN EQS:APPEND(EQS, [RATCOEFF2(ONEFORM,Z,I,W,J) = 0]))), SOLS:SOLVE(EQS,UNKNS),FORM:EV(FORM,SOLS),FORM:CONTENT(FORM)[2], FORM:HZ(DEGZ,HW(DEGW,FORM)),FORM) (C86) "make sure the magic works" (D86) "make sure the magic works" (C87) FMAGIC:MAGI(6,12,12,3,12,2,11,5) (D87) 91125*W2^12*Z1^6+(-133650*W1^2*W2^10+61560*W1*W2^11-193536*W2^12) *Z1^5*Z2 +(-66825*W1^4*W2^8+142560*W1^3*W2^9+133056*W1^2*W2^10 -61440*W1*W2^11+102400*W2^12) *Z1^4*Z2^2 +(5940*W1^6*W2^6+4752*W1^5*W2^7+63360*W1^4*W2^8 -140800*W1^3*W2^9) *Z1^3*Z2^3 +(-1485*W1^8*W2^4+3168*W1^7*W2^5-10560*W1^6*W2^6) *Z1^2*Z2^4+(-66*W1^10*W2^2+440*W1^9*W2^3)*Z1*Z2^5 +W1^12*Z2^6 (C88) IF RATSIMP(FHAT-FMAGIC) # 0 THEN ERROR("fmagic failed") (C89) TCHIMAGIC:MAGI(4,12,9,3,11,2,8,5) (D89) (-1215*W1*W2^11+648*W2^12)*Z1^4+(540*W1^3*W2^9+216*W1^2*W2^10 +1152*W1*W2^11-640*W2^12) *Z1^3*Z2 +(-378*W1^5*W2^7+504*W1^4*W2^8 -960*W1^3*W2^9) *Z1^2*Z2^2 +(-36*W1^7*W2^5+168*W1^6*W2^6)*Z1*Z2^3 +W1^9*W2^3*Z2^4 (C90) IF RATSIMP(TCHIHAT-RATSIMP(100*Z1*Z2*(Z2-Z1)*TCHIMAGIC)) # 0 THEN ERROR("tchimagic failed") (C91) "test root finding" (D91) "test root finding" (C92) TOP:FACTOR(NHZ(NHW(TCHIHAT))) (D92) 100*(-1+Z)*Z *(-W^9-168*W^6*Z+36*W^7*Z+960*W^3*Z^2-504*W^4*Z^2+378*W^5*Z^2+640*Z^3 -1152*W*Z^3-216*W^2*Z^3-540*W^3*Z^3-648*Z^4+1215*W*Z^4) (C93) BOTTOM:NHZ(NHW(FHAT)) (D93) W^12+(440*W^9-66*W^10)*Z+(-10560*W^6+3168*W^7-1485*W^8)*Z^2 +(-140800*W^3+63360*W^4+4752*W^5+5940*W^6)*Z^3 +(102400-61440*W+133056*W^2+142560*W^3-66825*W^4)*Z^4 +(-193536+61560*W-133650*W^2)*Z^5+91125*Z^6 (C94) ALPHA:(3*SQRT(15)*%I+5)/2 (D94) (5+3*SQRT(15)*%I)/2 (C95) BETA:(3*SQRT(15)*(-%I)+5)/2 (D95) (5-3*SQRT(15)*%I)/2 (C96) ROOT1:RATSIMP((ALPHA*W1-BETA*W2)/(ALPHA^2-BETA^2)) (D96) ((9-SQRT(15)*%I)*W1+(9+SQRT(15)*%I)*W2)/90 (C97) ROOT2:RATSIMP((ALPHA*W2-BETA*W1)/(ALPHA^2-BETA^2)) (D97) -((-9-SQRT(15)*%I)*W1+(-9+SQRT(15)*%I)*W2)/90 (C98) POLY(R,ZD):=R^5-10*ZD*R^3+45*ZD^2*R-ZD^2 (D98) POLY(R,ZD):=R^5-10*ZD*R^3+45*ZD^2*R-ZD^2 (C99) ZDTOZ(ZD):=1-1728*ZD (D99) ZDTOZ(ZD):=1-1728*ZD (C100) MODNEWT(F,V,D):=(V*DIFF(F,V)-D*F)/DIFF(F,V) (D100) MODNEWT(F,V,D):=(V*DIFF(F,V)-D*F)/DIFF(F,V) (C101) COMPUTE(EXPN,SUB):=BLOCK([],RETURN(RECTFORM(EV(EXPN,SUB)))) (D101) COMPUTE(EXPN,SUB):=BLOCK([],RETURN(RECTFORM(EV(EXPN,SUB)))) (C102) FPPREC:32 (D102) 32 (C103) FPPRINTPREC:16 (D103) 16 (C104) ZDVAL:1.0B-1 (D104) 1.0B-1 (C105) "We are trying to solve..." (D105) "We are trying to solve..." (C106) POLY(R,ZDVAL) = 0 (D106) -1.0B-2+4.5B-1*R-R^3+R^5 = 0 (C107) ZVAL:ZDTOZ(ZDVAL) (D107) -1.71B2 (C108) BOTTOMVAL:COMPUTE(BOTTOM,Z = ZVAL) (C109) TOPVAL:COMPUTE(TOP,Z = ZVAL) (C110) ITER:MODNEWT(BOTTOMVAL,W,12) (C111) ITER:BFLOAT(EV(ITER)) (C112) EXPAND(NUM(ITER))/EXPAND(DENOM(ITER)) (C113) DEFINE(F(W),%) (D113) F(W):= (-2.846492622523672B19+1.0193486996409B17*W-2.011843382962043B17*W^2 -1.124145130385781B15*W^3 +4.682867107583491B14*W^4 +1.6867237126924B11*W^5+1.825904833948B11*W^6 -4.67521401B8*W^7+1.75320525B8*W^8+2.2677B5*W^9 -2.2677B4*W^10) /(-9.266806360371822B15+4.023686765924087B16*W +3.747150434619271B14*W^2 -2.341433553791745B14*W^3 -1.204802651923B11*W^4-1.825904833948B11*W^5 +6.545299622B8*W^6-3.50641051B8*W^7 -6.8032B5*W^8+1.1338B5*W^9+1.2B1*W^11) (C114) WVAL:1.0B0 (D114) 1.0B0 (C115) FOR I THRU 10 DO DISPLAY(WVAL:F(WVAL)) WVAL = -9.181783349599415B2 WVAL = 2.038753731108551B0 WVAL = -4.022440139844757B2 WVAL = 4.335421660534365B0 WVAL = -2.076347337692839B2 WVAL = 6.48661350944532B0 WVAL = -1.776187580407692B2 WVAL = 6.6431593297797B0 WVAL = -1.775015690681409B2 WVAL = 6.643162535797368B0 (D115) DONE (C116) W1VAL:COMPUTE(TOPVAL/BOTTOMVAL,W = WVAL) (D116) 7.097739488138986B0 (C117) WVAL:F(WVAL) (D117) -1.775015690680918B2 (C118) W2VAL:COMPUTE(TOPVAL/BOTTOMVAL,W = WVAL) (D118) 4.744279751747713B-1 (C119) ROOT1:COMPUTE(BFLOAT(ROOT1),[W1 = W1VAL,W2 = W2VAL]) (D119) 7.572167463313758B-1-2.850219465161584B-1*%I (C120) ROOT2:COMPUTE(BFLOAT(ROOT2),[W1 = W1VAL,W2 = W2VAL]) (D120) 7.572167463313758B-1+2.850219465161584B-1*%I (C121) COMPUTE(POLY(ROOT1,ZDVAL),[]) (D121) 2.340397539902955B-3+1.221275706633973B-3*%I (C122) COMPUTE(POLY(ROOT2,ZDVAL),[]) (D122) 2.340397539902955B-3-1.221275706633973B-3*%I (C123) quit();