Metropoli BBS
VIEWER: sam301.txt MODE: TEXT (SF7)
apl>" <-APL2-------------------- sam301.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> '2Ox' graph 1,1,1,i,1e6,xpi     ,2   , 0  ,0 " cosdaty.tex

ÖbeginäfigureåÄtbhÅ
ÖcaptionäGraph of yÖ#11O2Ox+nX0j1å
Öbeginäcenterå
ÖsetlengthäÖunitlengthåä .716197inå
Öbeginäpictureå(6.283185,8.37758)
%Draw a frame around the picture
 Öput(0,0)äÖline(1,0)ä6.283185åå% bottom
 Öput(0,0)äÖline(0,1)ä8.37758åå% left
 Öput(0,8.37758)äÖline(1,0)ä6.283185åå% top
 Öput(6.283185,0)äÖline(0,1)ä8.37758åå% right
%Draw the x axis
 Öput(0,4.18879)äÖline(1,0)ä6.283185åå%x axis
  Öput(  .785398 , 4.18879 )äÖcircle*ä .0286234åå 
  Öput( 1.570796 , 4.18879 )äÖcircle*ä .0286234åå 
  Öput( 2.356194 , 4.18879 )äÖcircle*ä .0286234åå 
  Öput( 3.141593 , 4.18879 )äÖcircle*ä .0286234åå 
  Öput(  3.92699 , 4.18879 )äÖcircle*ä .0286234åå 
  Öput( 4.712389 , 4.18879 )äÖcircle*ä .0286234åå 
  Öput( 5.497787 , 4.18879 )äÖcircle*ä .0286234åå 
%Draw the x axis marker values in pi
  Öput(  .685398 , 3.993313 )ä$ -Öfracä3Öpiåä4å $å 
  Öput( 1.470796 , 3.993313 )ä$  -ÖfracäÖpiåä2å $å 
  Öput( 2.256194 , 3.993313 )ä$  -ÖfracäÖpiåä4å $å 
  Öput( 3.141593 , 3.993313 )ä$               0 $å 
  Öput(  3.92699 , 3.993313 )ä$   ÖfracäÖpiåä4å $å 
  Öput( 4.712389 , 3.993313 )ä$   ÖfracäÖpiåä2å $å 
  Öput( 5.497787 , 3.993313 )ä$  Öfracä3Öpiåä4å $å 
%Draw the y axis
 Öput(3.141593,0)äÖline(0,1)ä8.37758åå%y axis
%Draw the y axis markers
  Öput( 3.141593 ,   .95497 )äÖcircle*ä .0286234åå 
  Öput( 3.141593 ,  2.03291 )äÖcircle*ä .0286234åå 
  Öput( 3.141593 ,  3.11085 )äÖcircle*ä .0286234åå 
  Öput( 3.141593 ,  5.26673 )äÖcircle*ä .0286234åå 
  Öput( 3.141593 ,  6.34467 )äÖcircle*ä .0286234åå 
  Öput( 3.141593 , 7.422610 )äÖcircle*ä .0286234åå 
%Draw the y axis marker values
  Öput( 3.211406 ,  .862201 )ä$ -3 $å 
  Öput( 3.211406 ,  1.94014 )ä$ -2 $å 
  Öput( 3.211406 ,  3.01808 )ä$ -1 $å 
  Öput( 3.211406 ,  5.26673 )ä$  1 $å 
  Öput( 3.211406 ,  6.34467 )ä$  2 $å 
  Öput( 3.211406 , 7.422610 )ä$  3 $å 
%Label the curve
  Öput( 1.570796 , 8.098328   )änÖ#2å 
%Draw the data points
  Öput(  .03141593 ,   4.311592   )äÖcircle*ä .0286234åå 
  Öput(  .06283185 ,   4.434272   )äÖcircle*ä .0286234åå 
  Öput(  .09424778 ,    4.55671   )äÖcircle*ä .0286234åå 
  Öput(   .1256637 ,   4.678785   )äÖcircle*ä .0286234åå 
  Öput(  .15707963 ,   4.800377   )äÖcircle*ä .0286234åå 
  Öput(  .18849556 ,   4.921364   )äÖcircle*ä .0286234åå 
  Öput(  .21991149 ,   5.041629   )äÖcircle*ä .0286234åå 
  Öput(  .25132741 ,   5.161053   )äÖcircle*ä .0286234åå 
  Öput(  .28274334 ,   5.279516   )äÖcircle*ä .0286234åå 
  Öput(  .31415927 ,   5.396904   )äÖcircle*ä .0286234åå 
  Öput(  .34557519 ,   5.513099   )äÖcircle*ä .0286234åå 
  Öput(  .37699112 ,   5.627987   )äÖcircle*ä .0286234åå 
  Öput(  .40840704 ,   5.741455   )äÖcircle*ä .0286234åå 
  Öput(  .43982297 ,    5.85339   )äÖcircle*ä .0286234åå 
  Öput(  .47123890 ,   5.963683   )äÖcircle*ä .0286234åå 
  Öput(    .502655 ,   6.072224   )äÖcircle*ä .0286234åå 
  Öput(     .53407 ,   6.178907   )äÖcircle*ä .0286234åå 
  Öput(    .565487 ,   6.283625   )äÖcircle*ä .0286234åå 
  Öput(    .596903 ,   6.386276   )äÖcircle*ä .0286234åå 
  Öput(    .628319 ,   6.486759   )äÖcircle*ä .0286234åå 
  Öput(    .659734 ,   6.584973   )äÖcircle*ä .0286234åå 
  Öput(     .69115 ,   6.680823   )äÖcircle*ä .0286234åå 
  Öput(    .722566 ,   6.774214   )äÖcircle*ä .0286234åå 
  Öput(    .753982 ,   6.865053   )äÖcircle*ä .0286234åå 
  Öput(    .785398 ,    6.95325   )äÖcircle*ä .0286234åå 
  Öput(    .816814 ,    7.03872   )äÖcircle*ä .0286234åå 
  Öput(     .84823 ,   7.121378   )äÖcircle*ä .0286234åå 
  Öput(    .879646 ,    7.20114   )äÖcircle*ä .0286234åå 
  Öput(    .911062 ,    7.27793   )äÖcircle*ä .0286234åå 
  Öput(    .942478 ,   7.351673   )äÖcircle*ä .0286234åå 
  Öput(    .973894 ,   7.422293   )äÖcircle*ä .0286234åå 
  Öput(   1.005310 ,   7.489722   )äÖcircle*ä .0286234åå 
  Öput(   1.036726 ,   7.553893   )äÖcircle*ä .0286234åå 
  Öput(   1.068142 ,   7.614744   )äÖcircle*ä .0286234åå 
  Öput(   1.099557 ,   7.672214   )äÖcircle*ä .0286234åå 
  Öput(   1.130973 ,   7.726246   )äÖcircle*ä .0286234åå 
  Öput(   1.162389 ,   7.776786   )äÖcircle*ä .0286234åå 
  Öput(   1.193805 ,   7.823786   )äÖcircle*ä .0286234åå 
  Öput(   1.225221 ,   7.867199   )äÖcircle*ä .0286234åå 
  Öput(   1.256637 ,   7.906981   )äÖcircle*ä .0286234åå 
  Öput(   1.288053 ,   7.943094   )äÖcircle*ä .0286234åå 
  Öput(   1.319469 ,   7.975502   )äÖcircle*ä .0286234åå 
  Öput(   1.350885 ,   8.004173   )äÖcircle*ä .0286234åå 
  Öput(     1.3823 ,   8.029079   )äÖcircle*ä .0286234åå 
  Öput(   1.413717 ,   8.050195   )äÖcircle*ä .0286234åå 
  Öput(   1.445133 ,   8.067500   )äÖcircle*ä .0286234åå 
  Öput(   1.476549 ,   8.080977   )äÖcircle*ä .0286234åå 
  Öput(   1.507964 ,   8.090613   )äÖcircle*ä .0286234åå 
  Öput(    1.53938 ,   8.096399   )äÖcircle*ä .0286234åå 
  Öput(   1.570796 ,   8.098328   )äÖcircle*ä .0286234åå 
  Öput(   1.602212 ,   8.096399   )äÖcircle*ä .0286234åå 
  Öput(   1.633628 ,   8.090613   )äÖcircle*ä .0286234åå 
  Öput(   1.665044 ,   8.080977   )äÖcircle*ä .0286234åå 
  Öput(    1.69646 ,   8.067500   )äÖcircle*ä .0286234åå 
  Öput(   1.727876 ,   8.050195   )äÖcircle*ä .0286234åå 
  Öput(   1.759292 ,   8.029079   )äÖcircle*ä .0286234åå 
  Öput(   1.790708 ,   8.004173   )äÖcircle*ä .0286234åå 
  Öput(   1.822124 ,   7.975502   )äÖcircle*ä .0286234åå 
  Öput(   1.853540 ,   7.943094   )äÖcircle*ä .0286234åå 
  Öput(   1.884956 ,   7.906981   )äÖcircle*ä .0286234åå 
  Öput(   1.916372 ,   7.867199   )äÖcircle*ä .0286234åå 
  Öput(   1.947787 ,   7.823786   )äÖcircle*ä .0286234åå 
  Öput(   1.979203 ,   7.776786   )äÖcircle*ä .0286234åå 
  Öput(   2.010619 ,   7.726246   )äÖcircle*ä .0286234åå 
  Öput(   2.042035 ,   7.672214   )äÖcircle*ä .0286234åå 
  Öput(   2.073451 ,   7.614744   )äÖcircle*ä .0286234åå 
  Öput(   2.104867 ,   7.553893   )äÖcircle*ä .0286234åå 
  Öput(   2.136283 ,   7.489722   )äÖcircle*ä .0286234åå 
  Öput(   2.167699 ,   7.422293   )äÖcircle*ä .0286234åå 
  Öput(   2.199115 ,   7.351673   )äÖcircle*ä .0286234åå 
  Öput(    2.23053 ,    7.27793   )äÖcircle*ä .0286234åå 
  Öput(   2.261947 ,    7.20114   )äÖcircle*ä .0286234åå 
  Öput(   2.293363 ,   7.121378   )äÖcircle*ä .0286234åå 
  Öput(   2.324779 ,    7.03872   )äÖcircle*ä .0286234åå 
  Öput(   2.356194 ,    6.95325   )äÖcircle*ä .0286234åå 
  Öput(    2.38761 ,   6.865053   )äÖcircle*ä .0286234åå 
  Öput(   2.419026 ,   6.774214   )äÖcircle*ä .0286234åå 
  Öput(   2.450442 ,   6.680823   )äÖcircle*ä .0286234åå 
  Öput(   2.481858 ,   6.584973   )äÖcircle*ä .0286234åå 
  Öput(   2.513274 ,   6.486759   )äÖcircle*ä .0286234åå 
  Öput(    2.54469 ,   6.386276   )äÖcircle*ä .0286234åå 
  Öput(   2.576106 ,   6.283625   )äÖcircle*ä .0286234åå 
  Öput(   2.607522 ,   6.178907   )äÖcircle*ä .0286234åå 
  Öput(   2.638938 ,   6.072224   )äÖcircle*ä .0286234åå 
  Öput(   2.670354 ,   5.963683   )äÖcircle*ä .0286234åå 
  Öput(   2.701770 ,    5.85339   )äÖcircle*ä .0286234åå 
  Öput(   2.733186 ,   5.741455   )äÖcircle*ä .0286234åå 
  Öput(   2.764602 ,   5.627987   )äÖcircle*ä .0286234åå 
  Öput(   2.796017 ,   5.513099   )äÖcircle*ä .0286234åå 
  Öput(   2.827433 ,   5.396904   )äÖcircle*ä .0286234åå 
  Öput(   2.858849 ,   5.279516   )äÖcircle*ä .0286234åå 
  Öput(   2.890265 ,   5.161053   )äÖcircle*ä .0286234åå 
  Öput(   2.921681 ,   5.041629   )äÖcircle*ä .0286234åå 
  Öput(   2.953097 ,   4.921364   )äÖcircle*ä .0286234åå 
  Öput(   2.984513 ,   4.800377   )äÖcircle*ä .0286234åå 
  Öput(   3.015929 ,   4.678785   )äÖcircle*ä .0286234åå 
  Öput(   3.047345 ,    4.55671   )äÖcircle*ä .0286234åå 
  Öput(    3.07876 ,   4.434272   )äÖcircle*ä .0286234åå 
  Öput(   3.110177 ,   4.311592   )äÖcircle*ä .0286234åå 
  Öput(   3.141593 ,    4.18879   )äÖcircle*ä .0286234åå 
  Öput(   3.173009 ,   4.065989   )äÖcircle*ä .0286234åå 
  Öput(   3.204425 ,   3.943308   )äÖcircle*ä .0286234åå 
  Öput(    3.23584 ,    3.82087   )äÖcircle*ä .0286234åå 
  Öput(   3.267256 ,   3.698795   )äÖcircle*ä .0286234åå 
  Öput(   3.298672 ,   3.577204   )äÖcircle*ä .0286234åå 
  Öput(   3.330088 ,   3.456216   )äÖcircle*ä .0286234åå 
  Öput(   3.361504 ,   3.335951   )äÖcircle*ä .0286234åå 
  Öput(    3.39292 ,   3.216528   )äÖcircle*ä .0286234åå 
  Öput(   3.424336 ,   3.098064   )äÖcircle*ä .0286234åå 
  Öput(   3.455752 ,   2.980677   )äÖcircle*ä .0286234åå 
  Öput(   3.487168 ,   2.864482   )äÖcircle*ä .0286234åå 
  Öput(   3.518584 ,   2.749593   )äÖcircle*ä .0286234åå 
  Öput(   3.550000 ,   2.636126   )äÖcircle*ä .0286234åå 
  Öput(   3.581416 ,    2.52419   )äÖcircle*ä .0286234åå 
  Öput(   3.612832 ,   2.413897   )äÖcircle*ä .0286234åå 
  Öput(   3.644247 ,   2.305356   )äÖcircle*ä .0286234åå 
  Öput(   3.675663 ,   2.198674   )äÖcircle*ä .0286234åå 
  Öput(   3.707079 ,   2.093955   )äÖcircle*ä .0286234åå 
  Öput(   3.738495 ,   1.991304   )äÖcircle*ä .0286234åå 
  Öput(   3.769911 ,   1.890822   )äÖcircle*ä .0286234åå 
  Öput(   3.801327 ,   1.792607   )äÖcircle*ä .0286234åå 
  Öput(   3.832743 ,   1.696757   )äÖcircle*ä .0286234åå 
  Öput(   3.864159 ,   1.603367   )äÖcircle*ä .0286234åå 
  Öput(   3.895575 ,   1.512528   )äÖcircle*ä .0286234åå 
  Öput(    3.92699 ,   1.424330   )äÖcircle*ä .0286234åå 
  Öput(   3.958407 ,    1.33886   )äÖcircle*ä .0286234åå 
  Öput(   3.989823 ,   1.256203   )äÖcircle*ä .0286234åå 
  Öput(   4.021239 ,   1.176440   )äÖcircle*ä .0286234åå 
  Öput(   4.052655 ,   1.099650   )äÖcircle*ä .0286234åå 
  Öput(    4.08407 ,   1.025908   )äÖcircle*ä .0286234åå 
  Öput(   4.115486 ,   .955288    )äÖcircle*ä .0286234åå 
  Öput(   4.146902 ,   .887858    )äÖcircle*ä .0286234åå 
  Öput(   4.178318 ,   .823687    )äÖcircle*ä .0286234åå 
  Öput(   4.209734 ,   .762836    )äÖcircle*ä .0286234åå 
  Öput(    4.24115 ,   .705367    )äÖcircle*ä .0286234åå 
  Öput(   4.272566 ,   .651335    )äÖcircle*ä .0286234åå 
  Öput(   4.303982 ,   .600794    )äÖcircle*ä .0286234åå 
  Öput(   4.335398 ,   .553794    )äÖcircle*ä .0286234åå 
  Öput(   4.366814 ,   .510382    )äÖcircle*ä .0286234åå 
  Öput(   4.398230 , .47059907    )äÖcircle*ä .0286234åå 
  Öput(   4.429646 ,   .434486    )äÖcircle*ä .0286234åå 
  Öput(   4.461062 , .40207799    )äÖcircle*ä .0286234åå 
  Öput(   4.492477 ,   .373407    )äÖcircle*ä .0286234åå 
  Öput(   4.523893 , .34850134    )äÖcircle*ä .0286234åå 
  Öput(   4.555309 , .32738557    )äÖcircle*ä .0286234åå 
  Öput(   4.586725 , .31008055    )äÖcircle*ä .0286234åå 
  Öput(   4.618141 , .29660335    )äÖcircle*ä .0286234åå 
  Öput(   4.649557 , .28696726    )äÖcircle*ä .0286234åå 
  Öput(   4.680973 ,  .2811818    )äÖcircle*ä .0286234åå 
  Öput(   4.712389 , .27925268    )äÖcircle*ä .0286234åå 
  Öput(   4.743805 ,  .2811818    )äÖcircle*ä .0286234åå 
  Öput(    4.77522 , .28696726    )äÖcircle*ä .0286234åå 
  Öput(   4.806637 , .29660335    )äÖcircle*ä .0286234åå 
  Öput(   4.838053 , .31008055    )äÖcircle*ä .0286234åå 
  Öput(   4.869469 , .32738557    )äÖcircle*ä .0286234åå 
  Öput(   4.900885 , .34850134    )äÖcircle*ä .0286234åå 
  Öput(     4.9323 ,   .373407    )äÖcircle*ä .0286234åå 
  Öput(   4.963716 , .40207799    )äÖcircle*ä .0286234åå 
  Öput(   4.995132 ,   .434486    )äÖcircle*ä .0286234åå 
  Öput(   5.026548 , .47059907    )äÖcircle*ä .0286234åå 
  Öput(   5.057964 ,   .510382    )äÖcircle*ä .0286234åå 
  Öput(    5.08938 ,   .553794    )äÖcircle*ä .0286234åå 
  Öput(   5.120796 ,   .600794    )äÖcircle*ä .0286234åå 
  Öput(   5.152212 ,   .651335    )äÖcircle*ä .0286234åå 
  Öput(   5.183628 ,   .705367    )äÖcircle*ä .0286234åå 
  Öput(   5.215044 ,   .762836    )äÖcircle*ä .0286234åå 
  Öput(   5.246460 ,   .823687    )äÖcircle*ä .0286234åå 
  Öput(   5.277876 ,   .887858    )äÖcircle*ä .0286234åå 
  Öput(   5.309292 ,   .955288    )äÖcircle*ä .0286234åå 
  Öput(   5.340708 ,   1.025908   )äÖcircle*ä .0286234åå 
  Öput(   5.372123 ,   1.099650   )äÖcircle*ä .0286234åå 
  Öput(   5.403539 ,   1.176440   )äÖcircle*ä .0286234åå 
  Öput(   5.434955 ,   1.256203   )äÖcircle*ä .0286234åå 
  Öput(   5.466371 ,    1.33886   )äÖcircle*ä .0286234åå 
  Öput(   5.497787 ,   1.424330   )äÖcircle*ä .0286234åå 
  Öput(   5.529203 ,   1.512528   )äÖcircle*ä .0286234åå 
  Öput(   5.560619 ,   1.603367   )äÖcircle*ä .0286234åå 
  Öput(   5.592035 ,   1.696757   )äÖcircle*ä .0286234åå 
  Öput(    5.62345 ,   1.792607   )äÖcircle*ä .0286234åå 
  Öput(   5.654867 ,   1.890822   )äÖcircle*ä .0286234åå 
  Öput(   5.686283 ,   1.991304   )äÖcircle*ä .0286234åå 
  Öput(   5.717699 ,   2.093955   )äÖcircle*ä .0286234åå 
  Öput(   5.749115 ,   2.198674   )äÖcircle*ä .0286234åå 
  Öput(    5.78053 ,   2.305356   )äÖcircle*ä .0286234åå 
  Öput(   5.811946 ,   2.413897   )äÖcircle*ä .0286234åå 
  Öput(   5.843362 ,    2.52419   )äÖcircle*ä .0286234åå 
  Öput(   5.874778 ,   2.636126   )äÖcircle*ä .0286234åå 
  Öput(   5.906194 ,   2.749593   )äÖcircle*ä .0286234åå 
  Öput(    5.93761 ,   2.864482   )äÖcircle*ä .0286234åå 
  Öput(   5.969026 ,   2.980677   )äÖcircle*ä .0286234åå 
  Öput(   6.000442 ,   3.098064   )äÖcircle*ä .0286234åå 
  Öput(   6.031858 ,   3.216528   )äÖcircle*ä .0286234åå 
  Öput(   6.063274 ,   3.335951   )äÖcircle*ä .0286234åå 
  Öput(   6.094690 ,   3.456216   )äÖcircle*ä .0286234åå 
  Öput(   6.126106 ,   3.577204   )äÖcircle*ä .0286234åå 
  Öput(   6.157522 ,   3.698795   )äÖcircle*ä .0286234åå 
  Öput(   6.188938 ,    3.82087   )äÖcircle*ä .0286234åå 
  Öput(   6.220353 ,   3.943308   )äÖcircle*ä .0286234åå 
  Öput(   6.251769 ,   4.065989   )äÖcircle*ä .0286234åå 
%Finis.

apl> '2Ox' graph 3,1,1,i,1e6,xpi     ,1   , 0  ,0 " cosdaty.tex

%Label the curve
  Öput( 1.570796 , 5.455586   )änÖ#1å 
%Draw the data points
  Öput(  .03141593 , 4.228581   )äÖcircle*ä .0286234åå 
  Öput(  .06283185 , 4.268333   )äÖcircle*ä .0286234åå 
  Öput(  .09424778 , 4.308006   )äÖcircle*ä .0286234åå 
  Öput(   .1256637 , 4.347562   )äÖcircle*ä .0286234åå 
  Öput(  .15707963 ,  4.38696   )äÖcircle*ä .0286234åå 
  Öput(  .18849556 , 4.426164   )äÖcircle*ä .0286234åå 
  Öput(  .21991149 , 4.465133   )äÖcircle*ä .0286234åå 
  Öput(  .25132741 , 4.503830   )äÖcircle*ä .0286234åå 
  Öput(  .28274334 , 4.542215   )äÖcircle*ä .0286234åå 
  Öput(  .31415927 , 4.580252   )äÖcircle*ä .0286234åå 
  Öput(  .34557519 , 4.617902   )äÖcircle*ä .0286234åå 
  Öput(  .37699112 , 4.655129   )äÖcircle*ä .0286234åå 
  Öput(  .40840704 , 4.691896   )äÖcircle*ä .0286234åå 
  Öput(  .43982297 , 4.728166   )äÖcircle*ä .0286234åå 
  Öput(  .47123890 , 4.763904   )äÖcircle*ä .0286234åå 
  Öput(    .502655 , 4.799074   )äÖcircle*ä .0286234åå 
  Öput(     .53407 , 4.833642   )äÖcircle*ä .0286234åå 
  Öput(    .565487 , 4.867574   )äÖcircle*ä .0286234åå 
  Öput(    .596903 , 4.900835   )äÖcircle*ä .0286234åå 
  Öput(    .628319 , 4.933394   )äÖcircle*ä .0286234åå 
  Öput(    .659734 , 4.965219   )äÖcircle*ä .0286234åå 
  Öput(     .69115 , 4.996277   )äÖcircle*ä .0286234åå 
  Öput(    .722566 , 5.026538   )äÖcircle*ä .0286234åå 
  Öput(    .753982 , 5.055972   )äÖcircle*ä .0286234åå 
  Öput(    .785398 ,  5.08455   )äÖcircle*ä .0286234åå 
  Öput(    .816814 , 5.112245   )äÖcircle*ä .0286234åå 
  Öput(     .84823 , 5.139028   )äÖcircle*ä .0286234åå 
  Öput(    .879646 , 5.164873   )äÖcircle*ä .0286234åå 
  Öput(    .911062 , 5.189756   )äÖcircle*ä .0286234åå 
  Öput(    .942478 , 5.213650   )äÖcircle*ä .0286234åå 
  Öput(    .973894 , 5.236533   )äÖcircle*ä .0286234åå 
  Öput(   1.005310 , 5.258382   )äÖcircle*ä .0286234åå 
  Öput(   1.036726 , 5.279175   )äÖcircle*ä .0286234åå 
  Öput(   1.068142 , 5.298892   )äÖcircle*ä .0286234åå 
  Öput(   1.099557 , 5.317514   )äÖcircle*ä .0286234åå 
  Öput(   1.130973 , 5.335022   )äÖcircle*ä .0286234åå 
  Öput(   1.162389 , 5.351398   )äÖcircle*ä .0286234åå 
  Öput(   1.193805 , 5.366628   )äÖcircle*ä .0286234åå 
  Öput(   1.225221 , 5.380694   )äÖcircle*ä .0286234åå 
  Öput(   1.256637 , 5.393585   )äÖcircle*ä .0286234åå 
  Öput(   1.288053 , 5.405287   )äÖcircle*ä .0286234åå 
  Öput(   1.319469 , 5.415788   )äÖcircle*ä .0286234åå 
  Öput(   1.350885 , 5.425078   )äÖcircle*ä .0286234åå 
  Öput(     1.3823 , 5.433148   )äÖcircle*ä .0286234åå 
  Öput(   1.413717 ,  5.43999   )äÖcircle*ä .0286234åå 
  Öput(   1.445133 , 5.445597   )äÖcircle*ä .0286234åå 
  Öput(   1.476549 , 5.449964   )äÖcircle*ä .0286234åå 
  Öput(   1.507964 , 5.453087   )äÖcircle*ä .0286234åå 
  Öput(    1.53938 , 5.454961   )äÖcircle*ä .0286234åå 
  Öput(   1.570796 , 5.455586   )äÖcircle*ä .0286234åå 
  Öput(   1.602212 , 5.454961   )äÖcircle*ä .0286234åå 
  Öput(   1.633628 , 5.453087   )äÖcircle*ä .0286234åå 
  Öput(   1.665044 , 5.449964   )äÖcircle*ä .0286234åå 
  Öput(    1.69646 , 5.445597   )äÖcircle*ä .0286234åå 
  Öput(   1.727876 ,  5.43999   )äÖcircle*ä .0286234åå 
  Öput(   1.759292 , 5.433148   )äÖcircle*ä .0286234åå 
  Öput(   1.790708 , 5.425078   )äÖcircle*ä .0286234åå 
  Öput(   1.822124 , 5.415788   )äÖcircle*ä .0286234åå 
  Öput(   1.853540 , 5.405287   )äÖcircle*ä .0286234åå 
  Öput(   1.884956 , 5.393585   )äÖcircle*ä .0286234åå 
  Öput(   1.916372 , 5.380694   )äÖcircle*ä .0286234åå 
  Öput(   1.947787 , 5.366628   )äÖcircle*ä .0286234åå 
  Öput(   1.979203 , 5.351398   )äÖcircle*ä .0286234åå 
  Öput(   2.010619 , 5.335022   )äÖcircle*ä .0286234åå 
  Öput(   2.042035 , 5.317514   )äÖcircle*ä .0286234åå 
  Öput(   2.073451 , 5.298892   )äÖcircle*ä .0286234åå 
  Öput(   2.104867 , 5.279175   )äÖcircle*ä .0286234åå 
  Öput(   2.136283 , 5.258382   )äÖcircle*ä .0286234åå 
  Öput(   2.167699 , 5.236533   )äÖcircle*ä .0286234åå 
  Öput(   2.199115 , 5.213650   )äÖcircle*ä .0286234åå 
  Öput(    2.23053 , 5.189756   )äÖcircle*ä .0286234åå 
  Öput(   2.261947 , 5.164873   )äÖcircle*ä .0286234åå 
  Öput(   2.293363 , 5.139028   )äÖcircle*ä .0286234åå 
  Öput(   2.324779 , 5.112245   )äÖcircle*ä .0286234åå 
  Öput(   2.356194 ,  5.08455   )äÖcircle*ä .0286234åå 
  Öput(    2.38761 , 5.055972   )äÖcircle*ä .0286234åå 
  Öput(   2.419026 , 5.026538   )äÖcircle*ä .0286234åå 
  Öput(   2.450442 , 4.996277   )äÖcircle*ä .0286234åå 
  Öput(   2.481858 , 4.965219   )äÖcircle*ä .0286234åå 
  Öput(   2.513274 , 4.933394   )äÖcircle*ä .0286234åå 
  Öput(    2.54469 , 4.900835   )äÖcircle*ä .0286234åå 
  Öput(   2.576106 , 4.867574   )äÖcircle*ä .0286234åå 
  Öput(   2.607522 , 4.833642   )äÖcircle*ä .0286234åå 
  Öput(   2.638938 , 4.799074   )äÖcircle*ä .0286234åå 
  Öput(   2.670354 , 4.763904   )äÖcircle*ä .0286234åå 
  Öput(   2.701770 , 4.728166   )äÖcircle*ä .0286234åå 
  Öput(   2.733186 , 4.691896   )äÖcircle*ä .0286234åå 
  Öput(   2.764602 , 4.655129   )äÖcircle*ä .0286234åå 
  Öput(   2.796017 , 4.617902   )äÖcircle*ä .0286234åå 
  Öput(   2.827433 , 4.580252   )äÖcircle*ä .0286234åå 
  Öput(   2.858849 , 4.542215   )äÖcircle*ä .0286234åå 
  Öput(   2.890265 , 4.503830   )äÖcircle*ä .0286234åå 
  Öput(   2.921681 , 4.465133   )äÖcircle*ä .0286234åå 
  Öput(   2.953097 , 4.426164   )äÖcircle*ä .0286234åå 
  Öput(   2.984513 ,  4.38696   )äÖcircle*ä .0286234åå 
  Öput(   3.015929 , 4.347562   )äÖcircle*ä .0286234åå 
  Öput(   3.047345 , 4.308006   )äÖcircle*ä .0286234åå 
  Öput(    3.07876 , 4.268333   )äÖcircle*ä .0286234åå 
  Öput(   3.110177 , 4.228581   )äÖcircle*ä .0286234åå 
  Öput(   3.141593 ,  4.18879   )äÖcircle*ä .0286234åå 
  Öput(   3.173009 , 4.148999   )äÖcircle*ä .0286234åå 
  Öput(   3.204425 , 4.109247   )äÖcircle*ä .0286234åå 
  Öput(    3.23584 , 4.069574   )äÖcircle*ä .0286234åå 
  Öput(   3.267256 , 4.030019   )äÖcircle*ä .0286234åå 
  Öput(   3.298672 , 3.990620   )äÖcircle*ä .0286234åå 
  Öput(   3.330088 , 3.951416   )äÖcircle*ä .0286234åå 
  Öput(   3.361504 , 3.912447   )äÖcircle*ä .0286234åå 
  Öput(    3.39292 ,  3.87375   )äÖcircle*ä .0286234åå 
  Öput(   3.424336 , 3.835365   )äÖcircle*ä .0286234åå 
  Öput(   3.455752 , 3.797329   )äÖcircle*ä .0286234åå 
  Öput(   3.487168 , 3.759678   )äÖcircle*ä .0286234åå 
  Öput(   3.518584 , 3.722451   )äÖcircle*ä .0286234åå 
  Öput(   3.550000 , 3.685685   )äÖcircle*ä .0286234åå 
  Öput(   3.581416 , 3.649415   )äÖcircle*ä .0286234åå 
  Öput(   3.612832 , 3.613677   )äÖcircle*ä .0286234åå 
  Öput(   3.644247 , 3.578506   )äÖcircle*ä .0286234åå 
  Öput(   3.675663 , 3.543938   )äÖcircle*ä .0286234åå 
  Öput(   3.707079 , 3.510007   )äÖcircle*ä .0286234åå 
  Öput(   3.738495 , 3.476745   )äÖcircle*ä .0286234åå 
  Öput(   3.769911 , 3.444186   )äÖcircle*ä .0286234åå 
  Öput(   3.801327 , 3.412362   )äÖcircle*ä .0286234åå 
  Öput(   3.832743 , 3.381304   )äÖcircle*ä .0286234åå 
  Öput(   3.864159 , 3.351043   )äÖcircle*ä .0286234åå 
  Öput(   3.895575 , 3.321608   )äÖcircle*ä .0286234åå 
  Öput(    3.92699 ,  3.29303   )äÖcircle*ä .0286234åå 
  Öput(   3.958407 , 3.265335   )äÖcircle*ä .0286234åå 
  Öput(   3.989823 , 3.238552   )äÖcircle*ä .0286234åå 
  Öput(   4.021239 , 3.212707   )äÖcircle*ä .0286234åå 
  Öput(   4.052655 , 3.187825   )äÖcircle*ä .0286234åå 
  Öput(    4.08407 ,  3.16393   )äÖcircle*ä .0286234åå 
  Öput(   4.115486 , 3.141048   )äÖcircle*ä .0286234åå 
  Öput(   4.146902 , 3.119199   )äÖcircle*ä .0286234åå 
  Öput(   4.178318 , 3.098405   )äÖcircle*ä .0286234åå 
  Öput(   4.209734 , 3.078688   )äÖcircle*ä .0286234åå 
  Öput(    4.24115 , 3.060066   )äÖcircle*ä .0286234åå 
  Öput(   4.272566 , 3.042559   )äÖcircle*ä .0286234åå 
  Öput(   4.303982 , 3.026182   )äÖcircle*ä .0286234åå 
  Öput(   4.335398 , 3.010953   )äÖcircle*ä .0286234åå 
  Öput(   4.366814 , 2.996886   )äÖcircle*ä .0286234åå 
  Öput(   4.398230 , 2.983995   )äÖcircle*ä .0286234åå 
  Öput(   4.429646 , 2.972294   )äÖcircle*ä .0286234åå 
  Öput(   4.461062 , 2.961793   )äÖcircle*ä .0286234åå 
  Öput(   4.492477 , 2.952503   )äÖcircle*ä .0286234åå 
  Öput(   4.523893 , 2.944432   )äÖcircle*ä .0286234åå 
  Öput(   4.555309 ,  2.93759   )äÖcircle*ä .0286234åå 
  Öput(   4.586725 , 2.931983   )äÖcircle*ä .0286234åå 
  Öput(   4.618141 , 2.927616   )äÖcircle*ä .0286234åå 
  Öput(   4.649557 , 2.924494   )äÖcircle*ä .0286234åå 
  Öput(   4.680973 , 2.922619   )äÖcircle*ä .0286234åå 
  Öput(   4.712389 , 2.921994   )äÖcircle*ä .0286234åå 
  Öput(   4.743805 , 2.922619   )äÖcircle*ä .0286234åå 
  Öput(    4.77522 , 2.924494   )äÖcircle*ä .0286234åå 
  Öput(   4.806637 , 2.927616   )äÖcircle*ä .0286234åå 
  Öput(   4.838053 , 2.931983   )äÖcircle*ä .0286234åå 
  Öput(   4.869469 ,  2.93759   )äÖcircle*ä .0286234åå 
  Öput(   4.900885 , 2.944432   )äÖcircle*ä .0286234åå 
  Öput(     4.9323 , 2.952503   )äÖcircle*ä .0286234åå 
  Öput(   4.963716 , 2.961793   )äÖcircle*ä .0286234åå 
  Öput(   4.995132 , 2.972294   )äÖcircle*ä .0286234åå 
  Öput(   5.026548 , 2.983995   )äÖcircle*ä .0286234åå 
  Öput(   5.057964 , 2.996886   )äÖcircle*ä .0286234åå 
  Öput(    5.08938 , 3.010953   )äÖcircle*ä .0286234åå 
  Öput(   5.120796 , 3.026182   )äÖcircle*ä .0286234åå 
  Öput(   5.152212 , 3.042559   )äÖcircle*ä .0286234åå 
  Öput(   5.183628 , 3.060066   )äÖcircle*ä .0286234åå 
  Öput(   5.215044 , 3.078688   )äÖcircle*ä .0286234åå 
  Öput(   5.246460 , 3.098405   )äÖcircle*ä .0286234åå 
  Öput(   5.277876 , 3.119199   )äÖcircle*ä .0286234åå 
  Öput(   5.309292 , 3.141048   )äÖcircle*ä .0286234åå 
  Öput(   5.340708 ,  3.16393   )äÖcircle*ä .0286234åå 
  Öput(   5.372123 , 3.187825   )äÖcircle*ä .0286234åå 
  Öput(   5.403539 , 3.212707   )äÖcircle*ä .0286234åå 
  Öput(   5.434955 , 3.238552   )äÖcircle*ä .0286234åå 
  Öput(   5.466371 , 3.265335   )äÖcircle*ä .0286234åå 
  Öput(   5.497787 ,  3.29303   )äÖcircle*ä .0286234åå 
  Öput(   5.529203 , 3.321608   )äÖcircle*ä .0286234åå 
  Öput(   5.560619 , 3.351043   )äÖcircle*ä .0286234åå 
  Öput(   5.592035 , 3.381304   )äÖcircle*ä .0286234åå 
  Öput(    5.62345 , 3.412362   )äÖcircle*ä .0286234åå 
  Öput(   5.654867 , 3.444186   )äÖcircle*ä .0286234åå 
  Öput(   5.686283 , 3.476745   )äÖcircle*ä .0286234åå 
  Öput(   5.717699 , 3.510007   )äÖcircle*ä .0286234åå 
  Öput(   5.749115 , 3.543938   )äÖcircle*ä .0286234åå 
  Öput(    5.78053 , 3.578506   )äÖcircle*ä .0286234åå 
  Öput(   5.811946 , 3.613677   )äÖcircle*ä .0286234åå 
  Öput(   5.843362 , 3.649415   )äÖcircle*ä .0286234åå 
  Öput(   5.874778 , 3.685685   )äÖcircle*ä .0286234åå 
  Öput(   5.906194 , 3.722451   )äÖcircle*ä .0286234åå 
  Öput(    5.93761 , 3.759678   )äÖcircle*ä .0286234åå 
  Öput(   5.969026 , 3.797329   )äÖcircle*ä .0286234åå 
  Öput(   6.000442 , 3.835365   )äÖcircle*ä .0286234åå 
  Öput(   6.031858 ,  3.87375   )äÖcircle*ä .0286234åå 
  Öput(   6.063274 , 3.912447   )äÖcircle*ä .0286234åå 
  Öput(   6.094690 , 3.951416   )äÖcircle*ä .0286234åå 
  Öput(   6.126106 , 3.990620   )äÖcircle*ä .0286234åå 
  Öput(   6.157522 , 4.030019   )äÖcircle*ä .0286234åå 
  Öput(   6.188938 , 4.069574   )äÖcircle*ä .0286234åå 
  Öput(   6.220353 , 4.109247   )äÖcircle*ä .0286234åå 
  Öput(   6.251769 , 4.148999   )äÖcircle*ä .0286234åå 
%Finis.

apl> '2Ox' graph 3,1,1,i,1e6,xpi     ,-1  , 0  ,0 " cosdaty.tex

%Label the curve
  Öput( 1.570796 , 2.726517   )änÖ#-1å 
%Draw the data points
  Öput(  .03141593 , 4.148999   )äÖcircle*ä .0286234åå 
  Öput(  .06283185 , 4.109247   )äÖcircle*ä .0286234åå 
  Öput(  .09424778 , 4.069574   )äÖcircle*ä .0286234åå 
  Öput(   .1256637 , 4.030019   )äÖcircle*ä .0286234åå 
  Öput(  .15707963 , 3.990620   )äÖcircle*ä .0286234åå 
  Öput(  .18849556 , 3.951416   )äÖcircle*ä .0286234åå 
  Öput(  .21991149 , 3.912447   )äÖcircle*ä .0286234åå 
  Öput(  .25132741 ,  3.87375   )äÖcircle*ä .0286234åå 
  Öput(  .28274334 , 3.835365   )äÖcircle*ä .0286234åå 
  Öput(  .31415927 , 3.797329   )äÖcircle*ä .0286234åå 
  Öput(  .34557519 , 3.759678   )äÖcircle*ä .0286234åå 
  Öput(  .37699112 , 3.722451   )äÖcircle*ä .0286234åå 
  Öput(  .40840704 , 3.685685   )äÖcircle*ä .0286234åå 
  Öput(  .43982297 , 3.649415   )äÖcircle*ä .0286234åå 
  Öput(  .47123890 , 3.613677   )äÖcircle*ä .0286234åå 
  Öput(    .502655 , 3.578506   )äÖcircle*ä .0286234åå 
  Öput(     .53407 , 3.543938   )äÖcircle*ä .0286234åå 
  Öput(    .565487 , 3.510007   )äÖcircle*ä .0286234åå 
  Öput(    .596903 , 3.476745   )äÖcircle*ä .0286234åå 
  Öput(    .628319 , 3.444186   )äÖcircle*ä .0286234åå 
  Öput(    .659734 , 3.412362   )äÖcircle*ä .0286234åå 
  Öput(     .69115 , 3.381304   )äÖcircle*ä .0286234åå 
  Öput(    .722566 , 3.351043   )äÖcircle*ä .0286234åå 
  Öput(    .753982 , 3.321608   )äÖcircle*ä .0286234åå 
  Öput(    .785398 ,  3.29303   )äÖcircle*ä .0286234åå 
  Öput(    .816814 , 3.265335   )äÖcircle*ä .0286234åå 
  Öput(     .84823 , 3.238552   )äÖcircle*ä .0286234åå 
  Öput(    .879646 , 3.212707   )äÖcircle*ä .0286234åå 
  Öput(    .911062 , 3.187825   )äÖcircle*ä .0286234åå 
  Öput(    .942478 ,  3.16393   )äÖcircle*ä .0286234åå 
  Öput(    .973894 , 3.141048   )äÖcircle*ä .0286234åå 
  Öput(   1.005310 , 3.119199   )äÖcircle*ä .0286234åå 
  Öput(   1.036726 , 3.098405   )äÖcircle*ä .0286234åå 
  Öput(   1.068142 , 3.078688   )äÖcircle*ä .0286234åå 
  Öput(   1.099557 , 3.060066   )äÖcircle*ä .0286234åå 
  Öput(   1.130973 , 3.042559   )äÖcircle*ä .0286234åå 
  Öput(   1.162389 , 3.026182   )äÖcircle*ä .0286234åå 
  Öput(   1.193805 , 3.010953   )äÖcircle*ä .0286234åå 
  Öput(   1.225221 , 2.996886   )äÖcircle*ä .0286234åå 
  Öput(   1.256637 , 2.983995   )äÖcircle*ä .0286234åå 
  Öput(   1.288053 , 2.972294   )äÖcircle*ä .0286234åå 
  Öput(   1.319469 , 2.961793   )äÖcircle*ä .0286234åå 
  Öput(   1.350885 , 2.952503   )äÖcircle*ä .0286234åå 
  Öput(     1.3823 , 2.944432   )äÖcircle*ä .0286234åå 
  Öput(   1.413717 ,  2.93759   )äÖcircle*ä .0286234åå 
  Öput(   1.445133 , 2.931983   )äÖcircle*ä .0286234åå 
  Öput(   1.476549 , 2.927616   )äÖcircle*ä .0286234åå 
  Öput(   1.507964 , 2.924494   )äÖcircle*ä .0286234åå 
  Öput(    1.53938 , 2.922619   )äÖcircle*ä .0286234åå 
  Öput(   1.570796 , 2.921994   )äÖcircle*ä .0286234åå 
  Öput(   1.602212 , 2.922619   )äÖcircle*ä .0286234åå 
  Öput(   1.633628 , 2.924494   )äÖcircle*ä .0286234åå 
  Öput(   1.665044 , 2.927616   )äÖcircle*ä .0286234åå 
  Öput(    1.69646 , 2.931983   )äÖcircle*ä .0286234åå 
  Öput(   1.727876 ,  2.93759   )äÖcircle*ä .0286234åå 
  Öput(   1.759292 , 2.944432   )äÖcircle*ä .0286234åå 
  Öput(   1.790708 , 2.952503   )äÖcircle*ä .0286234åå 
  Öput(   1.822124 , 2.961793   )äÖcircle*ä .0286234åå 
  Öput(   1.853540 , 2.972294   )äÖcircle*ä .0286234åå 
  Öput(   1.884956 , 2.983995   )äÖcircle*ä .0286234åå 
  Öput(   1.916372 , 2.996886   )äÖcircle*ä .0286234åå 
  Öput(   1.947787 , 3.010953   )äÖcircle*ä .0286234åå 
  Öput(   1.979203 , 3.026182   )äÖcircle*ä .0286234åå 
  Öput(   2.010619 , 3.042559   )äÖcircle*ä .0286234åå 
  Öput(   2.042035 , 3.060066   )äÖcircle*ä .0286234åå 
  Öput(   2.073451 , 3.078688   )äÖcircle*ä .0286234åå 
  Öput(   2.104867 , 3.098405   )äÖcircle*ä .0286234åå 
  Öput(   2.136283 , 3.119199   )äÖcircle*ä .0286234åå 
  Öput(   2.167699 , 3.141048   )äÖcircle*ä .0286234åå 
  Öput(   2.199115 ,  3.16393   )äÖcircle*ä .0286234åå 
  Öput(    2.23053 , 3.187825   )äÖcircle*ä .0286234åå 
  Öput(   2.261947 , 3.212707   )äÖcircle*ä .0286234åå 
  Öput(   2.293363 , 3.238552   )äÖcircle*ä .0286234åå 
  Öput(   2.324779 , 3.265335   )äÖcircle*ä .0286234åå 
  Öput(   2.356194 ,  3.29303   )äÖcircle*ä .0286234åå 
  Öput(    2.38761 , 3.321608   )äÖcircle*ä .0286234åå 
  Öput(   2.419026 , 3.351043   )äÖcircle*ä .0286234åå 
  Öput(   2.450442 , 3.381304   )äÖcircle*ä .0286234åå 
  Öput(   2.481858 , 3.412362   )äÖcircle*ä .0286234åå 
  Öput(   2.513274 , 3.444186   )äÖcircle*ä .0286234åå 
  Öput(    2.54469 , 3.476745   )äÖcircle*ä .0286234åå 
  Öput(   2.576106 , 3.510007   )äÖcircle*ä .0286234åå 
  Öput(   2.607522 , 3.543938   )äÖcircle*ä .0286234åå 
  Öput(   2.638938 , 3.578506   )äÖcircle*ä .0286234åå 
  Öput(   2.670354 , 3.613677   )äÖcircle*ä .0286234åå 
  Öput(   2.701770 , 3.649415   )äÖcircle*ä .0286234åå 
  Öput(   2.733186 , 3.685685   )äÖcircle*ä .0286234åå 
  Öput(   2.764602 , 3.722451   )äÖcircle*ä .0286234åå 
  Öput(   2.796017 , 3.759678   )äÖcircle*ä .0286234åå 
  Öput(   2.827433 , 3.797329   )äÖcircle*ä .0286234åå 
  Öput(   2.858849 , 3.835365   )äÖcircle*ä .0286234åå 
  Öput(   2.890265 ,  3.87375   )äÖcircle*ä .0286234åå 
  Öput(   2.921681 , 3.912447   )äÖcircle*ä .0286234åå 
  Öput(   2.953097 , 3.951416   )äÖcircle*ä .0286234åå 
  Öput(   2.984513 , 3.990620   )äÖcircle*ä .0286234åå 
  Öput(   3.015929 , 4.030019   )äÖcircle*ä .0286234åå 
  Öput(   3.047345 , 4.069574   )äÖcircle*ä .0286234åå 
  Öput(    3.07876 , 4.109247   )äÖcircle*ä .0286234åå 
  Öput(   3.110177 , 4.148999   )äÖcircle*ä .0286234åå 
  Öput(   3.141593 ,  4.18879   )äÖcircle*ä .0286234åå 
  Öput(   3.173009 , 4.228581   )äÖcircle*ä .0286234åå 
  Öput(   3.204425 , 4.268333   )äÖcircle*ä .0286234åå 
  Öput(    3.23584 , 4.308006   )äÖcircle*ä .0286234åå 
  Öput(   3.267256 , 4.347562   )äÖcircle*ä .0286234åå 
  Öput(   3.298672 ,  4.38696   )äÖcircle*ä .0286234åå 
  Öput(   3.330088 , 4.426164   )äÖcircle*ä .0286234åå 
  Öput(   3.361504 , 4.465133   )äÖcircle*ä .0286234åå 
  Öput(    3.39292 , 4.503830   )äÖcircle*ä .0286234åå 
  Öput(   3.424336 , 4.542215   )äÖcircle*ä .0286234åå 
  Öput(   3.455752 , 4.580252   )äÖcircle*ä .0286234åå 
  Öput(   3.487168 , 4.617902   )äÖcircle*ä .0286234åå 
  Öput(   3.518584 , 4.655129   )äÖcircle*ä .0286234åå 
  Öput(   3.550000 , 4.691896   )äÖcircle*ä .0286234åå 
  Öput(   3.581416 , 4.728166   )äÖcircle*ä .0286234åå 
  Öput(   3.612832 , 4.763904   )äÖcircle*ä .0286234åå 
  Öput(   3.644247 , 4.799074   )äÖcircle*ä .0286234åå 
  Öput(   3.675663 , 4.833642   )äÖcircle*ä .0286234åå 
  Öput(   3.707079 , 4.867574   )äÖcircle*ä .0286234åå 
  Öput(   3.738495 , 4.900835   )äÖcircle*ä .0286234åå 
  Öput(   3.769911 , 4.933394   )äÖcircle*ä .0286234åå 
  Öput(   3.801327 , 4.965219   )äÖcircle*ä .0286234åå 
  Öput(   3.832743 , 4.996277   )äÖcircle*ä .0286234åå 
  Öput(   3.864159 , 5.026538   )äÖcircle*ä .0286234åå 
  Öput(   3.895575 , 5.055972   )äÖcircle*ä .0286234åå 
  Öput(    3.92699 ,  5.08455   )äÖcircle*ä .0286234åå 
  Öput(   3.958407 , 5.112245   )äÖcircle*ä .0286234åå 
  Öput(   3.989823 , 5.139028   )äÖcircle*ä .0286234åå 
  Öput(   4.021239 , 5.164873   )äÖcircle*ä .0286234åå 
  Öput(   4.052655 , 5.189756   )äÖcircle*ä .0286234åå 
  Öput(    4.08407 , 5.213650   )äÖcircle*ä .0286234åå 
  Öput(   4.115486 , 5.236533   )äÖcircle*ä .0286234åå 
  Öput(   4.146902 , 5.258382   )äÖcircle*ä .0286234åå 
  Öput(   4.178318 , 5.279175   )äÖcircle*ä .0286234åå 
  Öput(   4.209734 , 5.298892   )äÖcircle*ä .0286234åå 
  Öput(    4.24115 , 5.317514   )äÖcircle*ä .0286234åå 
  Öput(   4.272566 , 5.335022   )äÖcircle*ä .0286234åå 
  Öput(   4.303982 , 5.351398   )äÖcircle*ä .0286234åå 
  Öput(   4.335398 , 5.366628   )äÖcircle*ä .0286234åå 
  Öput(   4.366814 , 5.380694   )äÖcircle*ä .0286234åå 
  Öput(   4.398230 , 5.393585   )äÖcircle*ä .0286234åå 
  Öput(   4.429646 , 5.405287   )äÖcircle*ä .0286234åå 
  Öput(   4.461062 , 5.415788   )äÖcircle*ä .0286234åå 
  Öput(   4.492477 , 5.425078   )äÖcircle*ä .0286234åå 
  Öput(   4.523893 , 5.433148   )äÖcircle*ä .0286234åå 
  Öput(   4.555309 ,  5.43999   )äÖcircle*ä .0286234åå 
  Öput(   4.586725 , 5.445597   )äÖcircle*ä .0286234åå 
  Öput(   4.618141 , 5.449964   )äÖcircle*ä .0286234åå 
  Öput(   4.649557 , 5.453087   )äÖcircle*ä .0286234åå 
  Öput(   4.680973 , 5.454961   )äÖcircle*ä .0286234åå 
  Öput(   4.712389 , 5.455586   )äÖcircle*ä .0286234åå 
  Öput(   4.743805 , 5.454961   )äÖcircle*ä .0286234åå 
  Öput(    4.77522 , 5.453087   )äÖcircle*ä .0286234åå 
  Öput(   4.806637 , 5.449964   )äÖcircle*ä .0286234åå 
  Öput(   4.838053 , 5.445597   )äÖcircle*ä .0286234åå 
  Öput(   4.869469 ,  5.43999   )äÖcircle*ä .0286234åå 
  Öput(   4.900885 , 5.433148   )äÖcircle*ä .0286234åå 
  Öput(     4.9323 , 5.425078   )äÖcircle*ä .0286234åå 
  Öput(   4.963716 , 5.415788   )äÖcircle*ä .0286234åå 
  Öput(   4.995132 , 5.405287   )äÖcircle*ä .0286234åå 
  Öput(   5.026548 , 5.393585   )äÖcircle*ä .0286234åå 
  Öput(   5.057964 , 5.380694   )äÖcircle*ä .0286234åå 
  Öput(    5.08938 , 5.366628   )äÖcircle*ä .0286234åå 
  Öput(   5.120796 , 5.351398   )äÖcircle*ä .0286234åå 
  Öput(   5.152212 , 5.335022   )äÖcircle*ä .0286234åå 
  Öput(   5.183628 , 5.317514   )äÖcircle*ä .0286234åå 
  Öput(   5.215044 , 5.298892   )äÖcircle*ä .0286234åå 
  Öput(   5.246460 , 5.279175   )äÖcircle*ä .0286234åå 
  Öput(   5.277876 , 5.258382   )äÖcircle*ä .0286234åå 
  Öput(   5.309292 , 5.236533   )äÖcircle*ä .0286234åå 
  Öput(   5.340708 , 5.213650   )äÖcircle*ä .0286234åå 
  Öput(   5.372123 , 5.189756   )äÖcircle*ä .0286234åå 
  Öput(   5.403539 , 5.164873   )äÖcircle*ä .0286234åå 
  Öput(   5.434955 , 5.139028   )äÖcircle*ä .0286234åå 
  Öput(   5.466371 , 5.112245   )äÖcircle*ä .0286234åå 
  Öput(   5.497787 ,  5.08455   )äÖcircle*ä .0286234åå 
  Öput(   5.529203 , 5.055972   )äÖcircle*ä .0286234åå 
  Öput(   5.560619 , 5.026538   )äÖcircle*ä .0286234åå 
  Öput(   5.592035 , 4.996277   )äÖcircle*ä .0286234åå 
  Öput(    5.62345 , 4.965219   )äÖcircle*ä .0286234åå 
  Öput(   5.654867 , 4.933394   )äÖcircle*ä .0286234åå 
  Öput(   5.686283 , 4.900835   )äÖcircle*ä .0286234åå 
  Öput(   5.717699 , 4.867574   )äÖcircle*ä .0286234åå 
  Öput(   5.749115 , 4.833642   )äÖcircle*ä .0286234åå 
  Öput(    5.78053 , 4.799074   )äÖcircle*ä .0286234åå 
  Öput(   5.811946 , 4.763904   )äÖcircle*ä .0286234åå 
  Öput(   5.843362 , 4.728166   )äÖcircle*ä .0286234åå 
  Öput(   5.874778 , 4.691896   )äÖcircle*ä .0286234åå 
  Öput(   5.906194 , 4.655129   )äÖcircle*ä .0286234åå 
  Öput(    5.93761 , 4.617902   )äÖcircle*ä .0286234åå 
  Öput(   5.969026 , 4.580252   )äÖcircle*ä .0286234åå 
  Öput(   6.000442 , 4.542215   )äÖcircle*ä .0286234åå 
  Öput(   6.031858 , 4.503830   )äÖcircle*ä .0286234åå 
  Öput(   6.063274 , 4.465133   )äÖcircle*ä .0286234åå 
  Öput(   6.094690 , 4.426164   )äÖcircle*ä .0286234åå 
  Öput(   6.126106 ,  4.38696   )äÖcircle*ä .0286234åå 
  Öput(   6.157522 , 4.347562   )äÖcircle*ä .0286234åå 
  Öput(   6.188938 , 4.308006   )äÖcircle*ä .0286234åå 
  Öput(   6.220353 , 4.268333   )äÖcircle*ä .0286234åå 
  Öput(   6.251769 , 4.228581   )äÖcircle*ä .0286234åå 
%Finis.

apl> '2Ox' graph 2,1,1,i,1e6,xpi     ,-2  , 0  ,0 " cosdaty.tex

%Label the curve
  Öput( 1.570796 , .0837758    )änÖ#-2å 
%Draw the data points
  Öput(  .03141593 ,   4.065989   )äÖcircle*ä .0286234åå 
  Öput(  .06283185 ,   3.943308   )äÖcircle*ä .0286234åå 
  Öput(  .09424778 ,    3.82087   )äÖcircle*ä .0286234åå 
  Öput(   .1256637 ,   3.698795   )äÖcircle*ä .0286234åå 
  Öput(  .15707963 ,   3.577204   )äÖcircle*ä .0286234åå 
  Öput(  .18849556 ,   3.456216   )äÖcircle*ä .0286234åå 
  Öput(  .21991149 ,   3.335951   )äÖcircle*ä .0286234åå 
  Öput(  .25132741 ,   3.216528   )äÖcircle*ä .0286234åå 
  Öput(  .28274334 ,   3.098064   )äÖcircle*ä .0286234åå 
  Öput(  .31415927 ,   2.980677   )äÖcircle*ä .0286234åå 
  Öput(  .34557519 ,   2.864482   )äÖcircle*ä .0286234åå 
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Öendäpictureå
Öendäcenterå
%Finis.

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