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[/Title (postScript pictures: farbe.li.tu-berlin.de/her1/her1.htm)
/Author (compare K. Richter "Computergrafik ...": ISBN 3-8007-1775-1)
/Subject (goto: http://farbe.li.tu-berlin.de or http://color.li.tu-berlin.de)
/Keywords (image reproduction, colour devices)
/Creator (klaus.richter@mac.com)
/CreationDate (D:2024120112200)
/ModDate (D:20241201112200)
/DOCINFO pdfmark02
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} if %xchartl>=1
tfn %tfw
%*********************************************************************
%BEG Common text
xtr0 ytr0 translate
TBIK
/iyt0 2900 def %top text line
/iyt1 2300 def %lower yellow text line
/ixt2 2420 def %right red text line
/iyt2 1100 def %right red text line
/ix0 100 def
/ix1 750 def %for F(x)
/ix1a 850 def %for Fn(x)
/ix2 2200 def %text e
/ix3 1700 def
%ifunc 0 eq {/x_zp (x) def /x_zm (-x) def}
% {/x_zp (z) def /x_zm (-z) def /lne_10d 1 10 ln div def} ifelse
/x_zp (x) def /x_zm (-x) def
ioute 0 eq {/e_10 (e) def /lne_10 1 def}
{/e_10 (10) def /lne_10 1 def} ifelse
/expnp 10 array def
% 0 1 2 3 4 5 6 7 8 9
/expnp [1.0 1.0 0.7 0.5 1.0 0.7 0.5 1.0 0.7 0.5] def
/expnk 10 array def
% 0 1 2 3 4 5 6 7 8 9
/expnk [(1,0) (1,0) (0,7) (0,5) (1,0) (0,7) (0,5) (1,0) (0,7) (0,5)] def
%****************************************
tfw
30 setlinewidth
/jm1 0 def
/jm2 1 def
/iytj 0 def
xchartl 0 eq {/jm2 0 def}
{/jm2 1 def} ifelse
jm1 1 jm2 {/j exch def %j=jm1,jm2
j 0 eq {/iyta 0 def} if
j 1 eq {/iyta 0 def} if
0 1 1 {/k exch def %k=0,1
k 0 eq {%k=0
j 0 eq {[ ] 0 setdash tfw} if
j 1 eq {[ ] 0 setdash tfy} if
} if %k=0
k 1 eq {%k=1
j 0 eq {[100 100] 0 setdash tfn} if
j 1 eq {[100 100] 0 setdash tfn} if
} if %k=1
%font colour
j 0 eq {tfw} if
j 1 eq {tfy} if
j 0 eq {/ixtx ix0 def
/iytx iyt0 def} if
j 1 eq {/ixtx ixt2 def
/iytx iyt2 def} if
/iytxt iytx 050 add 50 sub j 0 eq {100 add} if def
ixtx 1100 add iytxt iyta add 50 add moveto %iyta=0
1050 ioute 1 eq {200 add} if 0 rlineto stroke %ioute=0
} for %k=0,1
ixtx iytxt moveto
TBIL
(F) show
-30 -80 rmoveto TBS (1,ar) show 0 80 rmoveto
TBL
(\050) show
LSxr
TBL
(\051) show
TBL
( = 2 ) show
ixtx 1100 add 400 add iytxt 070 add moveto
TBL e_10 show
0 100 rmoveto
SVxr
TBS (/a) show ioute 1 eq {(') show} if 0 -100 rmoveto
%TBL ( - ) show
%TBL e_10 show
%0 100 rmoveto
%SVxrn
%TBS (/a) show ioute 1 eq {(') show} if 0 -100 rmoveto
ixtx 1100 add iytxt 160 sub moveto
TBL e_10 show
0 100 rmoveto
SVxr
TBS (/a) show ioute 1 eq {(') show} if 0 -100 rmoveto
TBL ( + ) show
TBL e_10 show
0 100 rmoveto
SVxrn
TBS (/a) show ioute 1 eq {(') show} if 0 -100 rmoveto
ixtx 2300 add iytxt moveto
[ ] 0 setdash
TBL
( = 2 ) show
ixtx 2700 add iytxt 50 add moveto 0600 0 rlineto stroke
ixtx 2950 add iytxt 130 add moveto
TBIL (p) show
ixtx 2800 add iytxt 090 sub moveto
TBIL (p + q) show
4300 1000 moveto
LSxu TBL (=) show 30 0 rmoveto (0) show
4300 0750 moveto
TBIL (p) show
TBL (\050) show LSxu TBL (\051=) show
TBIL (q) show
TBL (\050) show LSxu TBL (\051=1) show
ix3 1400 add 800 add iyt0 250 add moveto
TBIL (p) show TBL ( = ) show
TBL e_10 show
0 100 rmoveto
SVxr
TBS (/a) show ioute 1 eq {(') show} if 0 -100 rmoveto
ix3 1400 add 1600 add iyt0 250 add moveto
TBIL (q) show TBL ( = ) show
TBL e_10 show
0 100 rmoveto
SVxrn
TBS (/a) show ioute 1 eq {(') show} if 0 -100 rmoveto
j 0 eq {%j=0, both sides
tfw
TBS
ix3 1400 add 600 add iyt0 000 add moveto
(a=1,00, b=1,00 e=2,718282) show
ioute 1 eq {%ioute=1
ix3 1400 add 600 add iyt0 200 sub moveto
(a'=a) show 30 0 rmoveto (ln(10)=) show
1.0 10 ln mul cvsshow3x
} if %ioute=1
} if %j=0, both sides
ioute 1 eq
xchartl 0 eq and { %ioute=1, xchartl=0 right side
ix3 1400 add 600 add iyt0 200 add moveto
TBL (10) show
0 100 rmoveto SVxrx 0 -100 rmoveto
TBL (=e) show
0 100 rmoveto TBS (ln(10)) show
30 0 rmoveto SVxrx 0 -100 rmoveto
TBL (, 10) show
0 100 rmoveto
SVxr TBS (/ln(10)) show 0 -100 rmoveto
TBL (=e) show
0 100 rmoveto SVxrx 0 -100 rmoveto
ix3 1400 add 600 add iyt0
ioute 0 eq {250 sub moveto}
{500 sub moveto} ifelse
TBL (10) show
ioute 0 eq {0 100 rmoveto SVxrx
TBS (/a) show 0 -100 rmoveto
} if
ioute 1 eq
expnr 6 le and {0 100 rmoveto SVxrx %zr for xchartl<=6
TBS (/a') show 0 -100 rmoveto
} if
ioute 1 eq
expnr 6 gt and {0 100 rmoveto SVxrx %zr for xchartl>6
TBS (/a') show 0 -100 rmoveto
} if
TBL (=) show
TBL (10) show
0 100 rmoveto SVxrx
TBS ( / [a) show 30 0 rmoveto (ln(10)]) show 0 -100 rmoveto
TBL (=) show
TBL (e) show
0 100 rmoveto SVxrx
TBS (/a) show 0 -100 rmoveto
} if %ioute=1, xchartl=0 right side
} for %j=jm1,jm2
idevi 1 eq {%idevi=1
/iyt1t iyt1 300 add def
30 setlinewidth
[ ] 0 setdash
tfg
ix0 iyt1t moveto
TBIL
(F') show
-50 -80 rmoveto TBS (1,ar) show 0 80 rmoveto
TBL
(\050) show
LSxrx
TBL
(\051) show
TBL
( = 4 / [) show
TBL e_10 show
0 80 rmoveto SVxr
TBS (/a) show ioute 1 eq {(') show} if
20 -80 rmoveto
TBL (+) show 20 0 rmoveto
TBL e_10 show
0 80 rmoveto TBS (-) show SVxr
TBS (/a) show ioute 1 eq {(') show} if
20 -80 rmoveto
TBL (]) show
0 80 rmoveto TBS (2) show 0 -80 rmoveto
ix0 2500 add iyt1t moveto
TBL
( = 4 / [) show
TBIL (p) show TBL ( + ) show TBIL (q) show
TBL (]) show
0 80 rmoveto TBS (2) show 0 -80 rmoveto
ix0 iyt1t 300 sub moveto
TBS
xchartl 0 eq {(a=1,00) show} if
xchartl 1 eq {(a=1,00) show} if
xchartl 2 eq {(a=2,00) show} if
xchartl 3 eq {(a=0,50) show} if
xchartl 4 eq {(a=2,00) show} if
xchartl 5 eq {(a=0,50) show} if
xchartl 6 eq {(a=1,00) show} if
xchartl 7 eq {(a=0,50) show} if
xchartl 1 ge {0 100 rmoveto TBS expnk expnr get show 0 -100 rmoveto} if
TBS
xchartl 0 eq {(; b=1,00) show} if
xchartl 1 eq {(; b=2,00) show} if
xchartl 2 eq {(; b=1,00) show} if
xchartl 3 eq {(; b=1,00) show} if
xchartl 4 eq {(; b=2,00) show} if
xchartl 5 eq {(; b=2,00) show} if
xchartl 6 eq {(; b=1,00) show} if
xchartl 7 eq {(; b=0,50) show} if
xchartl 1 le {%xchartl<=1 special text
%xchartl 0 eq {1620}{1820} ifelse 2150 moveto
xchartl 0 eq {1220}{1820} ifelse 2150 moveto %xchartl=0
tfg TBIL (F') show
-30 -80 rmoveto TBS (1,ar) show 0 80 rmoveto
xchartl 0 eq {TBL (\050) show LSxr TBL (\051) show} if
} if %xchartl<=1 special text
xchartl 1 eq {%xchartl=1 special text
0700 2000 moveto
tfg TBIL (F') show
-30 -80 rmoveto TBS (1_2) show 0 80 rmoveto
TBL (\050) show LSxr TBL (\051) show
tfw
} if %xchartl=1 special text
} if %idevi=1
tfw
[ ] 0 setdash
0 1500 moveto 4500 0 rlineto stroke
tfl [50 50] 0 setdash 0 2000 moveto 2000 0 rlineto stroke
tfn 200 2070 moveto TBL (Asymptote) show
%tfw [ ] 0 setdash 2000 1500 moveto 0 500 rlineto stroke
tfw [ ] 0 setdash 2000 1000 moveto 0 1000 rlineto stroke
xchartl 1 le {%xchartl<=1 special text
%4600 2000 50 sub moveto
4600 2500 50 sub moveto
tfw TBIL (F) show
-30 -80 rmoveto TBS (1,ar) show 0 80 rmoveto
TBL (\050) show LSxr TBL (\051) show
} if %xchartl<=1 special text
xchartl 1 eq {%xchartl=1 special text
3200 2300 moveto
tfy TBIL (F) show
-30 -80 rmoveto TBS (1_2) show 0 80 rmoveto
TBL (\050) show LSxr TBL (\051) show
} if %xchartl=1 special text
xtr0 neg ytr0 neg translate
%*********************************************************************
/C0i_FXi {%BEG C0i_FXi
xtr0 ytr0 translate
/xi 51 array def %range -4 bis +4 in steps of
/yi 51 array def %range -1 to +1
/epxi 51 array def
/emxi 51 array def
/esxi 51 array def
/Frui 51 array def
/MULX 500 def
/MULY 500 def
%ioute 0 eq {/e 2.7182818 def}
% {/e 10.0 def } ifelse
/e 2.7182818 def
/im 45 def
jm1 1 jm2 {/j exch def %j=jm1,jm2
j 0 eq {%j=0
/a 1.0 expnp expnr get exp def
/ai 1.0 expnp expnr get exp lne_10 mul def
/bi 1.0 def
} if %j=0
j 1 eq {%j=1
%xchartl 0 eq {/a 1.0 expnp expnr get exp def
% /ai 1.0 expnp expnr get exp lne_10 mul def
% /bi 1.0 def} if
xchartl 1 eq {/a 1.0 expnp expnr get exp def
/ai 1.0 expnp expnr get exp lne_10 mul def
/bi 2.0 def} if
xchartl 2 eq {/a 2.0 expnp expnr get exp def
/ai 2.0 expnp expnr get exp lne_10 mul def
/bi 1.0 def} if
xchartl 3 eq {/a 0.5 expnp expnr get exp def
/ai 0.5 expnp expnr get exp lne_10 mul def
/bi 1.0 def} if
xchartl 4 eq {/a 2.0 expnp expnr get exp def
/ai 2.0 expnp expnr get exp lne_10 mul def
/bi 2.0 def} if
xchartl 5 eq {/a 0.5 expnp expnr get exp def
/ai 0.5 expnp expnr get exp lne_10 mul def
/bi 2.0 def} if
xchartl 6 eq {/a 1.0 expnp expnr get exp def
/ai 1.0 expnp expnr get exp lne_10 mul def
/bi 0.5 def} if
xchartl 7 eq {/a 0.5 expnp expnr get exp def
/ai 0.5 expnp expnr get exp lne_10 mul def
/bi 0.5 def} if
} if %j=1
0 1 50 {/i exch def %i=0,50
xi i -4 i 0.2 mul add put
ioute 0 eq {%ioute=0
epxi i e xi i get ai div exp put
emxi i e xi i get ai div neg exp put
}
{%ioute=1
epxi i e xi i get lne_10 div ai div exp put
emxi i e xi i get lne_10 div ai div neg exp put
} ifelse
esxi i epxi i get emxi i get add put
Frui i epxi i get %emxi i get sub
epxi i get emxi i get add div bi mul 2 mul put
} for %i=0,50
40 setlinewidth
[ ] 0 setdash
0 1 1 {/k exch def %k=0,1
k 0 eq {%k=0
j 0 eq {[ ] 0 setdash tfw} if
j 1 eq {[ ] 0 setdash tfy} if
} if %k=0
k 1 eq {%k=1
j 0 eq {[100 100] 0 setdash tfn} if
%j 1 eq {[100 100] 0 setdash tfn} if
} if %k=1
0 1 im {/i exch def %i=0,im
i 0 eq {xi i get MULX mul 2000 add
Frui i get MULY mul 1500 add moveto} if
i 1 ge
i im 1 sub le and {xi i get MULX mul 2000 add
Frui i get MULY mul 1500 add lineto} if
i im eq {xi i get MULX mul 2000 add
Frui i get MULY mul 1500 add lineto stroke} if
} for %i=0,im
k 1 eq {%k=1
xchartl 1 ge {%xchartl>=1
tfy
j 1 eq {%j=1
/yta Frui 45 get MULY mul 070 add def
ixt2 2000 add 1500 yta add moveto
xchartl 1 eq {(a=1,00) show} if
xchartl 2 eq {(a=2,00) show} if
xchartl 3 eq {(a=0,50) show} if
xchartl 4 eq {(a=2,00) show} if
xchartl 5 eq {(a=0,50) show} if
xchartl 6 eq {(a=1,00) show} if
xchartl 7 eq {(a=0,50) show} if
xchartl 1 ge {0 100 rmoveto TBS expnk expnr get show 0 -100 rmoveto
TBS (=) show ai cvsshow3x
} if %1<=xchartl<=7} if
} if %j=1
j 1 eq {%j=1
ixt2 2000 add 1500 yta add 0250 sub moveto
ioute 1 eq {%ioute=1
xchartl 1 ge {(a'=) show ai 10 ln mul cvsshow3x
(, ) show} if
} if %ioute=1
xchartl 1 eq {(b=2,00) show} if
xchartl 2 eq {(b=1,00) show} if
xchartl 3 eq {(b=1,00) show} if
xchartl 4 eq {(b=2,00) show} if
xchartl 5 eq {(b=2,00) show} if
xchartl 6 eq {(b=0,50) show} if
xchartl 7 eq {(b=0,50) show} if
} if %j=1
} if %xchartl>=1
} if %k=1
} for %k=0,1
idevi 1 eq {%idevi=1
%integral dx/(a^2+x^2) = (1/a) arctan (x/a)
/edxi 51 array def
/Frudi 51 array def
/ai 1 def %special case
0 1 50 {/i exch def %i=0,50
xi i -4 i 0.2 mul add put
% ioute 0 eq {%ioute=0
% eqxi i e xi i get ai div exp put
% emxi i e xi i get ai div neg exp put
% }
% {%ioute=1
% eqxi i e xi i get lne_10 div ai div exp put
% emxi i e xi i get lne_10 div ai div neg exp put
% } ifelse
edxi i e xi i get exp
e xi i get neg exp add 2 exp put
edxi i 4 edxi i get ai mul div put
Frudi i edxi i get bi mul put
} for %i=0,50
0 1 1 {/k exch def %k=0,1
k 0 eq {%k=0
j 0 eq {[ ] 0 setdash tfg} if
j 1 eq {[ ] 0 setdash tfg} if
} if %k=0
k 1 eq {%k=1
j 0 eq {[100 100] 0 setdash tfn} if
%j 1 eq {[100 100] 0 setdash tfn} if
} if %k=1
50 setlinewidth
/im 45 def
0 1 im {/i exch def %i=0,im
i 0 eq {xi i get MULX mul 2000 add
Frudi i get MULY mul 1500 add moveto} if
i 1 ge
i im 1 sub le and {xi i get MULX mul 2000 add
Frudi i get MULY mul 1500 add lineto} if
i im eq {xi i get MULX mul 2000 add
Frudi i get MULY mul 1500 add lineto stroke} if
} for %i=0,im
} for %k=0,1
[ ] 0 setdash
20 setlinewidth
} if %idevi=1
%slope
/m0 Frui 21 get Frui 19 get sub
xi 21 get xi 19 get sub div def
%font colour
j 0 eq {tfw} if
j 1 eq {tfy} if
1650 0500 j 180 mul sub moveto
TBIS (m) show
0 -70 rmoveto TBV ai cvsshow1x bi cvishow 0 70 rmoveto
TBS (=) show m0 2 mul cvsshow2x
} for %j=jm1,jm2
tfl
/yshi 1500 def
30 setlinewidth
[100 100] 0 setdash
1600 0 moveto 1600 Frui 16 get MULY mul yshi add lineto stroke
2400 500 moveto 2400 Frui 24 get MULY mul yshi add lineto stroke
[ ] 0 setdash
20 setlinewidth
TBL %last circles
newpath
tfw 1600 Frui 16 get MULY mul yshi add 70 0 360 arc fill
tfn 1600 Frui 16 get MULY mul yshi add 50 0 360 arc fill
tfn 2400 Frui 24 get MULY mul yshi add 70 0 360 arc fill
tfw 2400 Frui 24 get MULY mul yshi add 50 0 360 arc fill
newpath
tfn 1600 100 add Frui 16 get MULY mul yshi add 100 sub moveto (N) show
tfw 2400 150 sub Frui 24 get MULY mul yshi add 100 add moveto (W) show
xtr0 neg ytr0 neg translate
} def %C0i_FXi %END C0i_FXi
%*********************************************************************
C0i_FXi
%**************************************************************
%special space for 'xm03'PROZ0.COM 2x before/after xchartl
% xchartl 0 eq { 100 neg 13000 neg translate} if
% xchartl 1 eq { 6150 neg 13000 neg translate} if
% xchartl 2 eq { 100 neg 08740 neg translate} if
% xchartl 3 eq { 6150 neg 08740 neg translate} if
% xchartl 4 eq { 100 neg 04480 neg translate} if
% xchartl 5 eq { 6150 neg 04480 neg translate} if
% xchartl 6 eq { 100 neg 00220 neg translate} if
% xchartl 7 eq { 6150 neg 00220 neg translate} if
grestore
%} for %xchartl=0,07
showpage
grestore
%%Trailer