{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 24 0 0 0 0 1 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 24 0 0 0 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 1 24 0 0 0 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 1 24 0 0 0 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Outpu t" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 263 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 265 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 266 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 267 1 {CSTYLE " " -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 268 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 269 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart;\ncurrentdir ();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q=Z:\\home\\www\\software\\abel map6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "with(algcurves):r ead(\"AbelMap_24March.mpl\");kernelopts(opaquemodules = false);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 256 29 "Define some algebraic curves." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "f[1]:=y^2-(x^2-1)*(x^2-4)*(x^2-9)*(x^2-16)*(x^2-2 5)*(x^2-36);f[2]:=y^2-x*(x^2-4)*(x^2-9)*(x^2-16)*(x^2-25)*(x^2-36);f[3 ]:=7*y^3-7*I*y^2*x^4-x+6-y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG 6#\"\"\",&*$)%\"yG\"\"#F'F'*.,&*$)%\"xGF,F'F'F'!\"\"F',&F/F'\"\"%F2F', &F/F'\"\"*F2F',&F/F'\"#;F2F',&F/F'\"#DF2F',&F/F'\"#OF2F'F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"#,&*$)%\"yGF'\"\"\"F,*.%\"xGF,, &*$)F.F'F,F,\"\"%!\"\"F,,&F0F,\"\"*F3F,,&F0F,\"#;F3F,,&F0F,\"#DF3F,,&F 0F,\"#OF3F,F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"$,,*&\" \"(\"\"\")%\"yGF'F+F+*(^#!\"(F+)F-\"\"#F+)%\"xG\"\"%F+F+F4!\"\"\"\"'F+ F-F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "seq(genus(f[i],x,y) ,i=1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&F#F#" }}}{EXCHG {PARA 269 "" 0 "" {TEXT -1 50 "Calculate the Abel map between two regu lar places." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "_EnvExplicit := false;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-_ EnvExplicitG%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "a1 := I;b1 := allvalues(solve(eval(f[1],x=a1),y),'implicit');a2 := -I;b2 := allvalues(solve(eval(f[1],x=a2),y),'implicit');" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#a1G^#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# b1G6$,$*&\"#5\"\"\"-%'RootOfG6$,&*$)%#_ZG\"\"#F)F)\"&aj\"!\"\"/%&index GF)F)F),$*&F(F)-F+6$F-/F5F1F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# a2G^#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b2G6$,$*&\"#5\"\"\"-% 'RootOfG6$,&*$)%#_ZG\"\"#F)F)\"&aj\"!\"\"/%&indexGF)F)F),$*&F(F)-F+6$F -/F5F1F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "AbelMap(f[1], x, y, [x = a1, y = b1[1]],[x = a2, y = b2[1]], 5);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#7'^$$!+IOToM!#6$\"+!)>Y$)zF'^$$\"+.a&H,#F'$!,y&oH,7F' ^$$\",/6da0%!#7$\",vo&*3w%F2^$$\",OI&*Q_(F2$!,0Y1EA$F2^$$!,(*y#[b9F2$! ,df1&HSF2" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 257 53 "Calculate Puiseux expansions for hyperelliptic curve " }{TEXT 263 4 "f[1]" }{TEXT 262 19 ". For this curve, " }{TEXT 264 3 "x=1" }{TEXT 265 28 " and x=5 ar e branch-points, " }{TEXT 266 10 "x=infinity" }{TEXT 267 8 " is not." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "P:=puiseux(f[1],x=1,y,1,t )[1];Q:=puiseux(f[1],x=5,y,1,t)[1];R:=puiseux(f[1],x=infinity,y,1,t)[1 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG7$/%\"xG,&*&\"'+[g\"\"\")% \"tG\"\"#F+!\"\"F+F+/%\"yG,$*&F*F+F-F+F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QG7$/%\"xG,&*&\"(gL)z\"\"\")%\"tG\"\"#F+!\"\"\"\"&F+/%\"yG,$ *&F*F+F-F+F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG7$/%\"xG*&\"\"\" F)%\"tG!\"\"/%\"yG*&,*F)F)*&#\"&ji\"\"#;F)*$)F*\"\"'F)F)F+*&#\"%JP\"\" )F)*$)F*\"\"%F)F)F)*&#\"#\"*\"\"#F)*$)F*FAF)F)F+F)F*!\"'" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 258 45 "Calculate the Abel map between branch \+ points." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A:=AbelMap(f[1],x,y,P,Q,5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% \"AG7'^$$\",+Zx1M\"!#6$\",+bxBn'F)^$$!,4$*ft,#F)$!,!f;*>U)F)^$$\",qG,1 0&F)$\",N(>\"HS(F)^$$!,[atAz%F)$!,cN?K8&F)^$$\",(QvJBVF)$\",#p199TF)" }}}{EXCHG {PARA 259 "" 0 "" {TEXT 259 36 "Check whether the representa tive of " }{TEXT 260 6 "A(P|Q)" }{TEXT 261 108 " in the fundamental pa rallelogram is a half-lattice vector as per Farkas&Kra. Will first ne ed periodmatrix." }{TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "B := periodmatrix(f[1],x,y,Riemann);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'RTABLEG6%\"*#4NS:-%'MATRIXG6# 7'7'^$$\"3=AN-<\\>y6!#<$\"3#\\5p#*pEt9#F1^$$!3;.'ROdN\"o7F1$!35#QWuZvW L\"F1^$$\"3f?>#o>li5\"F1$\"3eyTZ([D!*>\"F1^$$!336Ya)yH>2\"F1$!3M&=@b%H ,$[*!#=^$$\"3tx!4(eTf+\"*FC$\"3HLd7^E^G\")FC7'^$$!3=1&Hz^N\"o7F1$!3ywF ))HaZM8F1^$$\"32mJ&zo?Z.%FC$\"31;]7j#)R%o\"F1^$$!3'>&QJr-755F1$!3a2)4S N#e![\"F1^$$\"3c&=85-ZXe*FC$\"3\"\\G\"y\"4Wm-\"F1^$$!3o2&ecMNmk)FC$!3k *e9uR\"GG#)FC7'^$$\"3)G5.78li5\"F1$\"3%3?0pWD!*>\"F1^$$!3^X]\\M-755F1$ !3qi='oL#e![\"F1^$$\"3'\\*)yTw(4Q^FC$\"3M(zM$=8)ox\"F1^$$!3cXlKjS>\"*)FC7'^$$!31#f(HF(H>2 \"F1$!3)GRrNy7I[*FC^$$\"3yy\"RmiYXe*FC$\"3;mlXxSkE5F1^$$!3tV,*y8TL$**F C$!3;t>0p@/\\8F1^$$\"3o.3^wOu%z%FC$\"3'*\\W`Gr:E:F1^$$!3k5[1*eW\"R\")F C$!33yj%*R\"3W4\"F17'^$$\"3&H,BT*Rf+\"*FC$\"3ONO$p#H^G\")FC^$$!3'yS$f# GNmk)FC$!3#\\rMht\"GG#)FC^$$\"3O4X@;J%e'zFC$\"3yO@<[4%>\"*)FC^$$!3ro/Y rY9R\")FC$!3'=t$4o\"3W4\"F1^$$\"3/u(3b*))eRX!#>$\"3%zVOT4uF;\"F1%'Matr ixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "half_lattice_check:= AbelMap:-ModPeriodLattice(A,B,'fraction'):half_lattice_check;" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7,$\"++&*****\\!#5$\"31GW'RiF\"HB!#D$ \"3!4)\\%)H)RlQ\"F)$\"+5)*******F&$\"+R&*******F&$\"+s********F&$\"+n' *****\\F&$\"33@!))o_%3)o\"F)$\"3Uu#)\\D=*p*=!#E$\"+-&*******F&" }}} {EXCHG {PARA 260 "" 0 "" {TEXT -1 70 "It is a half-lattice vector as e ntries have approximately zero or 1/2." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 12 "Now compute " }{TEXT 268 6 "A(P|R)" } {TEXT -1 1 "." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A:=AbelMap(f[1],x,y,P,R,5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"AG7'^$$!,D/C[5%!#6$\",lvZRI\"F)^$$\",EL+Il$F)$!,Kw4 L`$F)^$$!,2;prp%!#7$\",O*f'G&GF)^$$\",uIM?U'F4$!,$zL+57F)^$$!,A4P#=XF4 $\",z4'f&H&F4" }}}{EXCHG {PARA 262 "" 0 "" {TEXT -1 10 "The point " } {TEXT 269 1 "R" }{TEXT -1 139 " is a discriminant point, but not a bra nch point, so no half-lattice vector is expected in the fundamental pa rallelogram, nor is one found." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 81 "half_lattice_check:=AbelMap:-ModPeriodLattic e(A,B,'fraction'):half_lattice_check;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7,$\"+e')yBQ!#5$\"3)p6X'*om**\\#!#=$\"+%)egs\")F&$\"3fL(R2x,u#=F)$ \"+na1+vF&$\"+j(*oB))F&$\"+=`vBjF&$\"3eK1R%f*G_x!#C$\"3)H*R4Vbl#p(F6$ \"+(fwin)F&" }}}{EXCHG {PARA 263 "" 0 "" {TEXT -1 77 "Do the same thin g with f[2], for which both 2 and infinity are branch points." } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "P:=puis eux(f[2],x=2,y,1,t)[1];R:=puiseux(f[2],x=infinity,y,1,t)[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG7$/%\"xG,&*&\"'gDK\"\"\")%\"tG\"\"#F+F +F.F+/%\"yG,$*&F*F+F-F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG7$/ %\"xG*&\"\"\"F)*$)%\"tG\"\"#F)!\"\"/%\"yG*&,**&\"$+)F))F,\"#8F)F.*&\"$ W%F))F,\"\"*F)F)*&\"#XF))F,\"\"&F)F.F,F)F)F,!#7" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "A:=AbelMap(f[2],x,y,P,R,9);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%\"AG7'^$$\",fU([_T!#6$!,h.'3hOF)^$$!,*38>2OF)$\",Z \\?jd&F)^$$\",n4o:h&!#7$!,WY!f)y%F)^$$!,-)R9r#)F4$\",rob)yFF)^$$\",SuY >M)F4$!,)yEq+=F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "B:=peri odmatrix(f[2],x,y,Riemann);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"BG- %'RTABLEG6%\"*C2CZ\"-%'MATRIXG6#7'7'^$$\"3?P5tp39.6!#<$\"38Vw`[!oY]\"F 1^$$!35*H$f6D]p6F1$!3\"*3m@/>.ZAr-[75F1$\"3I3sPGv^jjF9^$$ !3'pX6zsO6!)*F9$!3ete(3T&pMXF9^$$\"3!RAoz)))z%)*)F9$\"3!4\"Q)4R*HWLF97 '^$$!3UCnM7D]p6F1$!3ym'4`Ts@K(F9^$$\"3Q)3oUV`o'R5=x&*F9^$$\"3_2&)R#GrdM)F9$\"35%['3$R6xb&F9^$$!3J 0)QAm5;L)F9$!3-=s#GO09g$F97'^$$\"3wadxa-[75F1$\"3sj')HTy^jjF9^$$!3s)[% R\"H'ox))F9$!3+NZxh4=x&*F9^$$\"3clo(QGB(ySF9$\"3cY)**\\5BcH\"F1^$$!3$o 9,U$Q'pq)F9$!3we([tQ'fP#*F9^$$\"3y\")R;GjP'e(F9$\"3R@>6'G&*\\a%F97'^$$ !34PvFPn8,)*F9$!3=<1kPdpMXF9^$$\"3+-#4`ErdM)F9$\"3U#42uR6xb&F9^$$!3N,v S'*Q'pq)F9$!3&*RKD&['fP#*F9^$$\"3FsH#[%RxOMF9$\"3[7d%H\\ol6\"F1^$$!3pM VmRi&\\!zF9$!37qVt@:kYoF97'^$$\"3/:XvV*)z%)*)F9$\"38O/E0)*HWLF9^$$!3WQ Y3n2hJ$)F9$!3Ft(o$fbS,OF9^$$\"3+NEo$\\wje(F9$\"3;\"z.,]&*\\a%F9^$$!3o1 _/uj&\\!zF9$!3[)Q$\"3]&4j)R;L=!)F9%'Matri xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "half_lattice_check:=A belMap:-ModPeriodLattice(A,B,'fraction'):half_lattice_check;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7,$\"2A(f,+********!#<$\"+[******\\!#5$\"3k+ /7B******\\!#=$\"+4,++]F)$\"3`'Qt1<+++&F,$\"+s)*******F)$\"3'Hcv-))*** **\\F,$\"3W<>E]qkS>!#E$\"3!>We+XC2v\"!#D$\"3EXe$fV^+k#F:" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 159 "It is a half-lattice vector. Next try \+ near a discriminant point, and for very large x, but one for which the discriminant point at x=infinity will not be used." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "P:=AbelMap:-AllBranches(f[1],x,1+1/10,y, 1,t)[1];Q:=AbelMap:-AllBranches(f[1],x,5+I/10,y,1,t)[1];R:=AbelMap:-Al lBranches(f[1],x,100,y,1,t)[1];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% \"PG7'/%\"xG,&%\"tG\"\"\"#\"#6\"#5F*/%\"yG,&*&#\"/`c%\"QG7'/%\"xG,&%\"tG\"\"\"^ $\"\"&#F*\"#5F*/%\"yG,&*&,&*&#\"=\"o8)\\XxBOx^SbzW\"C+q2R'R1d?=Vz5Xh!G \\F*-%'RootOfG6$,&^$!3,T(GK!Rfi9\"3+10*))\\!o]zF**$)%#_ZG\"\"#F*F*/%&i ndexGFBF*F**&^##!B\"[_e2nODZv$ph)=Tv7\"G++&)Qt%\"RG7'/%\"xG,&%\"tG\"\" \"\"$+\"F*/%\"yG,&*&#\"3b?BwH=gX)*\"0jz^i%>F\")F**&-%'RootOfG6$,&*$)%# _ZG\"\"#F*F*\"1*)Qb(Qe\"QC!\"\"/%&indexGF;F*F)F*F*F**&\"&g,#F*F4F*F*/% *valuationGF*/%,dfdy_degreeG\"\"!/%*parameterGF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "A_1:=AbelMap(f[1],x,y,P,Q,5);A_2:=AbelMap(f[1 ],x,y,P,R,5);A_3:=AbelMap(f[1],x,y,R,Q,5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$A_1G7'^$$\",SkP#G(*!#6$\",yUvxT\"!#5^$$!,TUob,\"F,$! ,Sm#HxVF)^$$\",%yKEXcF)$\",S,n$\\NF)^$$!,W8gf,&F)$!,A0$zGKF)^$$\",\"Rz 2URF)$\",e)4%$A_2G7'^$$\",^) zMJT!#6$!,hNN=C\"F)^$$!,p<.>(QF)$\",9$e*\\K$F)^$$\",v(G;W')!#7$!,>=-#* 3$F)^$$!,f)Ht>cF4$\",jI_*f9F)^$$\",qxH\")[&F4$!+&en,z'F)" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%$A_3G7'^$$\",*e'*)of&!#6$\",M'*e>a\"!#5^$$!,S1 \"y$G'F)$!,a\\)G-xF)^$$\",1*p%3y%F)$\",e>p&QmF)^$$!,e$o)RX%F)$!,&e`u)o %F)^$$\",9'\\E$R$F)$\",Vu(=1PF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "f[3];is_hyperelliptic(f[3],x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&\"\"(\"\"\")%\"yG\"\"$F&F&*(^#!\"(F&)F(\"\"#F&)%\"xG\"\"%F&F &F0!\"\"\"\"'F&F(F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}} {EXCHG {PARA 265 "" 0 "" {TEXT -1 30 "The discriminant-points are..." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "DPs:= [seq(RootOf(6800*I-2268*I*_Z+756*_Z^4+189*I*_Z^2-126*_Z^5+7*I*_Z^8-117 6*_Z^12+196*_Z^13,index=i),i=1..13)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "DPs[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6 $,2^#\"%+o\"\"\"*&^#!%oAF)%#_ZGF)F)*&\"$c(F))F-\"\"%F)F)*&^#\"$*=F))F- \"\"#F)F)*&\"$E\"F))F-\"\"&F)!\"\"*&^#\"\"(F))F-\"\")F)F)*&\"%w6F))F- \"#7F)F;*&\"$'>F))F-\"#8F)F)/%&indexGF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "kernelopts(opaquemodules=false);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "P := AbelMap:-AllBranches(f[3], x, DPs[1], y, 0, t):Q := AbelMap:-All Branches(f[3], x, DPs[4], y, 0, t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "evalf(P[1]);evalf(P[2]);evalf(Q[1]);evalf(Q[2]);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7'/%\"xG,&*&^$$\"*z3_e)!#8$\"''**4\"! \"*\"\"\")%\"tG\"\"#F/F/^$$\"+,+++gF.$!+Q?tbF!#9F//%\"yG,*^$$\"+Y!R;1 \"F8$\"'\\!\\&!#5F/*&F(F/F1F/F/*&^$$!#S!\"'$\"(]%[V!#6F/)F1\"\"$F/F/*& ^$$!#@!\"($!*#3CVZFJF/F0F/F//%*valuationG$\"\"%\"\"!/%,dfdy_degreeG$F/ FX/%*parameterGF1" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7'/%\"xG,&%\"tG\" \"\"^$$\"+,+++g!\"*$!+Q?tbF!#9F(/%\"yG,&^$$\"+.#HGQ#!#6$\"+\"*)**fH\"! \"'F(*&^$$\"%\">\"!\"&$\"+#4.+k)!\"(F(F'F(F(/%*valuationG$F(\"\"!/%,df dy_degreeG$FEFE/%*parameterGF'" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7'/% \"xG,&%\"tG\"\"\"^$$\"+oq-8X!#5$\"+c'Rq.\"!\"*F(/%\"yG,&^$$!+7IFziF,$ \"+kv!yJ$!#6F(*&^$$\"+O#R0.$F,$!+&*[ZcoF,F(F'F(F(/%*valuationG$F(\"\"! /%,dfdy_degreeG$FBFB/%*parameterGF'" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #7'/%\"xG,&*&^$$\"+X&z&*>\"!\"*$!+j/UdSF+\"\"\")%\"tG\"\"#F.F.^$$\"+oq -8X!#5$\"+c'Rq.\"F+F./%\"yG,**&^$$!+ti30()F+$!+XV5bhF+F.F/F.F.*&F(F.F0 F.F.^$$\"+:)z*H6F+$!+;qXnu!#6F.*&^$$!+!4=8R#!\")$\"+%GY)[;FLF.)F0\"\"$ F.F./%*valuationG$\"\"%\"\"!/%,dfdy_degreeG$F.FU/%*parameterGF0" }}} {EXCHG {PARA 266 "" 0 "" {TEXT -1 79 "Compute the Abel map between two places with same x-value; one branch, one not." }{MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "AbelMap(f[3], x, y, P[1], P [2], 5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7'^$$\",,Y)*zQ%!#7$\",iP)[ />!#6^$$\",;Iuv^$F*$!,5IOBS\"!#5^$$!,KeUr0(F*$\",RK$)4e%F*^$$\",)*)*4H Q'F*$\",F!p?&e\"F*^$$!+vjfCBF'$!,FIi\"HQF*" }}}{EXCHG {PARA 267 "" 0 " " {TEXT -1 47 "Compute the Abel map between two branch-places." } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A:=Abel Map(f[3],x,y,Q[1],P[2],5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"AG7' ^$$!,1lx;r\"!#6$\"*j#zRpF)^$$\",A7FU%RF)$!,V\\\\!\\5!#5^$$!,\\5V?:'F)$ \",*G#GMj\"F)^$$\",kXO%\\eF)$!*sUTr(F)^$$!,y#z " 0 "" {MPLTEXT 1 0 101 "P:=AbelMap:-AllBranches(f[3],x,DPs[1]+1/20,y,0,t): Q :=AbelMap:-AllBranches(f[3],x,DPs[4]+I/20,y,0,t):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 24 "evalf(P[1]);evalf(Q[1]);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#7'/%\"xG,&%\"tG\"\"\"^$$\"+,++]g!\"*$!+Q?tbF!#9F(/%\" yG,&*&^$$!+dOX%f\"!#6$!+V3_z:F7F(F'F(F(^$$!+TLrK;!#7$!+%f*Rz:F=F(/%*va luationG$F(\"\"!/%,dfdy_degreeG$FCFC/%*parameterGF'" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#7'/%\"xG,&%\"tG\"\"\"^$$\"+oq-8X!#5$\"+c'Rq3\"!\"*F(/ %\"yG,&*&^$$!+N](Q<#F,$\"+WL_$*GF/F(F'F(F(^$$\"+;$*z!o(F,$!+h+2P6F,F(/ %*valuationG$F(\"\"!/%,dfdy_degreeG$FAFA/%*parameterGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A:=AbelMap(f[3],x,y,Q[1],P[1],5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"AG7'^$$\"+.ajrS!#6$!,!RfOMQ!#7^$ $\",8lfN9$F)$\",!fz1!4#F)^$$!+Sb,`OF)$\",cd'3ZYF,^$$!,],w%*R&F)$!,_XY= X\"F)^$$\",p#o.:FF)$!, " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "44 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 154035092 147240724 } {RTABLE M7R0 I6RTABLE_SAVE/154035092X,%)anythingG6"6"[gl("%!!!#:"&"&3FF2D9E2E9CEDF1340012DB9 9ED981E9BFF44A48780673B7BFF55A02E88A97D43FF1B34310F38F433FF32F354E987955BFF1269 FC925A759BFEE587BEC2990A33FED1F34E3BC95633FEA02E0B6D42364BFF44A4886FAD21BBFF55A 02F54F00703FD9D27C8314D27C3FFAF34B97D8FA75BFF02973D5C2F1F5BFF7B0771ABDB6173FEEA BA91CDAE33E3FF06D225714EDBEBFEBAB52D8FD5EF3BFEA549BBFFCB6703FF1B3432290D9B63FF3 2F35597C5A56BFF02973DFA51D40BFF7B0771F581BED3FE0712133428E9A3FFC6E1B1AF1F0EDBFE FC9649F9732DEBFF595AD3DD00CD03FE97D9E61DD773B3FEC84A97A741AACBFF1269FD996844DBF EE587BF4DB62D03FEEABA932071F6C3FF06D225AED50DCBFEFC964A6B15444BFF595AD3E0D98933 FDEAFB542153A173FF86B23BCB9CDBFBFEA0B965A4445F1BFF182B223A7016E3FED1F34EC92A31F 3FEA02E0A805769BBFEBAB52DC60218BBFEA549BADCD60F23FE97D9E5D091BAA3FEC84A9698B6E1 CBFEA0B9655D7D5FEBFF182B21C18BBF23FA73E2144DEB1B23FF29AB9022F3B80F& } {RTABLE M7R0 I6RTABLE_SAVE/147240724X,%)anythingG6"6"[gl("%!!!#:"&"&3FF1A6770A6603483FF8131E CDBCE295BFF2B6484431E77FBFE76E52DA3E2BB43FF0331E7EE1B8CA3FE45CFE6AB2D951BFEF5D1 759E0BD5FBFDD05A53F430D983FECC058E84E985C3FD5674D014A5251BFF2B64843FE2119BFE76E 52BECDC2DF3FD1D3F4A27BD5303FF1D81F2DF77731BFEC6899C19232ACBFEEA5A06BBBD4053FEAB 4DB170E141F3FE1C8E08EA7E75CBFEAA9416B186A7EBFD70C8AF96D93D03FF0331E834C15C03FE4 5CFE59E616D3BFEC6899CAE523B9BFEEA5A06FEA64743FDA1A9489D795473FF4BADF4AFEA93ABFE BDCBEACC812CDBFED8F7064F8FBAB3FE846C276B1A1D93FDD168547D5D7C6BFEF5D1759600368BF DD05A51C2D03213FEAB4DB17F8F3C53FE1C8E08E6C8592BFEBDCBEA9711DA6BFED8F705FB764E63 FD5FECF786B42E33FF1DD76EC8F222BBFE94BBD81C90F14BFE5E8C4D27D841E3FECC058E54FDFCC 3FD5674CD4CEC5BBBFEAA94165776D03BFD70C8AE45315923FE846C26DCEC2DC3FDD168530DBADD CBFE94BBD7A92246BBFE5E8C4CBCA82E73FB994AC6681205A3FE9A89E06056BC3F& }