apl>" <-APL2-------------------- sam303.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 (|y) 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>" | maxx = 3.14159....
apl>" | | xiv
apl>" | | |
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 \put statements for the data points to appear
apl>" on the graph.
apl>"
apl>Lex 'dodata'
1
apl>Gdodata
[1] xgc#(xwc_minx)%xpg " xgc=x graphic coordinates for data points.
[2] ygc#mgc+(ywc_miny)%ypg " ygc=y graphic coordinates for data points.
[3] $bylabXI0=nlb " Branch if the curve is not to be labelled.
[4] '%Label the curve'
[5] xt#1Y(u=S/u#|ywc)/xgc " x coord where maximum/mininum occurs
[6] yt#(_yadjX0>vs/ywc)+(vs#xt=xgc)/ygc " y coord of maximum/minimum
[7] " Note: Calculation for yt works only if all minima occur below
[8] " y axis, and all maxima occur above.
[9] pcon,(xt,',',[1.5]yt),`Z'){n\#',(Fhk),'}'
[10] bylab:'%Draw the data points'
[11] pcon,((xgc#-1U1Uxgc),',',[1.5](ygc#-1U1Uygc)),circon
[12] 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
[1] xwc#minx+(xlwc#maxx_minx)X(-1+Ipoints+1)%points
[2] $varyrealXIxr
[3] x#hk+0j1Xxwc " real part is constant, imaginary varies.
[4] $calcy " Branch to compute values of y for data points.
[5] varyreal:x#(hkX0j1)+xwc " Imaginary is constant, real varies.
[6] calcy:ywc#eOCfun " Compute values of y for data points
[7] ywcm#yabm>|ywc " Mask of keepers, magnitudes of y < yabm.
[8] xwc#ywcm/xwc " Pick the keepers.
[9] ywc#ywcm/ywc " Pick the keepers.
[10] G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Main graph routine.
apl>"
apl>Lex 'graph'
1
apl>Gfun graph a
[1] "Graphs the imaginary or real coefficient of result of fun.
[2] " fun = expression to evaluate.
[3] (htl nlb xr e yabm minx maxx xiv hk yiv yca)#a
[4] genxy " Generate the data points.
[5] $dataXIhtl>1 " Branch if htl greater than 1.
[6] scale " Calculate global scaling values.
[7] headers " Generate LaTeX figure headers.
[8] data:dodata " Process and graph data points.
[9] trailers " Generate Latex figure trailers, maybe.
[10] G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Generates the LaTeX statements to begin the graph.
apl>"
apl>Lex 'headers'
1
apl>Gheaders
[1] '\begin{figure}[tbh]'
[2] $gencapXI0=Rcaption " Branch if no caption override.
[3] '\caption{',caption,'}'
[4] $begin
[5] gencap:$realcapXI(xr=1)&hk=0 " Branch if x data are not complex.
[6] $ncaptionXInlb=0 " Branch if curves are not labelled with n value.
[7] '\caption{Graph of y\#',(Fe),'O',fun,'+nX0j1}'
[8] $begin
[9] ncaption:$cplxcapXIxr " Branch if varying real coefficient.
[10] '\caption{Graph of y\#',(Fe),'O',(-1Ufun),(Fhk),'+xX0j1}'
[11] $begin
[12] cplxcap:'\caption{Graph of y\#',(Fe),'O',fun,'+(n\#',(Fhk),')X0j1}'
[13] $begin
[14] realcap:'\caption{Graph of y\#',fun,'}'
[15] begin:'\begin{center}'
[16] '\setlength{\unitlength}{',(Flin),'in}'
[17] '\begin{picture}(',(Fxlin%lin),',',(Fylin%lin),')'
[18] '%Draw a frame around the picture'
[19] ' \put(0,0){\line(1,0){',(Fxlgc),'}}% bottom'
[20] ' \put(0,0){\line(0,1){',(Fylgc),'}}% left'
[21] ' \put(0,',(Fylgc),'){\line(1,0){',(Fxlgc),'}}% top'
[22] ' \put(',(Fxlgc),',0){\line(0,1){',(Fylgc),'}}% right'
[23] '%Draw the x axis'
[24] ' \put(0,',(Fxax),'){\line(1,0){',(Fxlgc),'}}%x axis'
[25] xt#xoff%xpg
[26] pcon,((xt,[1.5]','),xax),circon " Draw the x axis markers.
[27] xt#xt_xpgX.1Xxmk<0
[28] yt#xax+((.05%lin)Xxax=mgc)_yadjXxax>mgc
[29] $dopaxXIpix
[30] '%Draw the x axis marker values'
[31] pcon,xt,',',yt,econ,xmk,[1.5]scon
[32] $doyax
[33] dopax:'%Draw the x axis marker values in pi'
[34] picon#(`Z'\frac{') ,`1 '\pi}{4}' '\pi}{2}' '3\pi}{4}'
[35] picon#('-',`1`Rpicon),'0',picon
[36] pcon,xt,',',yt,econ,picon,[1.5]scon
[37] doyax:'%Draw the y axis'
[38] $putymkXI(yax=0)
[39] ' \put(',(Fyax),',0){\line(0,1){',(Fylgc),'}}%y axis'
[40] putymk:'%Draw the y axis markers'
[41] ymask#ymk^=0
[42] yt#ymask/mgc+(ymk_miny)%ypg
[43] pcon,yax,',',yt,[1.5]circon
[44] '%Draw the y axis marker values'
[45] xt#yax+.05%lin
[46] yt#yt_ypgX.1X(ymask/ymk)<0
[47] pcon,xt,',',yt,econ,(ymask/ymk),[1.5]scon
[48] G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Calculates a variety of values needed to produce the graph.
apl>"
apl>Lex 'scale'
1
apl>Gscale
[1] $byyXIyca " Branch if ylwc, maxy, miny are precalculated.
[2] ylwc#(maxy#S/ywc)_miny#D/ywc
[3] byy:ylap#ylin_2Xymgn " ylap=height allowed for data points.
[4] lin#(xlin%xlwc)Dylap%ylwc " unitlength in inches.
[5] yadj#.14%lin " y graphic coordinate adjustment to print text below line.
[6] mgc#ymgn%lin " Margin in graph coordinates.
[7] xpg#xlwc%xlgc#xlin%lin " Divide xwc by xpg to get gc.
[8] ypg#ylwc%(_2Xymgn%lin)+ylgc#ylin%lin " Divide ywc by ypg to get gc.
[9] xax#(yz#(minyK0)&maxyZ0)Xmgc+(|miny)%ypg " xaxis in graph coordinates.
[10] yax#(xz#(minx<0)&maxx>0)X(|minx)%xpg " yaxis in graph coordinates.
[11] $piaxisXIpix#(minx=O-1)&maxx=O1 " branch if pi units on x axis.
[12] xic#(yax=0)+Dxlwc%xiv
[13] $doyiv
[14] piaxis:xic#Dxlwc%xiv#O.25
[15] doyiv:$doyicXIyiv^=0
[16] yiv#10*D10@ylwc
[17] doyic:yic#yic+0=2|yic#Dylwc%yiv
[18] xoff#(I-1+xic)Xxiv " Offset from minx in world coord. of x markers.
[19] yoff#(_yiv)+(Iyic)Xyiv " Offset from miny in world coord. of y markers.
[20] $yoffplusXIminy>0
[21] ymk#yoff+miny+yiv||miny
[22] $yoffdone
[23] yoffplus:ymk#yoff+miny_yiv|miny " y for y axis markers in world coord.
[24] yoffdone:xmk#minx+xoff " x for x axis markers in world coord.
[25] circon#`Z'){\circle*{',(F.0205%lin),'}}'
[26] scon#`Z'$}'
[27] econ#`Z'){$'
[28] pcon#`Z' \put('
[29] G
apl>"
apl>" <----------------------------------------------------------------->
apl>" Generates the LaTeX statements to finish the graph.
apl>"
apl>Lex 'trailers'
1
apl>Gtrailers
[1] $epicXIhtl=0 " Branch if both headers and trailers.
[2] $eojckXInlb " Branch if graph already labelled.
[3] pcon,(1Yxgc+xpgX.1),',',(1Yygc),'){',fun,'}' " Label the graph.
[4] eojck:$eojXI(htl=1)+htl=3 " br if headers only, or neither.
[5] epic:'\end{picture}'
[6] '\end{center}'
[7] eoj:'%Finis.'
[8] caption#'' " Reset global caption
[9] G
apl>" htl: 0=both, 1=headers, 2=trailers, 3=neither.
apl>" | nlb 1 = Label the curve.
apl>" | | xr = 1=vary real x coeff, 0=vary imaginary coeff.
apl>" | | | e = i(11) or r(9) to select coefficient to graph.
apl>" | | | | yabm = maximum |y printed on graph.
apl>" | | | | | minx = minimum value of x.
apl>" | | | | | | maxx = maximum value of x.
apl>" | | | | | | | xiv = x axis marker interval.
apl>" | | | | | | | | hk = Constant coefficient of input.
apl>" | | | | | | | | | yiv = y axis marker interval, or 0.
apl>" | | | | | | | | | | yca = ylwc, maxy, miny are precalculated.
apl>" | | | | | | | | | | |
apl>" V V V V V V V V V V V
apl> points#300
apl> ylwc#(maxy#2.16)_miny#-2.16
apl> '3Ox' graph 1,1,1,i,1e6,-10,10,1,.5 , 0 ,1 " tandaty.tex
\begin{figure}[tbh]
\caption{Graph of y\#11O3Ox+nX0j1}
\begin{center}
\setlength{\unitlength}{ .225in}
\begin{picture}(20,26.66667)
%Draw a frame around the picture
\put(0,0){\line(1,0){20}}% bottom
\put(0,0){\line(0,1){26.66667}}% left
\put(0,26.66667){\line(1,0){20}}% top
\put(20,0){\line(0,1){26.66667}}% right
%Draw the x axis
\put(0,13.33333){\line(1,0){20}}%x axis
\put( 1 , 13.33333 ){\circle*{ .09111111}}
\put( 2 , 13.33333 ){\circle*{ .09111111}}
\put( 3 , 13.33333 ){\circle*{ .09111111}}
\put( 4 , 13.33333 ){\circle*{ .09111111}}
\put( 5 , 13.33333 ){\circle*{ .09111111}}
\put( 6 , 13.33333 ){\circle*{ .09111111}}
\put( 7 , 13.33333 ){\circle*{ .09111111}}
\put( 8 , 13.33333 ){\circle*{ .09111111}}
\put( 9 , 13.33333 ){\circle*{ .09111111}}
\put( 10 , 13.33333 ){\circle*{ .09111111}}
\put( 11 , 13.33333 ){\circle*{ .09111111}}
\put( 12 , 13.33333 ){\circle*{ .09111111}}
\put( 13 , 13.33333 ){\circle*{ .09111111}}
\put( 14 , 13.33333 ){\circle*{ .09111111}}
\put( 15 , 13.33333 ){\circle*{ .09111111}}
\put( 16 , 13.33333 ){\circle*{ .09111111}}
\put( 17 , 13.33333 ){\circle*{ .09111111}}
\put( 18 , 13.33333 ){\circle*{ .09111111}}
\put( 19 , 13.33333 ){\circle*{ .09111111}}
%Draw the x axis marker values
\put( .9 , 12.71111 ){$ -9 $}
\put( 1.9 , 12.71111 ){$ -8 $}
\put( 2.9 , 12.71111 ){$ -7 $}
\put( 3.9 , 12.71111 ){$ -6 $}
\put( 4.9 , 12.71111 ){$ -5 $}
\put( 5.9 , 12.71111 ){$ -4 $}
\put( 6.9 , 12.71111 ){$ -3 $}
\put( 7.9 , 12.71111 ){$ -2 $}
\put( 8.9 , 12.71111 ){$ -1 $}
\put( 10 , 12.71111 ){$ 0 $}
\put( 11 , 12.71111 ){$ 1 $}
\put( 12 , 12.71111 ){$ 2 $}
\put( 13 , 12.71111 ){$ 3 $}
\put( 14 , 12.71111 ){$ 4 $}
\put( 15 , 12.71111 ){$ 5 $}
\put( 16 , 12.71111 ){$ 6 $}
\put( 17 , 12.71111 ){$ 7 $}
\put( 18 , 12.71111 ){$ 8 $}
\put( 19 , 12.71111 ){$ 9 $}
%Draw the y axis
\put(10,0){\line(0,1){26.66667}}%y axis
%Draw the y axis markers
\put( 10 , 1.810700 ){\circle*{ .09111111}}
\put( 10 , 7.572016 ){\circle*{ .09111111}}
\put( 10 , 19.09465 ){\circle*{ .09111111}}
\put( 10 , 24.85597 ){\circle*{ .09111111}}
%Draw the y axis marker values
\put( 10.22222 , 1.793342 ){$ -2 $}
\put( 10.22222 , 7.554659 ){$ -1 $}
\put( 10.22222 , 19.09465 ){$ 1 $}
\put( 10.22222 , 24.85597 ){$ 2 $}
%Label the curve
\put( 2.133333 , 25.79317 ){n\# .5}
%Draw the data points
\put( .06666667 , 16.60594 ){\circle*{ .09111111}}
\put( .13333333 , 16.44299 ){\circle*{ .09111111}}
\put( .2 , 16.31017 ){\circle*{ .09111111}}
\put( .26666667 , 16.20394 ){\circle*{ .09111111}}
\put( .33333333 , 16.12155 ){\circle*{ .09111111}}
\put( .4 , 16.06093 ){\circle*{ .09111111}}
\put( .46666667 , 16.02054 ){\circle*{ .09111111}}
\put( .533333 , 15.99941 ){\circle*{ .09111111}}
\put( .6 , 15.99702 ){\circle*{ .09111111}}
\put( .666667 , 16.01331 ){\circle*{ .09111111}}
\put( .733333 , 16.04868 ){\circle*{ .09111111}}
\put( .8 , 16.10399 ){\circle*{ .09111111}}
\put( .866667 , 16.18061 ){\circle*{ .09111111}}
\put( .933333 , 16.28049 ){\circle*{ .09111111}}
\put( 1 , 16.40618 ){\circle*{ .09111111}}
\put( 1.066667 , 16.56101 ){\circle*{ .09111111}}
\put( 1.133333 , 16.74916 ){\circle*{ .09111111}}
\put( 1.2 , 16.9758 ){\circle*{ .09111111}}
\put( 1.266667 , 17.2473 ){\circle*{ .09111111}}
\put( 1.333333 , 17.57131 ){\circle*{ .09111111}}
\put( 1.4 , 17.95686 ){\circle*{ .09111111}}
\put( 1.466667 , 18.41426 ){\circle*{ .09111111}}
\put( 1.533333 , 18.95459 ){\circle*{ .09111111}}
\put( 1.6 , 19.58859 ){\circle*{ .09111111}}
\put( 1.666667 , 20.32426 ){\circle*{ .09111111}}
\put( 1.733333 , 21.16259 ){\circle*{ .09111111}}
\put( 1.8 , 22.09083 ){\circle*{ .09111111}}
\put( 1.866667 , 23.07343 ){\circle*{ .09111111}}
\put( 1.933333 , 24.04318 ){\circle*{ .09111111}}
\put( 2 , 24.89886 ){\circle*{ .09111111}}
\put( 2.066667 , 25.51859 ){\circle*{ .09111111}}
\put( 2.133333 , 25.79317 ){\circle*{ .09111111}}
\put( 2.2 , 25.66831 ){\circle*{ .09111111}}
\put( 2.266667 , 25.16916 ){\circle*{ .09111111}}
\put( 2.333333 , 24.38868 ){\circle*{ .09111111}}
\put( 2.4 , 23.44877 ){\circle*{ .09111111}}
\put( 2.466667 , 22.46123 ){\circle*{ .09111111}}
\put( 2.533333 , 21.50656 ){\circle*{ .09111111}}
\put( 2.6 , 20.63149 ){\circle*{ .09111111}}
\put( 2.666667 , 19.8563 ){\circle*{ .09111111}}
\put( 2.733333 , 19.18429 ){\circle*{ .09111111}}
\put( 2.8 , 18.60950 ){\circle*{ .09111111}}
\put( 2.866667 , 18.12186 ){\circle*{ .09111111}}
\put( 2.933333 , 17.71024 ){\circle*{ .09111111}}
\put( 3 , 17.36395 ){\circle*{ .09111111}}
\put( 3.066667 , 17.07345 ){\circle*{ .09111111}}
\put( 3.133333 , 16.83055 ){\circle*{ .09111111}}
\put( 3.2 , 16.62843 ){\circle*{ .09111111}}
\put( 3.266667 , 16.46146 ){\circle*{ .09111111}}
\put( 3.333333 , 16.32511 ){\circle*{ .09111111}}
\put( 3.4 , 16.21576 ){\circle*{ .09111111}}
\put( 3.466667 , 16.13054 ){\circle*{ .09111111}}
\put( 3.533333 , 16.06731 ){\circle*{ .09111111}}
\put( 3.6 , 16.02449 ){\circle*{ .09111111}}
\put( 3.666667 , 16.001 ){\circle*{ .09111111}}
\put( 3.733333 , 15.9963 ){\circle*{ .09111111}}
\put( 3.8 , 16.01027 ){\circle*{ .09111111}}
\put( 3.866667 , 16.04324 ){\circle*{ .09111111}}
\put( 3.933333 , 16.09601 ){\circle*{ .09111111}}
\put( 4 , 16.1699 ){\circle*{ .09111111}}
\put( 4.066667 , 16.26677 ){\circle*{ .09111111}}
\put( 4.133333 , 16.3891 ){\circle*{ .09111111}}
\put( 4.2 , 16.54012 ){\circle*{ .09111111}}
\put( 4.266667 , 16.72387 ){\circle*{ .09111111}}
\put( 4.333333 , 16.94543 ){\circle*{ .09111111}}
\put( 4.4 , 17.21098 ){\circle*{ .09111111}}
\put( 4.466667 , 17.52802 ){\circle*{ .09111111}}
\put( 4.533333 , 17.90542 ){\circle*{ .09111111}}
\put( 4.6 , 18.35332 ){\circle*{ .09111111}}
\put( 4.666667 , 18.88277 ){\circle*{ .09111111}}
\put( 4.733333 , 19.50465 ){\circle*{ .09111111}}
\put( 4.8 , 20.22747 ){\circle*{ .09111111}}
\put( 4.866667 , 21.05341 ){\circle*{ .09111111}}
\put( 4.933333 , 21.97189 ){\circle*{ .09111111}}
\put( 5 , 22.95069 ){\circle*{ .09111111}}
\put( 5.066667 , 23.92688 ){\circle*{ .09111111}}
\put( 5.133333 , 24.80313 ){\circle*{ .09111111}}
\put( 5.2 , 25.45868 ){\circle*{ .09111111}}
\put( 5.266667 , 25.78045 ){\circle*{ .09111111}}
\put( 5.333333 , 25.70537 ){\circle*{ .09111111}}
\put( 5.4 , 25.24862 ){\circle*{ .09111111}}
\put( 5.466667 , 24.49653 ){\circle*{ .09111111}}
\put( 5.533333 , 23.56982 ){\circle*{ .09111111}}
\put( 5.6 , 22.58309 ){\circle*{ .09111111}}
\put( 5.666667 , 21.62117 ){\circle*{ .09111111}}
\put( 5.733333 , 20.73470 ){\circle*{ .09111111}}
\put( 5.8 , 19.94669 ){\circle*{ .09111111}}
\put( 5.866667 , 19.26209 ){\circle*{ .09111111}}
\put( 5.933333 , 18.67575 ){\circle*{ .09111111}}
\put( 6 , 18.17792 ){\circle*{ .09111111}}
\put( 6.066667 , 17.75749 ){\circle*{ .09111111}}
\put( 6.133333 , 17.40365 ){\circle*{ .09111111}}
\put( 6.2 , 17.1067 ){\circle*{ .09111111}}
\put( 6.266667 , 16.8583 ){\circle*{ .09111111}}
\put( 6.333333 , 16.65146 ){\circle*{ .09111111}}
\put( 6.4 , 16.4804 ){\circle*{ .09111111}}
\put( 6.466667 , 16.34048 ){\circle*{ .09111111}}
\put( 6.533333 , 16.22794 ){\circle*{ .09111111}}
\put( 6.6 , 16.13987 ){\circle*{ .09111111}}
\put( 6.666667 , 16.07401 ){\circle*{ .09111111}}
\put( 6.733333 , 16.02873 ){\circle*{ .09111111}}
\put( 6.8 , 16.00289 ){\circle*{ .09111111}}
\put( 6.866667 , 15.99588 ){\circle*{ .09111111}}
\put( 6.933333 , 16.00752 ){\circle*{ .09111111}}
\put( 7 , 16.03810 ){\circle*{ .09111111}}
\put( 7.066667 , 16.08836 ){\circle*{ .09111111}}
\put( 7.133333 , 16.15955 ){\circle*{ .09111111}}
\put( 7.2 , 16.25344 ){\circle*{ .09111111}}
\put( 7.266667 , 16.37246 ){\circle*{ .09111111}}
\put( 7.333333 , 16.51972 ){\circle*{ .09111111}}
\put( 7.4 , 16.69917 ){\circle*{ .09111111}}
\put( 7.466667 , 16.91573 ){\circle*{ .09111111}}
\put( 7.533333 , 17.17545 ){\circle*{ .09111111}}
\put( 7.6 , 17.48566 ){\circle*{ .09111111}}
\put( 7.666667 , 17.85505 ){\circle*{ .09111111}}
\put( 7.733333 , 18.29363 ){\circle*{ .09111111}}
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%Finis.
apl> '3Ox' graph 3,1,1,i,1e6,-10,10,1,1 , 0 ,1 " tandaty.tex
%Label the curve
\put( 2.133333 , 20.89726 ){n\#1}
%Draw the data points
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%Finis.
apl> '3Ox' graph 3,1,1,i,1e6,-10,10,1,2 , 0 ,1 " tandaty.tex
%Label the curve
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%Draw the data points
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%Finis.
apl> '3Ox' graph 3,1,1,i,1e6,-10,10,1,-.5 , 0 ,1 " tandaty.tex
%Label the curve
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%Draw the data points
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\put( 18.6 , 8.709805 ){\circle*{ .09111111}}
\put( 18.66667 , 9.095357 ){\circle*{ .09111111}}
\put( 18.73333 , 9.419367 ){\circle*{ .09111111}}
\put( 18.8 , 9.69087 ){\circle*{ .09111111}}
\put( 18.86667 , 9.91751 ){\circle*{ .09111111}}
\put( 18.93333 , 10.10565 ){\circle*{ .09111111}}
\put( 19 , 10.26048 ){\circle*{ .09111111}}
\put( 19.06667 , 10.38618 ){\circle*{ .09111111}}
\put( 19.13333 , 10.48605 ){\circle*{ .09111111}}
\put( 19.2 , 10.56268 ){\circle*{ .09111111}}
\put( 19.26667 , 10.61799 ){\circle*{ .09111111}}
\put( 19.33333 , 10.65335 ){\circle*{ .09111111}}
\put( 19.4 , 10.66964 ){\circle*{ .09111111}}
\put( 19.46667 , 10.66725 ){\circle*{ .09111111}}
\put( 19.53333 , 10.64612 ){\circle*{ .09111111}}
\put( 19.6 , 10.60574 ){\circle*{ .09111111}}
\put( 19.66667 , 10.54511 ){\circle*{ .09111111}}
\put( 19.73333 , 10.46273 ){\circle*{ .09111111}}
\put( 19.8 , 10.3565 ){\circle*{ .09111111}}
\put( 19.86667 , 10.22368 ){\circle*{ .09111111}}
\put( 19.93333 , 10.06073 ){\circle*{ .09111111}}
%Finis.
apl> '3Ox' graph 3,1,1,i,1e6,-10,10,1,-1 , 0 ,1 " tandaty.tex
%Label the curve
\put( 2.133333 , 5.14718 ){n\#-1}
%Draw the data points
\put( .06666667 , 8.460342 ){\circle*{ .09111111}}
\put( .13333333 , 8.580503 ){\circle*{ .09111111}}
\put( .2 , 8.683258 ){\circle*{ .09111111}}
\put( .26666667 , 8.768756 ){\circle*{ .09111111}}
\put( .33333333 , 8.837204 ){\circle*{ .09111111}}
\put( .4 , 8.888823 ){\circle*{ .09111111}}
\put( .46666667 , 8.92381 ){\circle*{ .09111111}}
\put( .533333 , 8.942314 ){\circle*{ .09111111}}
\put( .6 , 8.944417 ){\circle*{ .09111111}}
\put( .666667 , 8.930128 ){\circle*{ .09111111}}
\put( .733333 , 8.899383 ){\circle*{ .09111111}}
\put( .8 , 8.852049 ){\circle*{ .09111111}}
\put( .866667 , 8.787941 ){\circle*{ .09111111}}
\put( .933333 , 8.706841 ){\circle*{ .09111111}}
\put( 1 , 8.608532 ){\circle*{ .09111111}}
\put( 1.066667 , 8.492847 ){\circle*{ .09111111}}
\put( 1.133333 , 8.359726 ){\circle*{ .09111111}}
\put( 1.2 , 8.209301 ){\circle*{ .09111111}}
\put( 1.266667 , 8.041994 ){\circle*{ .09111111}}
\put( 1.333333 , 7.85864 ){\circle*{ .09111111}}
\put( 1.4 , 7.660633 ){\circle*{ .09111111}}
\put( 1.466667 , 7.450079 ){\circle*{ .09111111}}
\put( 1.533333 , 7.229961 ){\circle*{ .09111111}}
\put( 1.6 , 7.004276 ){\circle*{ .09111111}}
\put( 1.666667 , 6.778119 ){\circle*{ .09111111}}
\put( 1.733333 , 6.557686 ){\circle*{ .09111111}}
\put( 1.8 , 6.350124 ){\circle*{ .09111111}}
\put( 1.866667 , 6.16323 ){\circle*{ .09111111}}
\put( 1.933333 , 6.004949 ){\circle*{ .09111111}}
\put( 2 , 5.882728 ){\circle*{ .09111111}}
\put( 2.066667 , 5.802782 ){\circle*{ .09111111}}
\put( 2.133333 , 5.769402 ){\circle*{ .09111111}}
\put( 2.2 , 5.784433 ){\circle*{ .09111111}}
\put( 2.266667 , 5.84704 ){\circle*{ .09111111}}
\put( 2.333333 , 5.953816 ){\circle*{ .09111111}}
\put( 2.4 , 6.099201 ){\circle*{ .09111111}}
\put( 2.466667 , 6.276131 ){\circle*{ .09111111}}
\put( 2.533333 , 6.476768 ){\circle*{ .09111111}}
\put( 2.6 , 6.693189 ){\circle*{ .09111111}}
\put( 2.666667 , 6.917955 ){\circle*{ .09111111}}
\put( 2.733333 , 7.14448 ){\circle*{ .09111111}}
\put( 2.8 , 7.367247 ){\circle*{ .09111111}}
\put( 2.866667 , 7.581844 ){\circle*{ .09111111}}
\put( 2.933333 , 7.784919 ){\circle*{ .09111111}}
\put( 3 , 7.974048 ){\circle*{ .09111111}}
\put( 3.066667 , 8.147588 ){\circle*{ .09111111}}
\put( 3.133333 , 8.304506 ){\circle*{ .09111111}}
\put( 3.2 , 8.44424 ){\circle*{ .09111111}}
\put( 3.266667 , 8.566562 ){\circle*{ .09111111}}
\put( 3.333333 , 8.671468 ){\circle*{ .09111111}}
\put( 3.4 , 8.759093 ){\circle*{ .09111111}}
\put( 3.466667 , 8.829641 ){\circle*{ .09111111}}
\put( 3.533333 , 8.883334 ){\circle*{ .09111111}}
\put( 3.6 , 8.920373 ){\circle*{ .09111111}}
\put( 3.666667 , 8.940913 ){\circle*{ .09111111}}
\put( 3.733333 , 8.945045 ){\circle*{ .09111111}}
\put( 3.8 , 8.932789 ){\circle*{ .09111111}}
\put( 3.866667 , 8.904089 ){\circle*{ .09111111}}
\put( 3.933333 , 8.858820 ){\circle*{ .09111111}}
\put( 4 , 8.796801 ){\circle*{ .09111111}}
\put( 4.066667 , 8.717818 ){\circle*{ .09111111}}
\put( 4.133333 , 8.621652 ){\circle*{ .09111111}}
\put( 4.2 , 8.508125 ){\circle*{ .09111111}}
\put( 4.266667 , 8.377162 ){\circle*{ .09111111}}
\put( 4.333333 , 8.228866 ){\circle*{ .09111111}}
\put( 4.4 , 8.063614 ){\circle*{ .09111111}}
\put( 4.466667 , 7.882186 ){\circle*{ .09111111}}
\put( 4.533333 , 7.685895 ){\circle*{ .09111111}}
\put( 4.6 , 7.476753 ){\circle*{ .09111111}}
\put( 4.666667 , 7.257625 ){\circle*{ .09111111}}
\put( 4.733333 , 7.032376 ){\circle*{ .09111111}}
\put( 4.8 , 6.805963 ){\circle*{ .09111111}}
\put( 4.866667 , 6.584450 ){\circle*{ .09111111}}
\put( 4.933333 , 6.374879 ){\circle*{ .09111111}}
\put( 5 , 6.184991 ){\circle*{ .09111111}}
\put( 5.066667 , 6.022744 ){\circle*{ .09111111}}
\put( 5.133333 , 5.895686 ){\circle*{ .09111111}}
\put( 5.2 , 5.810225 ){\circle*{ .09111111}}
\put( 5.266667 , 5.770923 ){\circle*{ .09111111}}
\put( 5.333333 , 5.779946 ){\circle*{ .09111111}}
\put( 5.4 , 5.836795 ){\circle*{ .09111111}}
\put( 5.466667 , 5.938362 ){\circle*{ .09111111}}
\put( 5.533333 , 6.079323 ){\circle*{ .09111111}}
\put( 5.6 , 6.252762 ){\circle*{ .09111111}}
\put( 5.666667 , 6.450896 ){\circle*{ .09111111}}
\put( 5.733333 , 6.665780 ){\circle*{ .09111111}}
\put( 5.8 , 6.889889 ){\circle*{ .09111111}}
\put( 5.866667 , 7.116519 ){\circle*{ .09111111}}
\put( 5.933333 , 7.340013 ){\circle*{ .09111111}}
\put( 6 , 7.555824 ){\circle*{ .09111111}}
\put( 6.066667 , 7.760475 ){\circle*{ .09111111}}
\put( 6.133333 , 7.951436 ){\circle*{ .09111111}}
\put( 6.2 , 8.126974 ){\circle*{ .09111111}}
\put( 6.266667 , 8.28599 ){\circle*{ .09111111}}
\put( 6.333333 , 8.427872 ){\circle*{ .09111111}}
\put( 6.4 , 8.552355 ){\circle*{ .09111111}}
\put( 6.466667 , 8.659413 ){\circle*{ .09111111}}
\put( 6.533333 , 8.749169 ){\circle*{ .09111111}}
\put( 6.6 , 8.82182 ){\circle*{ .09111111}}
\put( 6.666667 , 8.877590 ){\circle*{ .09111111}}
\put( 6.733333 , 8.916682 ){\circle*{ .09111111}}
\put( 6.8 , 8.939260 ){\circle*{ .09111111}}
\put( 6.866667 , 8.945422 ){\circle*{ .09111111}}
\put( 6.933333 , 8.935198 ){\circle*{ .09111111}}
\put( 7 , 8.90854 ){\circle*{ .09111111}}
\put( 7.066667 , 8.865333 ){\circle*{ .09111111}}
\put( 7.133333 , 8.8054 ){\circle*{ .09111111}}
\put( 7.2 , 8.728532 ){\circle*{ .09111111}}
\put( 7.266667 , 8.634505 ){\circle*{ .09111111}}
\put( 7.333333 , 8.523136 ){\circle*{ .09111111}}
\put( 7.4 , 8.394332 ){\circle*{ .09111111}}
\put( 7.466667 , 8.248169 ){\circle*{ .09111111}}
\put( 7.533333 , 8.084986 ){\circle*{ .09111111}}
\put( 7.6 , 7.905502 ){\circle*{ .09111111}}
\put( 7.666667 , 7.710960 ){\circle*{ .09111111}}
\put( 7.733333 , 7.503273 ){\circle*{ .09111111}}
\put( 7.8 , 7.285194 ){\circle*{ .09111111}}
\put( 7.866667 , 7.060456 ){\circle*{ .09111111}}
\put( 7.933333 , 6.83388 ){\circle*{ .09111111}}
\put( 8 , 6.611396 ){\circle*{ .09111111}}
\put( 8.066667 , 6.399937 ){\circle*{ .09111111}}
\put( 8.133333 , 6.207177 ){\circle*{ .09111111}}
\put( 8.2 , 6.04108 ){\circle*{ .09111111}}
\put( 8.266667 , 5.909285 ){\circle*{ .09111111}}
\put( 8.333333 , 5.818380 ){\circle*{ .09111111}}
\put( 8.4 , 5.773188 ){\circle*{ .09111111}}
\put( 8.466667 , 5.776197 ){\circle*{ .09111111}}
\put( 8.533333 , 5.827239 ){\circle*{ .09111111}}
\put( 8.6 , 5.923514 ){\circle*{ .09111111}}
\put( 8.666667 , 6.059945 ){\circle*{ .09111111}}
\put( 8.733333 , 6.229772 ){\circle*{ .09111111}}
\put( 8.8 , 6.42528 ){\circle*{ .09111111}}
\put( 8.866667 , 6.63851 ){\circle*{ .09111111}}
\put( 8.933333 , 6.86186 ){\circle*{ .09111111}}
\put( 9 , 7.088508 ){\circle*{ .09111111}}
\put( 9.066667 , 7.312659 ){\circle*{ .09111111}}
\put( 9.133333 , 7.529632 ){\circle*{ .09111111}}
\put( 9.2 , 7.735821 ){\circle*{ .09111111}}
\put( 9.266667 , 7.928587 ){\circle*{ .09111111}}
\put( 9.333333 , 8.106106 ){\circle*{ .09111111}}
\put( 9.4 , 8.267211 ){\circle*{ .09111111}}
\put( 9.466667 , 8.411236 ){\circle*{ .09111111}}
\put( 9.53333 , 8.537879 ){\circle*{ .09111111}}
\put( 9.6 , 8.647092 ){\circle*{ .09111111}}
\put( 9.66667 , 8.738982 ){\circle*{ .09111111}}
\put( 9.73333 , 8.81374 ){\circle*{ .09111111}}
\put( 9.8 , 8.871589 ){\circle*{ .09111111}}
\put( 9.86667 , 8.912738 ){\circle*{ .09111111}}
\put( 9.93333 , 8.937355 ){\circle*{ .09111111}}
\put( 10 , 8.945548 ){\circle*{ .09111111}}
\put( 10.06667 , 8.937355 ){\circle*{ .09111111}}
\put( 10.13333 , 8.912738 ){\circle*{ .09111111}}
\put( 10.2 , 8.871589 ){\circle*{ .09111111}}
\put( 10.26667 , 8.81374 ){\circle*{ .09111111}}
\put( 10.33333 , 8.738982 ){\circle*{ .09111111}}
\put( 10.4 , 8.647092 ){\circle*{ .09111111}}
\put( 10.46667 , 8.537879 ){\circle*{ .09111111}}
\put( 10.53333 , 8.411236 ){\circle*{ .09111111}}
\put( 10.6 , 8.267211 ){\circle*{ .09111111}}
\put( 10.66667 , 8.106106 ){\circle*{ .09111111}}
\put( 10.73333 , 7.928587 ){\circle*{ .09111111}}
\put( 10.8 , 7.735821 ){\circle*{ .09111111}}
\put( 10.86667 , 7.529632 ){\circle*{ .09111111}}
\put( 10.93333 , 7.312659 ){\circle*{ .09111111}}
\put( 11 , 7.088508 ){\circle*{ .09111111}}
\put( 11.06667 , 6.86186 ){\circle*{ .09111111}}
\put( 11.13333 , 6.63851 ){\circle*{ .09111111}}
\put( 11.2 , 6.42528 ){\circle*{ .09111111}}
\put( 11.26667 , 6.229772 ){\circle*{ .09111111}}
\put( 11.33333 , 6.059945 ){\circle*{ .09111111}}
\put( 11.4 , 5.923514 ){\circle*{ .09111111}}
\put( 11.46667 , 5.827239 ){\circle*{ .09111111}}
\put( 11.53333 , 5.776197 ){\circle*{ .09111111}}
\put( 11.6 , 5.773188 ){\circle*{ .09111111}}
\put( 11.66667 , 5.818380 ){\circle*{ .09111111}}
\put( 11.73333 , 5.909285 ){\circle*{ .09111111}}
\put( 11.8 , 6.04108 ){\circle*{ .09111111}}
\put( 11.86667 , 6.207177 ){\circle*{ .09111111}}
\put( 11.93333 , 6.399937 ){\circle*{ .09111111}}
\put( 12 , 6.611396 ){\circle*{ .09111111}}
\put( 12.06667 , 6.83388 ){\circle*{ .09111111}}
\put( 12.13333 , 7.060456 ){\circle*{ .09111111}}
\put( 12.2 , 7.285194 ){\circle*{ .09111111}}
\put( 12.26667 , 7.503273 ){\circle*{ .09111111}}
\put( 12.33333 , 7.710960 ){\circle*{ .09111111}}
\put( 12.4 , 7.905502 ){\circle*{ .09111111}}
\put( 12.46667 , 8.084986 ){\circle*{ .09111111}}
\put( 12.53333 , 8.248169 ){\circle*{ .09111111}}
\put( 12.6 , 8.394332 ){\circle*{ .09111111}}
\put( 12.66667 , 8.523136 ){\circle*{ .09111111}}
\put( 12.73333 , 8.634505 ){\circle*{ .09111111}}
\put( 12.8 , 8.728532 ){\circle*{ .09111111}}
\put( 12.86667 , 8.8054 ){\circle*{ .09111111}}
\put( 12.93333 , 8.865333 ){\circle*{ .09111111}}
\put( 13 , 8.90854 ){\circle*{ .09111111}}
\put( 13.06667 , 8.935198 ){\circle*{ .09111111}}
\put( 13.13333 , 8.945422 ){\circle*{ .09111111}}
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\put( 13.33333 , 8.877590 ){\circle*{ .09111111}}
\put( 13.4 , 8.82182 ){\circle*{ .09111111}}
\put( 13.46667 , 8.749169 ){\circle*{ .09111111}}
\put( 13.53333 , 8.659413 ){\circle*{ .09111111}}
\put( 13.6 , 8.552355 ){\circle*{ .09111111}}
\put( 13.66667 , 8.427872 ){\circle*{ .09111111}}
\put( 13.73333 , 8.28599 ){\circle*{ .09111111}}
\put( 13.8 , 8.126974 ){\circle*{ .09111111}}
\put( 13.86667 , 7.951436 ){\circle*{ .09111111}}
\put( 13.93333 , 7.760475 ){\circle*{ .09111111}}
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\put( 14.06667 , 7.340013 ){\circle*{ .09111111}}
\put( 14.13333 , 7.116519 ){\circle*{ .09111111}}
\put( 14.2 , 6.889889 ){\circle*{ .09111111}}
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\put( 14.33333 , 6.450896 ){\circle*{ .09111111}}
\put( 14.4 , 6.252762 ){\circle*{ .09111111}}
\put( 14.46667 , 6.079323 ){\circle*{ .09111111}}
\put( 14.53333 , 5.938362 ){\circle*{ .09111111}}
\put( 14.6 , 5.836795 ){\circle*{ .09111111}}
\put( 14.66667 , 5.779946 ){\circle*{ .09111111}}
\put( 14.73333 , 5.770923 ){\circle*{ .09111111}}
\put( 14.8 , 5.810225 ){\circle*{ .09111111}}
\put( 14.86667 , 5.895686 ){\circle*{ .09111111}}
\put( 14.93333 , 6.022744 ){\circle*{ .09111111}}
\put( 15 , 6.184991 ){\circle*{ .09111111}}
\put( 15.06667 , 6.374879 ){\circle*{ .09111111}}
\put( 15.13333 , 6.584450 ){\circle*{ .09111111}}
\put( 15.2 , 6.805963 ){\circle*{ .09111111}}
\put( 15.26667 , 7.032376 ){\circle*{ .09111111}}
\put( 15.33333 , 7.257625 ){\circle*{ .09111111}}
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\put( 15.46667 , 7.685895 ){\circle*{ .09111111}}
\put( 15.53333 , 7.882186 ){\circle*{ .09111111}}
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\put( 16.53333 , 8.829641 ){\circle*{ .09111111}}
\put( 16.6 , 8.759093 ){\circle*{ .09111111}}
\put( 16.66667 , 8.671468 ){\circle*{ .09111111}}
\put( 16.73333 , 8.566562 ){\circle*{ .09111111}}
\put( 16.8 , 8.44424 ){\circle*{ .09111111}}
\put( 16.86667 , 8.304506 ){\circle*{ .09111111}}
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\put( 17.06667 , 7.784919 ){\circle*{ .09111111}}
\put( 17.13333 , 7.581844 ){\circle*{ .09111111}}
\put( 17.2 , 7.367247 ){\circle*{ .09111111}}
\put( 17.26667 , 7.14448 ){\circle*{ .09111111}}
\put( 17.33333 , 6.917955 ){\circle*{ .09111111}}
\put( 17.4 , 6.693189 ){\circle*{ .09111111}}
\put( 17.46667 , 6.476768 ){\circle*{ .09111111}}
\put( 17.53333 , 6.276131 ){\circle*{ .09111111}}
\put( 17.6 , 6.099201 ){\circle*{ .09111111}}
\put( 17.66667 , 5.953816 ){\circle*{ .09111111}}
\put( 17.73333 , 5.84704 ){\circle*{ .09111111}}
\put( 17.8 , 5.784433 ){\circle*{ .09111111}}
\put( 17.86667 , 5.769402 ){\circle*{ .09111111}}
\put( 17.93333 , 5.802782 ){\circle*{ .09111111}}
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\put( 18.06667 , 6.004949 ){\circle*{ .09111111}}
\put( 18.13333 , 6.16323 ){\circle*{ .09111111}}
\put( 18.2 , 6.350124 ){\circle*{ .09111111}}
\put( 18.26667 , 6.557686 ){\circle*{ .09111111}}
\put( 18.33333 , 6.778119 ){\circle*{ .09111111}}
\put( 18.4 , 7.004276 ){\circle*{ .09111111}}
\put( 18.46667 , 7.229961 ){\circle*{ .09111111}}
\put( 18.53333 , 7.450079 ){\circle*{ .09111111}}
\put( 18.6 , 7.660633 ){\circle*{ .09111111}}
\put( 18.66667 , 7.85864 ){\circle*{ .09111111}}
\put( 18.73333 , 8.041994 ){\circle*{ .09111111}}
\put( 18.8 , 8.209301 ){\circle*{ .09111111}}
\put( 18.86667 , 8.359726 ){\circle*{ .09111111}}
\put( 18.93333 , 8.492847 ){\circle*{ .09111111}}
\put( 19 , 8.608532 ){\circle*{ .09111111}}
\put( 19.06667 , 8.706841 ){\circle*{ .09111111}}
\put( 19.13333 , 8.787941 ){\circle*{ .09111111}}
\put( 19.2 , 8.852049 ){\circle*{ .09111111}}
\put( 19.26667 , 8.899383 ){\circle*{ .09111111}}
\put( 19.33333 , 8.930128 ){\circle*{ .09111111}}
\put( 19.4 , 8.944417 ){\circle*{ .09111111}}
\put( 19.46667 , 8.942314 ){\circle*{ .09111111}}
\put( 19.53333 , 8.92381 ){\circle*{ .09111111}}
\put( 19.6 , 8.888823 ){\circle*{ .09111111}}
\put( 19.66667 , 8.837204 ){\circle*{ .09111111}}
\put( 19.73333 , 8.768756 ){\circle*{ .09111111}}
\put( 19.8 , 8.683258 ){\circle*{ .09111111}}
\put( 19.86667 , 8.580503 ){\circle*{ .09111111}}
\put( 19.93333 , 8.460342 ){\circle*{ .09111111}}
%Finis.
apl> points#100
apl> '3Ox' graph 2,1,1,i,1e6,-10,10,1,-2 , 0 ,1 " tandaty.tex
%Label the curve
\put( 8.4 , 6.735200 ){n\#-2}
%Draw the data points
\put( .2 , 7.726058 ){\circle*{ .09111111}}
\put( .4 , 7.767314 ){\circle*{ .09111111}}
\put( .6 , 7.779024 ){\circle*{ .09111111}}
\put( .8 , 7.759702 ){\circle*{ .09111111}}
\put( 1 , 7.711810 ){\circle*{ .09111111}}
\put( 1.2 , 7.641689 ){\circle*{ .09111111}}
\put( 1.4 , 7.559245 ){\circle*{ .09111111}}
\put( 1.6 , 7.477088 ){\circle*{ .09111111}}
\put( 1.8 , 7.408841 ){\circle*{ .09111111}}
\put( 2 , 7.366637 ){\circle*{ .09111111}}
\put( 2.2 , 7.358357 ){\circle*{ .09111111}}
\put( 2.4 , 7.38558 ){\circle*{ .09111111}}
\put( 2.6 , 7.443154 ){\circle*{ .09111111}}
\put( 2.8 , 7.520577 ){\circle*{ .09111111}}
\put( 3 , 7.604566 ){\circle*{ .09111111}}
\put( 3.2 , 7.681780 ){\circle*{ .09111111}}
\put( 3.4 , 7.740916 ){\circle*{ .09111111}}
\put( 3.6 , 7.773930 ){\circle*{ .09111111}}
\put( 3.8 , 7.776555 ){\circle*{ .09111111}}
\put( 4 , 7.748459 ){\circle*{ .09111111}}
\put( 4.2 , 7.693252 ){\circle*{ .09111111}}
\put( 4.4 , 7.618365 ){\circle*{ .09111111}}
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\end{picture}
\end{center}
%Finis.
apl>)off
