{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 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "restart: with(algcur ves):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2225 "`algcurves/lift_ exp` := proc(v, f, x, y)\nlocal i, ii, r, res, v7, vv7, v3, ext, a, j, n, np, ram, j3;\n if v[5] = 1 then return \{v\} end if;\n v3 := degree(v[3], x);\n res := \{\};\n r := v[1] + y*x^v[2];\n vv 7 := v[7]*v3 + v[2] - 1;\n vv7 := vv7 + v[5];\n ii := `algcurves /truncate_subs`(subs(x = v[3], f), x, y, r, vv7 + 1,\n v[4]);\n if ii = 0 then error \"degree estimate was wrong\" end if;\n v7 := (ldegree(ii, x) - v[2])/v3;\n r := `algcurves/v_ext_m`(\n \+ `algcurves/g_factors`(tcoeff(ii, x), y, v[4]), y);\n for i in r d o res := res union `algcurves/lift_exp`([\n v[1] + x^v[2]*i[1], v[2] + 1, v[3], [op(i[3]), op(v[4])], i[2],\n v[6]*i[4], v7, [ op(v[8]), [op(1 .. 4, v)]]], f, x, y)\n end do;\n if add(i[5]*i[ 6]*degree(i[3], x)/(v[6]*v3), i = res) <>\n degree(tcoeff(ii, x), y ) then error \"found wrong number of expansions\"\n end if;\n if v[5] = degree(tcoeff(ii, x), y) then\n if ldegree(ii, x) <> vv 7 then error \"degree estimate was wrong\"\n end if;\n r eturn res\n end if;\n ii := collect(ii, y);\n ii := add(`algc urves/normal_tcoeff`(coeff(ii, y, i), x)*y^i,\n i = 0 .. degree (ii, y));\n np := `algcurves/Newtonpolygon`(ii, x, y);\n if nops (np) = 2 and np[1][3] = 0 then\n error \"found wrong number of \+ expansions\"\n end if;\n for j in np do\n if 2 < nops(j) \+ and 0 < j[3] and j[3] < 1 then\n r := `algcurves/g_factors` (j[4], x, v[4]);\n r := `algcurves/v_ext_m`(r, x);\n \+ for i in r do\n j3 := j[3] - v[2];\n \+ ext := [op(i[3]), op(v[4])];\n n := mods(1/numer(j3), denom(j3));\n ram := i[1]^n*x^denom(j3);\n \+ a := v[2]*denom(j3) - numer(j[3]);\n res := res uni on `algcurves/lift_exp`([collect(\n subs(x = ram, v [1])\n + x^a*i[1]^((1 - n*numer(j3))/denom(j3)), x , normal),\n a + 1, normal(subs(x = ram, v[3])), ex t, i[2],\n v[6]*i[4],\n (j[2] - \+ j[1]*j[3] - a/degree(ram, x))/degree(v[3], x),\n [o p(v[8]), [op(1 .. 4, v)]]], f, x, y)\n end do\n end \+ if\n end do;\n res\nend proc:" }}}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "A:=(x+y)^2*(x-y)* y+x^5+g*x^4*y+h*x^3*y^2+j*x^2*y^3+k*x*y^4+l*y^5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,0*(),&%\"xG\"\"\"%\"yGF*\"\"#F*,&F)F*F+!\"\"F*F+ F*F**$)F)\"\"&F*F**(%\"gGF*)F)\"\"%F*F+F*F**(%\"hGF*)F)\"\"$F*)F+F,F*F **(%\"jGF*)F)F,F*)F+F9F*F**(%\"kGF*F)F*)F+F5F*F**&%\"lGF*)F+F1F*F*" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y,0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<&\"\"!%\"xG*&\"\"\"F'%\"lG!\"\",&*(\" \"%F),.%\"gGF'%\"hGF)%\"kGF)%\"jGF'F'F)F(F'\"\"#*&F%F',.*&F2F)F.F'F)*& F2F)F/F'F'*&F2F)F0F'F'*&F2F)F1F'F)#F'F2F'*&F2F)F(F'F)F)#\"\"$F2F'*(,.* &F2F)F.F'F'*&F2F)F/F'F)*&F2F)F0F'F)*&F2F)F1F'F'#F'F2F)*&F2F)F(F'F'F'F% F'F4F)F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "A1:=eval(A,g=h+ k-j+1-l);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,0*(),&%\"xG\"\"\"% \"yGF*\"\"#F*,&F)F*F+!\"\"F*F+F*F**$)F)\"\"&F*F**(,,%\"hGF*%\"kGF*%\"j GF.F*F*%\"lGF.F*)F)\"\"%F*F+F*F**(F4F*)F)\"\"$F*)F+F,F*F**(F6F*)F)F,F* )F+F " 0 "" {MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'\"\"!%\"xG,$F%!\"\"*&\"\"\"F)%\"lGF',&F%F'*&)F%\"\"#F),,*&F.F' %\"hGF)F'*(\"\"$F)F.F'%\"kGF)F'%\"jGF)#F)F.F)*&F.F)F*F)F)F)F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"%\"yGF&F&,:*$)F%\"\"%F&F&*()F%\"\"$ F&%\"gGF&F'F&F&*&F-F&F'F&!\"\"*()F%\"\"#F&)F'F4F&%\"lGF&F&*(F3F&F5F&% \"jGF&F&*&F'F&F3F&F&*(F3F&F5F&%\"kGF&F1*(F4F&F5F&F%F&F&*(F%F&)F'F.F&F6 F&F1*(F%F&F>F&F;F&F&*$F>F&F&*&)F'F+F&F6F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }