apl>" <-APL2-------------------- sam316.txt ---------------------------->
apl>)run cap2/sample/graph.inc
apl>" <-APL2-------------------- graph.txt ----------------------------->
apl>" Legend describing various global values:
apl>"
apl>" World coordinates(wc) are those of the real data.
apl>" Graph coordinates(gc) are those of the graph.
apl>"
apl>" caption - Override to text for graph caption. If null, a caption
apl>" will be generated. The graph function resets the global
apl>" caption variable to null at the end of its processing.
apl>"
apl>" hk ------ Constant coefficient of input. If xr=1 (see below) then
apl>" hk becomes the constant imaginary coefficient for all
apl>" values of x on the graph. If xr=0, hk will be the constant
apl>" real coefficient.
apl>"
apl>" htl ----- 0 = both, 1 = headers, 2 = trailers, 3 = neither.
apl>"
apl>" maxx ---- Maximum x axis value in world coordinates.
apl>"
apl>" maxy ---- Maximum y axis value in world coordinates.
apl>"
apl>" minx ---- Minimum x axis value in world coordinates.
apl>"
apl>" miny ---- Minimum y axis value in world coordinates.
apl>"
apl>" mgc ----- Vertical margin in graphic coordinates.
apl>"
apl>" n ------- Synonymous with hk (see above). The x values to which
apl>" the function is applied to obtain y values are derived
apl>" by first creating xwc as a vector of integers uniformly
apl>" distributed between minx and maxx inclusive. Then, either
apl>" 'x#(nX0j1)+xwc' or 'x#n+0j1Xxwc' is evaluated.
apl>"
apl>" nlb ----- 1 = Label the curve with the n value.
apl>"
apl>" points -- Number of points to generate.
apl>"
apl>" xgc ----- Array of x values for data points in graph coordinates.
apl>"
apl>" xiv ----- x axis marker interval in world coordinates.
apl>"
apl>" xlin ---- Width of graph in inches.
apl>"
apl>" xpg ----- Divide xwc by xpg to get xgc.
apl>"
apl>" xpi ----- Array of three values for minx, maxx, and xiv, used when
apl>" invoking the graph function and the array of x values
apl>" spans -pi to +pi.
apl>"
apl>" xr ------ 1=vary real x coefficient, 0=vary imaginary coefficient,
apl>" holding the other coefficient to the constant hk (see above.).
apl>"
apl>" xt ------ Used in a variety of places to temporarily generate
apl>" graphics coordinates.
apl>"
apl>" xwc ----- Array of x values in world coordinates.
apl>"
apl>" yadj ---- Adjustment down to print text below a line.
apl>"
apl>" yabm ---- Maximum absolute value (öy) to appear on graph.
apl>"
apl>" ygc ----- Array of y values for data points in graph coordinates.
apl>"
apl>" ylin ---- Height of graph in inches.
apl>"
apl>" ymgn ---- Margin in inches at top and bottom of y axis.
apl>"
apl>" ypg ----- Divide ywc by ypg to get ygc.
apl>"
apl>" yt ------ Used in a variety of places to temporarily generate
apl>" graphics coordinates.
apl>"
apl>" ywc ----- Array of y values for data points in world coordinates.
apl>"
apl>" Set global values. -------------------------------------------->
apl>"
apl>caption#'' " Empty caption causes one to be generated.
apl>i#11 " Circle function code to extract imag. coef. of complex number.
apl>points#200 " Number of data points to generate on graph.
apl>r#9 " Circle function code to extract real coef. of complex number.
apl>xlin#4.5 " Width of graph in inches.
apl>" minx = -3.14159....
apl>" ö maxx = 3.14159....
apl>" ö ö xiv
apl>" ö ö ö
apl>" V V V
apl>xpi#(O-1),(O1),O.25
apl>ylin#6 " Height of graph in inches.
apl>ymgn#.2 " Margin in inches at top and bottom of y axis.
apl>"
apl>" <----------------------------------------------------------------->
apl>" Generates the LaTeX Öput statements for the data points to appear
apl>" on the graph.
apl>"
apl>Lex 'dodata'
1
apl>Gdodata
Ä1Å xgc#(xwc_minx)%xpg " xgc=x graphic coordinates for data points.
Ä2Å ygc#mgc+(ywc_miny)%ypg " ygc=y graphic coordinates for data points.
Ä3Å $bylabXI0=nlb " Branch if the curve is not to be labelled.
Ä4Å '%Label the curve'
Ä5Å xt#1Y(u=S/u#öywc)/xgc " x coord where maximum/mininum occurs
Ä6Å yt#(_yadjX0>vs/ywc)+(vs#xt=xgc)/ygc " y coord of maximum/minimum
Ä7Å " Note: Calculation for yt works only if all minima occur below
Ä8Å " y axis, and all maxima occur above.
Ä9Å pcon,(xt,',',Ä1.5Åyt),`Z')änÖ#',(Fhk),'å'
Ä10Å bylab:'%Draw the data points'
Ä11Å pcon,((xgc#-1U1Uxgc),',',Ä1.5Å(ygc#-1U1Uygc)),circon
Ä12Å G
apl>" <----------------------------------------------------------------->
apl>" Generate xwc and ywc, the arrays of x/y coordinates for the data
apl>" points to appear on the graph.
apl>"
apl>Lex 'genxy'
1
apl>Ggenxy
Ä1Å xwc#minx+(xlwc#maxx_minx)X(-1+Ipoints+1)%points
Ä2Å $varyrealXIxr
Ä3Å x#hk+0j1Xxwc " real part is constant, imaginary varies.
Ä4Å $calcy " Branch to compute values of y for data points.
Ä5Å varyreal:x#(hkX0j1)+xwc " Imaginary is constant, real varies.
Ä6Å calcy:ywc#eOCfun " Compute values of y for data points
Ä7Å ywcm#yabm>öywc " Mask of keepers, magnitudes of y < yabm.
Ä8Å xwc#ywcm/xwc " Pick the keepers.
Ä9Å ywc#ywcm/ywc " Pick the keepers.
Ä10Å G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Main graph routine.
apl>"
apl>Lex 'graph'
1
apl>Gfun graph a
Ä1Å "Graphs the imaginary or real coefficient of result of fun.
Ä2Å " fun = expression to evaluate.
Ä3Å (htl nlb xr e yabm minx maxx xiv hk yiv yca)#a
Ä4Å genxy " Generate the data points.
Ä5Å $dataXIhtl>1 " Branch if htl greater than 1.
Ä6Å scale " Calculate global scaling values.
Ä7Å headers " Generate LaTeX figure headers.
Ä8Å data:dodata " Process and graph data points.
Ä9Å trailers " Generate Latex figure trailers, maybe.
Ä10Å G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Generates the LaTeX statements to begin the graph.
apl>"
apl>Lex 'headers'
1
apl>Gheaders
Ä1Å 'ÖbeginäfigureåÄtbhÅ'
Ä2Å $gencapXI0=Rcaption " Branch if no caption override.
Ä3Å 'Öcaptionä',caption,'å'
Ä4Å $begin
Ä5Å gencap:$realcapXI(xr=1)&hk=0 " Branch if x data are not complex.
Ä6Å $ncaptionXInlb=0 " Branch if curves are not labelled with n value.
Ä7Å 'ÖcaptionäGraph of yÖ#',(Fe),'O',fun,'+nX0j1å'
Ä8Å $begin
Ä9Å ncaption:$cplxcapXIxr " Branch if varying real coefficient.
Ä10Å 'ÖcaptionäGraph of yÖ#',(Fe),'O',(-1Ufun),(Fhk),'+xX0j1å'
Ä11Å $begin
Ä12Å cplxcap:'ÖcaptionäGraph of yÖ#',(Fe),'O',fun,'+(nÖ#',(Fhk),')X0j1å'
Ä13Å $begin
Ä14Å realcap:'ÖcaptionäGraph of yÖ#',fun,'å'
Ä15Å begin:'Öbeginäcenterå'
Ä16Å 'ÖsetlengthäÖunitlengthåä',(Flin),'inå'
Ä17Å 'Öbeginäpictureå(',(Fxlin%lin),',',(Fylin%lin),')'
Ä18Å '%Draw a frame around the picture'
Ä19Å ' Öput(0,0)äÖline(1,0)ä',(Fxlgc),'åå% bottom'
Ä20Å ' Öput(0,0)äÖline(0,1)ä',(Fylgc),'åå% left'
Ä21Å ' Öput(0,',(Fylgc),')äÖline(1,0)ä',(Fxlgc),'åå% top'
Ä22Å ' Öput(',(Fxlgc),',0)äÖline(0,1)ä',(Fylgc),'åå% right'
Ä23Å '%Draw the x axis'
Ä24Å ' Öput(0,',(Fxax),')äÖline(1,0)ä',(Fxlgc),'åå%x axis'
Ä25Å xt#xoff%xpg
Ä26Å pcon,((xt,Ä1.5Å','),xax),circon " Draw the x axis markers.
Ä27Å xt#xt_xpgX.1Xxmk<0
Ä28Å yt#xax+((.05%lin)Xxax=mgc)_yadjXxax>mgc
Ä29Å $dopaxXIpix
Ä30Å '%Draw the x axis marker values'
Ä31Å pcon,xt,',',yt,econ,xmk,Ä1.5Åscon
Ä32Å $doyax
Ä33Å dopax:'%Draw the x axis marker values in pi'
Ä34Å picon#(`Z'Öfracä') ,`1 'Öpiåä4å' 'Öpiåä2å' '3Öpiåä4å'
Ä35Å picon#('-',`1`Rpicon),'0',picon
Ä36Å pcon,xt,',',yt,econ,picon,Ä1.5Åscon
Ä37Å doyax:'%Draw the y axis'
Ä38Å $putymkXI(yax=0)
Ä39Å ' Öput(',(Fyax),',0)äÖline(0,1)ä',(Fylgc),'åå%y axis'
Ä40Å putymk:'%Draw the y axis markers'
Ä41Å ymask#ymk^=0
Ä42Å yt#ymask/mgc+(ymk_miny)%ypg
Ä43Å pcon,yax,',',yt,Ä1.5Åcircon
Ä44Å '%Draw the y axis marker values'
Ä45Å xt#yax+.05%lin
Ä46Å yt#yt_ypgX.1X(ymask/ymk)<0
Ä47Å pcon,xt,',',yt,econ,(ymask/ymk),Ä1.5Åscon
Ä48Å G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Calculates a variety of values needed to produce the graph.
apl>"
apl>Lex 'scale'
1
apl>Gscale
Ä1Å $byyXIyca " Branch if ylwc, maxy, miny are precalculated.
Ä2Å ylwc#(maxy#S/ywc)_miny#D/ywc
Ä3Å byy:ylap#ylin_2Xymgn " ylap=height allowed for data points.
Ä4Å lin#(xlin%xlwc)Dylap%ylwc " unitlength in inches.
Ä5Å yadj#.14%lin " y graphic coordinate adjustment to print text below line.
Ä6Å mgc#ymgn%lin " Margin in graph coordinates.
Ä7Å xpg#xlwc%xlgc#xlin%lin " Divide xwc by xpg to get gc.
Ä8Å ypg#ylwc%(_2Xymgn%lin)+ylgc#ylin%lin " Divide ywc by ypg to get gc.
Ä9Å xax#(yz#(minyK0)&maxyZ0)Xmgc+(öminy)%ypg " xaxis in graph coordinates.
Ä10Å yax#(xz#(minx<0)&maxx>0)X(öminx)%xpg " yaxis in graph coordinates.
Ä11Å $piaxisXIpix#(minx=O-1)&maxx=O1 " branch if pi units on x axis.
Ä12Å xic#(yax=0)+Dxlwc%xiv
Ä13Å $doyiv
Ä14Å piaxis:xic#Dxlwc%xiv#O.25
Ä15Å doyiv:$doyicXIyiv^=0
Ä16Å yiv#10*D10@ylwc
Ä17Å doyic:yic#yic+0=2öyic#Dylwc%yiv
Ä18Å xoff#(I-1+xic)Xxiv " Offset from minx in world coord. of x markers.
Ä19Å yoff#(_yiv)+(Iyic)Xyiv " Offset from miny in world coord. of y markers.
Ä20Å $yoffplusXIminy>0
Ä21Å ymk#yoff+miny+yivööminy
Ä22Å $yoffdone
Ä23Å yoffplus:ymk#yoff+miny_yivöminy " y for y axis markers in world coord.
Ä24Å yoffdone:xmk#minx+xoff " x for x axis markers in world coord.
Ä25Å circon#`Z')äÖcircle*ä',(F.0205%lin),'åå'
Ä26Å scon#`Z'$å'
Ä27Å econ#`Z')ä$'
Ä28Å pcon#`Z' Öput('
Ä29Å G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Generates the LaTeX statements to finish the graph.
apl>"
apl>Lex 'trailers'
1
apl>Gtrailers
Ä1Å $epicXIhtl=0 " Branch if both headers and trailers.
Ä2Å $eojckXInlb " Branch if graph already labelled.
Ä3Å pcon,(1Yxgc+xpgX.1),',',(1Yygc),')ä',fun,'å' " Label the graph.
Ä4Å eojck:$eojXI(htl=1)+htl=3 " br if headers only, or neither.
Ä5Å epic:'Öendäpictureå'
Ä6Å 'Öendäcenterå'
Ä7Å eoj:'%Finis.'
Ä8Å caption#'' " Reset global caption
Ä9Å G
apl>" htl: 0=both, 1=headers, 2=trailers, 3=neither.
apl>" ö nlb 1 = Label the curve.
apl>" ö ö xr = 1=vary real x coeff, 0=vary imaginary coeff.
apl>" ö ö ö e = i(11) or r(9) to select coefficient to graph.
apl>" ö ö ö ö yabm = maximum öy printed on graph.
apl>" ö ö ö ö ö minx = minimum value of x.
apl>" ö ö ö ö ö ö maxx = maximum value of x.
apl>" ö ö ö ö ö ö ö xiv = x axis marker interval.
apl>" ö ö ö ö ö ö ö ö hk = Constant coefficient of input.
apl>" ö ö ö ö ö ö ö ö ö yiv = y axis marker interval, or 0.
apl>" ö ö ö ö ö ö ö ö ö ö yca = ylwc, maxy, miny are precalculated.
apl>" ö ö ö ö ö ö ö ö ö ö ö
apl>" V V V V V V V V V V V
apl> '6Ox' graph 1,1,1,i,5 ,xpi ,0.5 , 0 ,0 " coshdaty.tex
ÖbeginäfigureåÄtbhÅ
ÖcaptionäGraph of yÖ#11O6Ox+nX0j1å
Öbeginäcenterå
ÖsetlengthäÖunitlengthåä .573733inå
Öbeginäpictureå(7.843374,10.45783)
%Draw a frame around the picture
Öput(0,0)äÖline(1,0)ä7.843374åå% bottom
Öput(0,0)äÖline(0,1)ä10.45783åå% left
Öput(0,10.45783)äÖline(1,0)ä7.843374åå% top
Öput(7.843374,0)äÖline(0,1)ä10.45783åå% right
%Draw the x axis
Öput(0,5.228916)äÖline(1,0)ä7.843374åå%x axis
Öput( .980422 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 1.960844 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 2.941265 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 4.902109 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 5.88253 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 6.862953 , 5.228916 )äÖcircle*ä .03573093åå
%Draw the x axis marker values in pi
Öput( .900314 , 4.9849 )ä$ -Öfracä3Öpiåä4å $å
Öput( 1.880735 , 4.9849 )ä$ -ÖfracäÖpiåä2å $å
Öput( 2.861157 , 4.9849 )ä$ -ÖfracäÖpiåä4å $å
Öput( 3.921687 , 4.9849 )ä$ 0 $å
Öput( 4.902109 , 4.9849 )ä$ ÖfracäÖpiåä4å $å
Öput( 5.88253 , 4.9849 )ä$ ÖfracäÖpiåä2å $å
Öput( 6.862953 , 4.9849 )ä$ Öfracä3Öpiåä4å $å
%Draw the y axis
Öput(3.921687,0)äÖline(0,1)ä10.45783åå%y axis
%Draw the y axis markers
Öput( 3.921687 , 1.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 2.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 3.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 4.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 6.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 7.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 8.228916 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 9.228916 )äÖcircle*ä .03573093åå
%Draw the y axis marker values
Öput( 4.008836 , 1.128916 )ä$ -4 $å
Öput( 4.008836 , 2.128916 )ä$ -3 $å
Öput( 4.008836 , 3.128916 )ä$ -2 $å
Öput( 4.008836 , 4.128916 )ä$ -1 $å
Öput( 4.008836 , 6.228916 )ä$ 1 $å
Öput( 4.008836 , 7.228916 )ä$ 2 $å
Öput( 4.008836 , 8.228916 )ä$ 3 $å
Öput( 4.008836 , 9.228916 )ä$ 4 $å
%Label the curve
Öput( .15686749 , .10457832 )änÖ# .5å
%Draw the data points
Öput( .19608436 , .500269 )äÖcircle*ä .03573093åå
Öput( .23530123 , .647276 )äÖcircle*ä .03573093åå
Öput( .2745181 , .789761 )äÖcircle*ä .03573093åå
Öput( .31373497 , .927865 )äÖcircle*ä .03573093åå
Öput( .35295185 , 1.061723 )äÖcircle*ä .03573093åå
Öput( .39216872 , 1.191468 )äÖcircle*ä .03573093åå
Öput( .43138559 , 1.317227 )äÖcircle*ä .03573093åå
Öput( .47060246 , 1.439126 )äÖcircle*ä .03573093åå
Öput( .509819 , 1.557284 )äÖcircle*ä .03573093åå
Öput( .549036 , 1.671818 )äÖcircle*ä .03573093åå
Öput( .588253 , 1.782841 )äÖcircle*ä .03573093åå
Öput( .62747 , 1.890463 )äÖcircle*ä .03573093åå
Öput( .666687 , 1.994789 )äÖcircle*ä .03573093åå
Öput( .705904 , 2.095923 )äÖcircle*ä .03573093åå
Öput( .74512 , 2.193965 )äÖcircle*ä .03573093åå
Öput( .784337 , 2.289011 )äÖcircle*ä .03573093åå
Öput( .823554 , 2.381156 )äÖcircle*ä .03573093åå
Öput( .862771 , 2.470489 )äÖcircle*ä .03573093åå
Öput( .901988 , 2.5571 )äÖcircle*ä .03573093åå
Öput( .941205 , 2.641074 )äÖcircle*ä .03573093åå
Öput( .980422 , 2.722493 )äÖcircle*ä .03573093åå
Öput( 1.019639 , 2.801438 )äÖcircle*ä .03573093åå
Öput( 1.058856 , 2.877988 )äÖcircle*ä .03573093åå
Öput( 1.098072 , 2.952217 )äÖcircle*ä .03573093åå
Öput( 1.137289 , 3.024198 )äÖcircle*ä .03573093åå
Öput( 1.176506 , 3.094004 )äÖcircle*ä .03573093åå
Öput( 1.215723 , 3.161702 )äÖcircle*ä .03573093åå
Öput( 1.254940 , 3.22736 )äÖcircle*ä .03573093åå
Öput( 1.294157 , 3.291042 )äÖcircle*ä .03573093åå
Öput( 1.333374 , 3.352812 )äÖcircle*ä .03573093åå
Öput( 1.37259 , 3.412729 )äÖcircle*ä .03573093åå
Öput( 1.411807 , 3.470854 )äÖcircle*ä .03573093åå
Öput( 1.451024 , 3.527244 )äÖcircle*ä .03573093åå
Öput( 1.490241 , 3.581954 )äÖcircle*ä .03573093åå
Öput( 1.529458 , 3.635039 )äÖcircle*ä .03573093åå
Öput( 1.568675 , 3.68655 )äÖcircle*ä .03573093åå
Öput( 1.607892 , 3.736539 )äÖcircle*ä .03573093åå
Öput( 1.647109 , 3.785055 )äÖcircle*ä .03573093åå
Öput( 1.686325 , 3.832146 )äÖcircle*ä .03573093åå
Öput( 1.725542 , 3.877858 )äÖcircle*ä .03573093åå
Öput( 1.764759 , 3.922236 )äÖcircle*ä .03573093åå
Öput( 1.803976 , 3.965325 )äÖcircle*ä .03573093åå
Öput( 1.843193 , 4.007166 )äÖcircle*ä .03573093åå
Öput( 1.882410 , 4.047802 )äÖcircle*ä .03573093åå
Öput( 1.921627 , 4.087272 )äÖcircle*ä .03573093åå
Öput( 1.960844 , 4.125615 )äÖcircle*ä .03573093åå
Öput( 2.00006 , 4.162869 )äÖcircle*ä .03573093åå
Öput( 2.039277 , 4.19907 )äÖcircle*ä .03573093åå
Öput( 2.078494 , 4.234256 )äÖcircle*ä .03573093åå
Öput( 2.117711 , 4.268459 )äÖcircle*ä .03573093åå
Öput( 2.156928 , 4.301715 )äÖcircle*ä .03573093åå
Öput( 2.196145 , 4.334055 )äÖcircle*ä .03573093åå
Öput( 2.235362 , 4.365512 )äÖcircle*ä .03573093åå
Öput( 2.274579 , 4.396117 )äÖcircle*ä .03573093åå
Öput( 2.313795 , 4.425899 )äÖcircle*ä .03573093åå
Öput( 2.353012 , 4.454889 )äÖcircle*ä .03573093åå
Öput( 2.392229 , 4.483116 )äÖcircle*ä .03573093åå
Öput( 2.431446 , 4.510606 )äÖcircle*ä .03573093åå
Öput( 2.470663 , 4.537387 )äÖcircle*ä .03573093åå
Öput( 2.509880 , 4.563485 )äÖcircle*ä .03573093åå
Öput( 2.549097 , 4.588927 )äÖcircle*ä .03573093åå
Öput( 2.588314 , 4.613737 )äÖcircle*ä .03573093åå
Öput( 2.62753 , 4.637939 )äÖcircle*ä .03573093åå
Öput( 2.666747 , 4.661559 )äÖcircle*ä .03573093åå
Öput( 2.705964 , 4.684618 )äÖcircle*ä .03573093åå
Öput( 2.745181 , 4.70714 )äÖcircle*ä .03573093åå
Öput( 2.784398 , 4.729147 )äÖcircle*ä .03573093åå
Öput( 2.823615 , 4.750661 )äÖcircle*ä .03573093åå
Öput( 2.862832 , 4.771703 )äÖcircle*ä .03573093åå
Öput( 2.902049 , 4.792294 )äÖcircle*ä .03573093åå
Öput( 2.941265 , 4.812453 )äÖcircle*ä .03573093åå
Öput( 2.980482 , 4.832202 )äÖcircle*ä .03573093åå
Öput( 3.019699 , 4.851559 )äÖcircle*ä .03573093åå
Öput( 3.058916 , 4.870543 )äÖcircle*ä .03573093åå
Öput( 3.098133 , 4.889174 )äÖcircle*ä .03573093åå
Öput( 3.137350 , 4.907469 )äÖcircle*ä .03573093åå
Öput( 3.176567 , 4.925447 )äÖcircle*ä .03573093åå
Öput( 3.215783 , 4.943126 )äÖcircle*ä .03573093åå
Öput( 3.255 , 4.960522 )äÖcircle*ä .03573093åå
Öput( 3.294217 , 4.977654 )äÖcircle*ä .03573093åå
Öput( 3.333434 , 4.994537 )äÖcircle*ä .03573093åå
Öput( 3.372651 , 5.011189 )äÖcircle*ä .03573093åå
Öput( 3.411868 , 5.027627 )äÖcircle*ä .03573093åå
Öput( 3.451085 , 5.043865 )äÖcircle*ä .03573093åå
Öput( 3.490302 , 5.059921 )äÖcircle*ä .03573093åå
Öput( 3.529518 , 5.07581 )äÖcircle*ä .03573093åå
Öput( 3.568735 , 5.091549 )äÖcircle*ä .03573093åå
Öput( 3.607952 , 5.107151 )äÖcircle*ä .03573093åå
Öput( 3.647169 , 5.122633 )äÖcircle*ä .03573093åå
Öput( 3.686386 , 5.13801 )äÖcircle*ä .03573093åå
Öput( 3.725603 , 5.153298 )äÖcircle*ä .03573093åå
Öput( 3.764820 , 5.168511 )äÖcircle*ä .03573093åå
Öput( 3.804037 , 5.183665 )äÖcircle*ä .03573093åå
Öput( 3.843253 , 5.198773 )äÖcircle*ä .03573093åå
Öput( 3.88247 , 5.213852 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 3.960904 , 5.24398 )äÖcircle*ä .03573093åå
Öput( 4.000121 , 5.259059 )äÖcircle*ä .03573093åå
Öput( 4.039338 , 5.274168 )äÖcircle*ä .03573093åå
Öput( 4.078555 , 5.289321 )äÖcircle*ä .03573093åå
Öput( 4.117772 , 5.304534 )äÖcircle*ä .03573093åå
Öput( 4.156988 , 5.319822 )äÖcircle*ä .03573093åå
Öput( 4.196205 , 5.335199 )äÖcircle*ä .03573093åå
Öput( 4.235422 , 5.350682 )äÖcircle*ä .03573093åå
Öput( 4.274639 , 5.366284 )äÖcircle*ä .03573093åå
Öput( 4.313856 , 5.382022 )äÖcircle*ä .03573093åå
Öput( 4.353073 , 5.397911 )äÖcircle*ä .03573093åå
Öput( 4.392290 , 5.413967 )äÖcircle*ä .03573093åå
Öput( 4.431507 , 5.430206 )äÖcircle*ä .03573093åå
Öput( 4.470723 , 5.446643 )äÖcircle*ä .03573093åå
Öput( 4.50994 , 5.463295 )äÖcircle*ä .03573093åå
Öput( 4.549157 , 5.480179 )äÖcircle*ä .03573093åå
Öput( 4.588374 , 5.49731 )äÖcircle*ä .03573093åå
Öput( 4.62759 , 5.514707 )äÖcircle*ä .03573093åå
Öput( 4.666808 , 5.532385 )äÖcircle*ä .03573093åå
Öput( 4.706025 , 5.550363 )äÖcircle*ä .03573093åå
Öput( 4.745241 , 5.568659 )äÖcircle*ä .03573093åå
Öput( 4.784458 , 5.587289 )äÖcircle*ä .03573093åå
Öput( 4.823675 , 5.606274 )äÖcircle*ä .03573093åå
Öput( 4.862892 , 5.62563 )äÖcircle*ä .03573093åå
Öput( 4.902109 , 5.645379 )äÖcircle*ä .03573093åå
Öput( 4.941326 , 5.665539 )äÖcircle*ä .03573093åå
Öput( 4.980543 , 5.686129 )äÖcircle*ä .03573093åå
Öput( 5.019760 , 5.707171 )äÖcircle*ä .03573093åå
Öput( 5.058976 , 5.728685 )äÖcircle*ä .03573093åå
Öput( 5.098193 , 5.750692 )äÖcircle*ä .03573093åå
Öput( 5.13741 , 5.773214 )äÖcircle*ä .03573093åå
Öput( 5.176627 , 5.796274 )äÖcircle*ä .03573093åå
Öput( 5.215844 , 5.819893 )äÖcircle*ä .03573093åå
Öput( 5.25506 , 5.844096 )äÖcircle*ä .03573093åå
Öput( 5.294278 , 5.868906 )äÖcircle*ä .03573093åå
Öput( 5.333495 , 5.894347 )äÖcircle*ä .03573093åå
Öput( 5.372711 , 5.920446 )äÖcircle*ä .03573093åå
Öput( 5.411928 , 5.947227 )äÖcircle*ä .03573093åå
Öput( 5.451145 , 5.974717 )äÖcircle*ä .03573093åå
Öput( 5.490362 , 6.002943 )äÖcircle*ä .03573093åå
Öput( 5.529579 , 6.031933 )äÖcircle*ä .03573093åå
Öput( 5.568796 , 6.061716 )äÖcircle*ä .03573093åå
Öput( 5.608013 , 6.09232 )äÖcircle*ä .03573093åå
Öput( 5.647230 , 6.123778 )äÖcircle*ä .03573093åå
Öput( 5.686446 , 6.156118 )äÖcircle*ä .03573093åå
Öput( 5.725663 , 6.189373 )äÖcircle*ä .03573093åå
Öput( 5.76488 , 6.223577 )äÖcircle*ä .03573093åå
Öput( 5.804097 , 6.258762 )äÖcircle*ä .03573093åå
Öput( 5.843314 , 6.294964 )äÖcircle*ä .03573093åå
Öput( 5.88253 , 6.332218 )äÖcircle*ä .03573093åå
Öput( 5.921748 , 6.37056 )äÖcircle*ä .03573093åå
Öput( 5.960965 , 6.41003 )äÖcircle*ä .03573093åå
Öput( 6.000181 , 6.450666 )äÖcircle*ä .03573093åå
Öput( 6.039398 , 6.492508 )äÖcircle*ä .03573093åå
Öput( 6.078615 , 6.535596 )äÖcircle*ä .03573093åå
Öput( 6.117832 , 6.579975 )äÖcircle*ä .03573093åå
Öput( 6.157049 , 6.625687 )äÖcircle*ä .03573093åå
Öput( 6.196266 , 6.672778 )äÖcircle*ä .03573093åå
Öput( 6.235483 , 6.721293 )äÖcircle*ä .03573093åå
Öput( 6.274699 , 6.771282 )äÖcircle*ä .03573093åå
Öput( 6.313916 , 6.822794 )äÖcircle*ä .03573093åå
Öput( 6.353133 , 6.875878 )äÖcircle*ä .03573093åå
Öput( 6.39235 , 6.930588 )äÖcircle*ä .03573093åå
Öput( 6.431567 , 6.986978 )äÖcircle*ä .03573093åå
Öput( 6.470784 , 7.045103 )äÖcircle*ä .03573093åå
Öput( 6.51 , 7.10502 )äÖcircle*ä .03573093åå
Öput( 6.549218 , 7.16679 )äÖcircle*ä .03573093åå
Öput( 6.588434 , 7.230473 )äÖcircle*ä .03573093åå
Öput( 6.627651 , 7.29613 )äÖcircle*ä .03573093åå
Öput( 6.666868 , 7.363829 )äÖcircle*ä .03573093åå
Öput( 6.706085 , 7.433634 )äÖcircle*ä .03573093åå
Öput( 6.745302 , 7.505616 )äÖcircle*ä .03573093åå
Öput( 6.784519 , 7.579845 )äÖcircle*ä .03573093åå
Öput( 6.823736 , 7.656394 )äÖcircle*ä .03573093åå
Öput( 6.862953 , 7.735339 )äÖcircle*ä .03573093åå
Öput( 6.902169 , 7.816759 )äÖcircle*ä .03573093åå
Öput( 6.941386 , 7.900732 )äÖcircle*ä .03573093åå
Öput( 6.980603 , 7.987343 )äÖcircle*ä .03573093åå
Öput( 7.01982 , 8.076677 )äÖcircle*ä .03573093åå
Öput( 7.059037 , 8.168821 )äÖcircle*ä .03573093åå
Öput( 7.098254 , 8.263867 )äÖcircle*ä .03573093åå
Öput( 7.13747 , 8.361909 )äÖcircle*ä .03573093åå
Öput( 7.176688 , 8.463043 )äÖcircle*ä .03573093åå
Öput( 7.215904 , 8.567370 )äÖcircle*ä .03573093åå
Öput( 7.255121 , 8.674991 )äÖcircle*ä .03573093åå
Öput( 7.294338 , 8.786014 )äÖcircle*ä .03573093åå
Öput( 7.333555 , 8.900548 )äÖcircle*ä .03573093åå
Öput( 7.372772 , 9.018706 )äÖcircle*ä .03573093åå
Öput( 7.411989 , 9.140605 )äÖcircle*ä .03573093åå
Öput( 7.451206 , 9.266365 )äÖcircle*ä .03573093åå
Öput( 7.490423 , 9.396110 )äÖcircle*ä .03573093åå
Öput( 7.529639 , 9.52997 )äÖcircle*ä .03573093åå
Öput( 7.568856 , 9.66807 )äÖcircle*ä .03573093åå
Öput( 7.608073 , 9.81056 )äÖcircle*ä .03573093åå
Öput( 7.64729 , 9.95756 )äÖcircle*ä .03573093åå
%Finis.
apl> '6Ox' graph 2,1,1,i,5 ,xpi ,2 , 0 ,0 " coshdaty.tex
%Label the curve
Öput( .941205 , .07669564 )änÖ#2å
%Draw the data points
Öput( .980422 , .47513482 )äÖcircle*ä .03573093åå
Öput( 1.019639 , .624866 )äÖcircle*ä .03573093åå
Öput( 1.058856 , .770052 )äÖcircle*ä .03573093åå
Öput( 1.098072 , .910838 )äÖcircle*ä .03573093åå
Öput( 1.137289 , 1.047361 )äÖcircle*ä .03573093åå
Öput( 1.176506 , 1.179757 )äÖcircle*ä .03573093åå
Öput( 1.215723 , 1.308156 )äÖcircle*ä .03573093åå
Öput( 1.254940 , 1.432685 )äÖcircle*ä .03573093åå
Öput( 1.294157 , 1.553468 )äÖcircle*ä .03573093åå
Öput( 1.333374 , 1.670622 )äÖcircle*ä .03573093åå
Öput( 1.37259 , 1.784264 )äÖcircle*ä .03573093åå
Öput( 1.411807 , 1.894507 )äÖcircle*ä .03573093åå
Öput( 1.451024 , 2.001458 )äÖcircle*ä .03573093åå
Öput( 1.490241 , 2.105223 )äÖcircle*ä .03573093åå
Öput( 1.529458 , 2.205905 )äÖcircle*ä .03573093åå
Öput( 1.568675 , 2.303604 )äÖcircle*ä .03573093åå
Öput( 1.607892 , 2.398415 )äÖcircle*ä .03573093åå
Öput( 1.647109 , 2.490432 )äÖcircle*ä .03573093åå
Öput( 1.686325 , 2.579746 )äÖcircle*ä .03573093åå
Öput( 1.725542 , 2.666445 )äÖcircle*ä .03573093åå
Öput( 1.764759 , 2.750615 )äÖcircle*ä .03573093åå
Öput( 1.803976 , 2.832339 )äÖcircle*ä .03573093åå
Öput( 1.843193 , 2.911697 )äÖcircle*ä .03573093åå
Öput( 1.882410 , 2.988768 )äÖcircle*ä .03573093åå
Öput( 1.921627 , 3.063628 )äÖcircle*ä .03573093åå
Öput( 1.960844 , 3.136351 )äÖcircle*ä .03573093åå
Öput( 2.00006 , 3.207008 )äÖcircle*ä .03573093åå
Öput( 2.039277 , 3.27567 )äÖcircle*ä .03573093åå
Öput( 2.078494 , 3.342404 )äÖcircle*ä .03573093åå
Öput( 2.117711 , 3.407275 )äÖcircle*ä .03573093åå
Öput( 2.156928 , 3.470349 )äÖcircle*ä .03573093åå
Öput( 2.196145 , 3.531687 )äÖcircle*ä .03573093åå
Öput( 2.235362 , 3.591349 )äÖcircle*ä .03573093åå
Öput( 2.274579 , 3.649395 )äÖcircle*ä .03573093åå
Öput( 2.313795 , 3.705883 )äÖcircle*ä .03573093åå
Öput( 2.353012 , 3.760866 )äÖcircle*ä .03573093åå
Öput( 2.392229 , 3.814401 )äÖcircle*ä .03573093åå
Öput( 2.431446 , 3.866540 )äÖcircle*ä .03573093åå
Öput( 2.470663 , 3.917334 )äÖcircle*ä .03573093åå
Öput( 2.509880 , 3.966833 )äÖcircle*ä .03573093åå
Öput( 2.549097 , 4.015087 )äÖcircle*ä .03573093åå
Öput( 2.588314 , 4.062142 )äÖcircle*ä .03573093åå
Öput( 2.62753 , 4.108046 )äÖcircle*ä .03573093åå
Öput( 2.666747 , 4.152844 )äÖcircle*ä .03573093åå
Öput( 2.705964 , 4.196579 )äÖcircle*ä .03573093åå
Öput( 2.745181 , 4.239295 )äÖcircle*ä .03573093åå
Öput( 2.784398 , 4.281035 )äÖcircle*ä .03573093åå
Öput( 2.823615 , 4.321839 )äÖcircle*ä .03573093åå
Öput( 2.862832 , 4.361748 )äÖcircle*ä .03573093åå
Öput( 2.902049 , 4.4008 )äÖcircle*ä .03573093åå
Öput( 2.941265 , 4.439036 )äÖcircle*ä .03573093åå
Öput( 2.980482 , 4.476492 )äÖcircle*ä .03573093åå
Öput( 3.019699 , 4.513205 )äÖcircle*ä .03573093åå
Öput( 3.058916 , 4.549211 )äÖcircle*ä .03573093åå
Öput( 3.098133 , 4.584547 )äÖcircle*ä .03573093åå
Öput( 3.137350 , 4.619247 )äÖcircle*ä .03573093åå
Öput( 3.176567 , 4.653345 )äÖcircle*ä .03573093åå
Öput( 3.215783 , 4.686875 )äÖcircle*ä .03573093åå
Öput( 3.255 , 4.719869 )äÖcircle*ä .03573093åå
Öput( 3.294217 , 4.752362 )äÖcircle*ä .03573093åå
Öput( 3.333434 , 4.784384 )äÖcircle*ä .03573093åå
Öput( 3.372651 , 4.815967 )äÖcircle*ä .03573093åå
Öput( 3.411868 , 4.847143 )äÖcircle*ä .03573093åå
Öput( 3.451085 , 4.877941 )äÖcircle*ä .03573093åå
Öput( 3.490302 , 4.908394 )äÖcircle*ä .03573093åå
Öput( 3.529518 , 4.938530 )äÖcircle*ä .03573093åå
Öput( 3.568735 , 4.968379 )äÖcircle*ä .03573093åå
Öput( 3.607952 , 4.997971 )äÖcircle*ä .03573093åå
Öput( 3.647169 , 5.027336 )äÖcircle*ä .03573093åå
Öput( 3.686386 , 5.056501 )äÖcircle*ä .03573093åå
Öput( 3.725603 , 5.085496 )äÖcircle*ä .03573093åå
Öput( 3.764820 , 5.114350 )äÖcircle*ä .03573093åå
Öput( 3.804037 , 5.14309 )äÖcircle*ä .03573093åå
Öput( 3.843253 , 5.171746 )äÖcircle*ä .03573093åå
Öput( 3.88247 , 5.200345 )äÖcircle*ä .03573093åå
Öput( 3.921687 , 5.228916 )äÖcircle*ä .03573093åå
Öput( 3.960904 , 5.257487 )äÖcircle*ä .03573093åå
Öput( 4.000121 , 5.286087 )äÖcircle*ä .03573093åå
Öput( 4.039338 , 5.314742 )äÖcircle*ä .03573093åå
Öput( 4.078555 , 5.343483 )äÖcircle*ä .03573093åå
Öput( 4.117772 , 5.372336 )äÖcircle*ä .03573093åå
Öput( 4.156988 , 5.401332 )äÖcircle*ä .03573093åå
Öput( 4.196205 , 5.430497 )äÖcircle*ä .03573093åå
Öput( 4.235422 , 5.459861 )äÖcircle*ä .03573093åå
Öput( 4.274639 , 5.489453 )äÖcircle*ä .03573093åå
Öput( 4.313856 , 5.519303 )äÖcircle*ä .03573093åå
Öput( 4.353073 , 5.549439 )äÖcircle*ä .03573093åå
Öput( 4.392290 , 5.579891 )äÖcircle*ä .03573093åå
Öput( 4.431507 , 5.610690 )äÖcircle*ä .03573093åå
Öput( 4.470723 , 5.641865 )äÖcircle*ä .03573093åå
Öput( 4.50994 , 5.673449 )äÖcircle*ä .03573093åå
Öput( 4.549157 , 5.70547 )äÖcircle*ä .03573093åå
Öput( 4.588374 , 5.737963 )äÖcircle*ä .03573093åå
Öput( 4.62759 , 5.770958 )äÖcircle*ä .03573093åå
Öput( 4.666808 , 5.804488 )äÖcircle*ä .03573093åå
Öput( 4.706025 , 5.838586 )äÖcircle*ä .03573093åå
Öput( 4.745241 , 5.873285 )äÖcircle*ä .03573093åå
Öput( 4.784458 , 5.908621 )äÖcircle*ä .03573093åå
Öput( 4.823675 , 5.944628 )äÖcircle*ä .03573093åå
Öput( 4.862892 , 5.98134 )äÖcircle*ä .03573093åå
Öput( 4.902109 , 6.018797 )äÖcircle*ä .03573093åå
Öput( 4.941326 , 6.057032 )äÖcircle*ä .03573093åå
Öput( 4.980543 , 6.096085 )äÖcircle*ä .03573093åå
Öput( 5.019760 , 6.135993 )äÖcircle*ä .03573093åå
Öput( 5.058976 , 6.176797 )äÖcircle*ä .03573093åå
Öput( 5.098193 , 6.218537 )äÖcircle*ä .03573093åå
Öput( 5.13741 , 6.261253 )äÖcircle*ä .03573093åå
Öput( 5.176627 , 6.304989 )äÖcircle*ä .03573093åå
Öput( 5.215844 , 6.349786 )äÖcircle*ä .03573093åå
Öput( 5.25506 , 6.39569 )äÖcircle*ä .03573093åå
Öput( 5.294278 , 6.442746 )äÖcircle*ä .03573093åå
Öput( 5.333495 , 6.490999 )äÖcircle*ä .03573093åå
Öput( 5.372711 , 6.540499 )äÖcircle*ä .03573093åå
Öput( 5.411928 , 6.591293 )äÖcircle*ä .03573093åå
Öput( 5.451145 , 6.643431 )äÖcircle*ä .03573093åå
Öput( 5.490362 , 6.696966 )äÖcircle*ä .03573093åå
Öput( 5.529579 , 6.75195 )äÖcircle*ä .03573093åå
Öput( 5.568796 , 6.808437 )äÖcircle*ä .03573093åå
Öput( 5.608013 , 6.866483 )äÖcircle*ä .03573093åå
Öput( 5.647230 , 6.926146 )äÖcircle*ä .03573093åå
Öput( 5.686446 , 6.987484 )äÖcircle*ä .03573093åå
Öput( 5.725663 , 7.050557 )äÖcircle*ä .03573093åå
Öput( 5.76488 , 7.115429 )äÖcircle*ä .03573093åå
Öput( 5.804097 , 7.182162 )äÖcircle*ä .03573093åå
Öput( 5.843314 , 7.250824 )äÖcircle*ä .03573093åå
Öput( 5.88253 , 7.321481 )äÖcircle*ä .03573093åå
Öput( 5.921748 , 7.394204 )äÖcircle*ä .03573093åå
Öput( 5.960965 , 7.469064 )äÖcircle*ä .03573093åå
Öput( 6.000181 , 7.546135 )äÖcircle*ä .03573093åå
Öput( 6.039398 , 7.625494 )äÖcircle*ä .03573093åå
Öput( 6.078615 , 7.707217 )äÖcircle*ä .03573093åå
Öput( 6.117832 , 7.791387 )äÖcircle*ä .03573093åå
Öput( 6.157049 , 7.878087 )äÖcircle*ä .03573093åå
Öput( 6.196266 , 7.9674 )äÖcircle*ä .03573093åå
Öput( 6.235483 , 8.059418 )äÖcircle*ä .03573093åå
Öput( 6.274699 , 8.154229 )äÖcircle*ä .03573093åå
Öput( 6.313916 , 8.251927 )äÖcircle*ä .03573093åå
Öput( 6.353133 , 8.352609 )äÖcircle*ä .03573093åå
Öput( 6.39235 , 8.456375 )äÖcircle*ä .03573093åå
Öput( 6.431567 , 8.563326 )äÖcircle*ä .03573093åå
Öput( 6.470784 , 8.673568 )äÖcircle*ä .03573093åå
Öput( 6.51 , 8.78721 )äÖcircle*ä .03573093åå
Öput( 6.549218 , 8.904365 )äÖcircle*ä .03573093åå
Öput( 6.588434 , 9.025147 )äÖcircle*ä .03573093åå
Öput( 6.627651 , 9.149676 )äÖcircle*ä .03573093åå
Öput( 6.666868 , 9.278076 )äÖcircle*ä .03573093åå
Öput( 6.706085 , 9.410472 )äÖcircle*ä .03573093åå
Öput( 6.745302 , 9.54699 )äÖcircle*ä .03573093åå
Öput( 6.784519 , 9.68778 )äÖcircle*ä .03573093åå
Öput( 6.823736 , 9.83297 )äÖcircle*ä .03573093åå
Öput( 6.862953 , 9.98270 )äÖcircle*ä .03573093åå
Öendäpictureå
Öendäcenterå
%Finis.
apl>)off