<JSP>
{ Taala-JSP CODE FOR JSX CONVERSION 29.11.2019 MEP }
{ Muista täpättää LaTeX points: }

{ Lineaarialgebra: PNS-yhtälöryhmän ratkaisu 3x2 }
{ 1. Kolmen yhtälön PNS-ratkaisuista }

{ JSX board name: PNS_YR3x2 }
{ JSX element id: pns_yr3x2 }

#CODE	 = "GSP.class"
#CODEBASE = "../jsp"
#ARCHIVE = "jsp4.jar"
#WIDTH = 400
#HEIGHT = 430
#ALIGN = Center
*Frame = 1
*TextFont       =   "Courier"
*TextBold       =   0
*TextSize       =  14
*LabelFont      =   "Courier"
*LabelBold      =   0
*LabelSize      =  14
*MeasureFont        =   "Courier"
*MeasureSize        =  14
*MeasureBold        =   0
*MeasureInDegrees = 1
*DirectedAngles	 = 0
*BackBlue = 230
*BackGreen	= 255
*BackRed	= 255


$xText FixedText(400,192,'x1')[bold, black, justifyCenter];
{,text('\\( x \\)')}
$yText FixedText(240, 15,'x2')[bold, black, justifyCenter];
{,text('\\( y \\)')}

{ For scaling }
$RO	FixedPoint(200,400)[black,label('0')];
{,labelAlign(-4,-12)}
$Ref	Translation($RO,40,0)[hidden];
$Ray	Ray($Ref,$RO)[black, hidden];
$Rykk	Point on object($Ray,1)[white, label('1'), hidden];
$R1Vis	FixedPoint(240,400)[white,label('1')];
{,labelAlign(-4,-12)}
$RL	Line($Rykk,$RO)[black];
{,arrowL}
$Rpta	Point on object($RL,1)[label('a'), red, layer(10), hidden];
{,labelAlign(-2,4),highlight}
$Ra	Ratio/Points($RO,$Rykk,$Rpta,320,35,'a = ')[red];
$Rptb	Point on object($RL,2)[label('b'), color(0,150,0), layer(15), hidden];
{,labelAlign(-2,10),highlight}
$Rb	Ratio/Points($RO,$Rykk,$Rptb,320,55,'b = ')[color(0,150,0)];
$Rptc	Point on object($RL,3)[label('c'), blue, layer(20), hidden];
{,labelAlign(-2,12),highlight}
$Rc	Ratio/Points($RO,$Rykk,$Rptc,320,75,'c = ')[blue];

$LUpp	FixedPoint(0,380)[hidden];
$LLow	FixedPoint(0,430)[hidden];
$RLow	FixedPoint(400,430)[hidden];
$RUpp	FixedPoint(400,380)[hidden];
$RectA	Polygon($LUpp,$LLow,$RLow,$RUpp,$LUpp)[yellow];

$SBRL	ShowButton( 5,352,'Scale equations')($RO,$R1Vis,$RL,$Rpta,$Rptb,$Rptc,$RectA)[black];
$HBRL	HideButton(100,352,'Fix')( $RO,$R1Vis,$RL,$Rpta,$Rptb,$Rptc,$RectA)[black];

{ The Plane Coordinate System }
$O	FixedPoint(200, 200) [black, label('0')];
$unitp UnitPoint($O, 40) [white, label('1'),hidden];
$ykk	FixedPoint(240,200)[white, label('1')];
$coord Origin&Unit($O, $unitp)[black];
$Xax AxisX($coord)[black];
$Yax AxisY($coord)[black,hidden];
$YaxStart FixedPoint(200,380)[hidden];
$YaxVis Ray($O,$YaxStart)[black];
{,arrowL}
$Sunit	Segment($O,$unitp)[hidden];

{ The lines defined by a point and direction }

$P1	Point(70,220)[red, label('P1')];
{,label('PSUB{1}'),LabelAlign(5,5),psize(3),highlight}
$CirP	Circle by radius($P1,$Sunit)[red];
{,dash(1)}
$P2	Point on object($CirP, 1)[red, label('P2')];
{,label('PSUB{2}'),LabelAlign(5,5),highlight}
$LP1P2	Line($P1,$P2)[red,hidden];

$CoP1	Coordinates($P1,$coord,20,100,'P1 = ')[red,hidden];
$CoP2	Coordinates($P2,$coord,20, 60,'P2 = ')[red,hidden];

$a11pr Calculate( 0,35,'','#B2 #A2 -')($CoP1,$CoP2)[red,suffix('x'), hidden];
$a12pr Calculate( 57,35,'+(','#A1 #B1 -')($CoP1,$CoP2)[red,suffix(')y = '), hidden];
$b1pr Calculate(152,35,'','#B2 #A2- #A1* #B1 #A1- #A2* -')($CoP1,$CoP2)[red, hidden];
$a11	Calculate(0,35,'','AB*')($a11pr,$Ra)[red, suffix('x'), hidden];
$a12	Calculate(57,35,'+(','AB*')($a12pr,$Ra)[red, suffix(')y = '), hidden];
$b1	Calculate(152,35,'','AB*')($b1pr,$Ra)[red, hidden];

$Q1	Point(200,320)[color(0,150,0), label('Q1')];
{,label('QSUB{1}'),LabelAlign(5,5),psize(3),highlight}
$CirQ	Circle by radius($Q1,$Sunit)[color(0,150,0)];
{,dash(1)}
$Q2	Point on object($CirQ, 3)[color(0,150,0), label('Q2')];
{,label('QSUB{2}'),LabelAlign(5,5),highlight}
$LQ1Q2	Line($Q1,$Q2)[color(0,150,0),hidden];

$CoQ1	Coordinates($Q1,$coord,20,100,'Q1 = ')[color(0,150,0),hidden];
$CoQ2	Coordinates($Q2,$coord,20, 60,'Q2 = ')[color(0,150,0),hidden];

$a21pr Calculate( 0,55,'','#B2 #A2 -')($CoQ1,$CoQ2)[color(0,150,0),suffix('x'), hidden];
$a22pr Calculate( 57,55,'+(','#A1 #B1 -')($CoQ1,$CoQ2)[color(0,150,0),suffix(')y = '), hidden];
$b2pr Calculate(152,55,'','#B2 #A2- #A1* #B1 #A1- #A2* -')($CoQ1,$CoQ2)[color(0,150,0), hidden];
$a21	Calculate( 0,55,'','AB*')($a21pr,$Rb)[color(0,150,0), suffix('x'), hidden];
$a22	Calculate(57,55,'+(','AB*')($a22pr,$Rb)[color(0,150,0), suffix(')y = '), hidden];
$b2	Calculate(152,55,'','AB*')($b2pr,$Rb)[color(0,150,0), hidden];

$R1	Point(120,240)[blue, label('R1')];
{,label('RSUB{1}'),LabelAlign(5,5),psize(3),highlight}
$CirR	Circle by radius($R1,$Sunit)[blue];
{,dash(1)}
$R2	Point on object($CirR, 5)[blue, label('R2')];
{,label('RSUB{2}'),LabelAlign(5,5),highlight}
$LR1R2	Line($R1,$R2)[blue,hidden];

$CoR1	Coordinates($R1,$coord,20,100,'R1 = ')[blue,hidden];
$CoR2	Coordinates($R2,$coord,20, 60,'R2 = ')[blue,hidden];

$a31pr Calculate( 0,75,'','#B2 #A2 -')($CoR1,$CoR2)[blue,suffix('x'), hidden];
$a32pr Calculate( 57,75,'+(','#A1 #B1 -')($CoR1,$CoR2)[blue,suffix(')y = '), hidden];
$b3pr Calculate(152,75,'','#B2 #A2- #A1* #B1 #A1- #A2* -')($CoR1,$CoR2)[blue, hidden];
$a31	Calculate( 0,75,'','AB*')($a31pr,$Rc)[blue, suffix('x'), hidden];
$a32	Calculate(57,75,'+(','AB*')($a32pr,$Rc)[blue, suffix(')y = '), hidden];
$b3	Calculate(152,75,'','AB*')($b3pr,$Rc)[blue, hidden];

$A	Calculate(205, 10,'A = ','A2^ B2^ + C2^ +')($a11,$a21,$a31)[black,hidden];	
$B	Calculate(205, 25,'B = ','AD* BE* + CF* +')($a11,$a21,$a31,$a12,$a22,$a32)[black,hidden];
$C	Calculate(205, 40,'C = ','A2^ B2^ + C2^ +')($a12,$a22,$a32)[black,hidden];	
$D	Calculate(205, 55,'D = ','AD* BE* + CF* +')($a11,$a21,$a31,$b1,$b2,$b3)[black,hidden];
$E	Calculate(205, 70,'E = ','AD* BE* + CF* +')($a12,$a22,$a32,$b1,$b2,$b3)[black,hidden];
$det	Calculate(205, 85,'det = ','AC* BB* -')($A,$B,$C)[black,hidden];
$x1	Calculate(205,100,'x1 = ','AD* BC* - E /')($D,$B,$E,$C,$det)[black,hidden];
$x2	Calculate(205,115,'x2 = ','AD* BC* - E /')($A,$D,$B,$E,$det)[black,hidden];
$x	PlotXY($x2,$coord,$x1)[magenta, label('x'), layer(10)];
{,label(' \\widehat {(x,y)}'),LabelAlign(5,10)}
$xtr	PlotXY($x2,$coord,$x1)[magenta, label('x'), layer(10), traced, hidden];
{,label(' \\widehat {(x,y)}'),LabelAlign(5,10)}

$Cx	Coordinates($x,$coord,60,132,'')[magenta, bold];
$CxText FixedText(100,125,'')[bold, black, justifyCenter];
{,text('\\( \\widehat {(x,y)} = \\)')}

$SBCircles	ShowButton( 280,120,'Show circles')($CirP, $CirQ, $CirR)[black];
$HBCircles	HideButton(360,120,'Hide')($CirP, $CirQ, $CirR)[black];

$SBxtr	ShowButton( 5,145,'Trace x')($xtr)[magenta];
{,text('Trace \\( \\widehat {(x,y)} \\)')}	
$HBxtr	HideButton(85,150,'Stop')($xtr)[magenta];	

$SBeq	ShowButton(5,0,'Equations')($a11,$a12,$b1,$a21,$a22,$b2,$a31,$a32,$b3)[black,bold];
$HBeq	HideButton(70,0,'Hide')($a11,$a12,$b1,$a21,$a22,$b2,$a31,$a32,$b3)[black,bold];

$YV	FixedPoint(0,0)[hidden];
$YO	FixedPoint(400,0)[hidden];
$AV	FixedPoint(0,380)[hidden];
$AO	FixedPoint(400,380)[hidden];

$LYVYO	Segment($YV,$YO)[black,hidden];
$LAVAO	Segment($AV,$AO)[black,hidden];
$LYVAV	Segment($YV,$AV)[black,hidden];
$LYOAO	Segment($YO,$AO)[black,hidden];

$IYLP1P2	Intersect($LYVYO,$LP1P2)[hidden];
$IALP1P2	Intersect($LAVAO,$LP1P2)[hidden];
$IVLP1P2	Intersect($LYVAV,$LP1P2)[hidden];
$IOLP1P2	Intersect($LYOAO,$LP1P2)[hidden];
$SP1		Segment($IYLP1P2,$IALP1P2)[red];
$SP2		Segment($IYLP1P2,$IVLP1P2)[red,hidden];
$SP3		Segment($IYLP1P2,$IOLP1P2)[red,hidden];
$SP4		Segment($IALP1P2,$IVLP1P2)[red,hidden];
$SP5		Segment($IOLP1P2,$IVLP1P2)[red,hidden];
$SP6		Segment($IALP1P2,$IOLP1P2)[red,hidden];

$IYLQ1Q2	Intersect($LYVYO,$LQ1Q2)[hidden];
$IALQ1Q2	Intersect($LAVAO,$LQ1Q2)[hidden];
$IVLQ1Q2	Intersect($LYVAV,$LQ1Q2)[hidden];
$IOLQ1Q2	Intersect($LYOAO,$LQ1Q2)[hidden];
$SQ1		Segment($IYLQ1Q2,$IALQ1Q2)[color(0,150,0)];
$SQ2		Segment($IYLQ1Q2,$IVLQ1Q2)[color(0,150,0),hidden];
$SQ3		Segment($IYLQ1Q2,$IOLQ1Q2)[color(0,150,0),hidden];
$SQ4		Segment($IALQ1Q2,$IVLQ1Q2)[color(0,150,0),hidden];
$SQ5		Segment($IOLQ1Q2,$IVLQ1Q2)[color(0,150,0),hidden];
$SQ6		Segment($IALQ1Q2,$IOLQ1Q2)[color(0,150,0),hidden];

$IYLR1R2	Intersect($LYVYO,$LR1R2)[hidden];
$IALR1R2	Intersect($LAVAO,$LR1R2)[hidden];
$IVLR1R2	Intersect($LYVAV,$LR1R2)[hidden];
$IOLR1R2	Intersect($LYOAO,$LR1R2)[hidden];
$SR1		Segment($IYLR1R2,$IALR1R2)[blue];
$SR2		Segment($IYLR1R2,$IVLR1R2)[blue,hidden];
$SR3		Segment($IYLR1R2,$IOLR1R2)[blue,hidden];
$SR4		Segment($IALR1R2,$IVLR1R2)[blue,hidden];
$SR5		Segment($IOLR1R2,$IVLR1R2)[blue,hidden];
$SR6		Segment($IALR1R2,$IOLR1R2)[blue,hidden];
</JSP>