# Revision history [back]

This works under Linux; First pass :

sage: %cpaste
Pasting code; enter '--' alone on the line to stop or use Ctrl-D.
:var('x,y,z,')
:var('xLow,xUp')
:var('yLow,yUp')
:rNum=1
:
:#xLow=sqrt(4*y^2/(sqrt(2) - 2) + sqrt(2)/(sqrt(2) - 2) - 2/(sqrt(2) - 2))
:#xUp=y*sin(1/9*pi)/cos(1/9*pi)
:
:#yLow=0.379024477
:#yUp=0.921891033
:zLow=0
:zUp=sqrt(-x^2 - y^2 + 1)
:zInt=integrate(1,z,zLow,zUp)
:print(zInt)
:yIntegr=integrate(zInt,y,yLow,yUp,algorithm="giac")
:xIntegr=integrate(zInt,x,xLow,xUp,algorithm="giac")
:print("yIntegr : " , yIntegr)
:print("xIntegr : " , xIntegr)
:--
(x, y, z)
(xLow, xUp)
(yLow, yUp)
sqrt(-x^2 - y^2 + 1)
yIntegr :  1/2*x^2*arcsin(yLow/sqrt(-x^2 + 1)) - 1/2*x^2*arcsin(yUp/sqrt(-x^2 + 1)) - 1/2*sqrt(-x^2 - yLow^2 + 1)*yLow + 1/2*sqrt(-x^2 - yUp^2 + 1)*yUp - 1/2*arcsin(yLow/sqrt(-x^2 + 1)) + 1/2*arcsin(yUp/sqrt(-x^2 + 1))
xIntegr :  1/2*y^2*arcsin(xLow/sqrt(-y^2 + 1)) - 1/2*y^2*arcsin(xUp/sqrt(-y^2 + 1)) - 1/2*sqrt(-xLow^2 - y^2 + 1)*xLow + 1/2*sqrt(-xUp^2 - y^2 + 1)*xUp - 1/2*arcsin(xLow/sqrt(-y^2 + 1)) + 1/2*arcsin(xUp/sqrt(-y^2 + 1))


Second pass :

sage: reset()
sage: %cpaste
Pasting code; enter '--' alone on the line to stop or use Ctrl-D.
:var('x,y,z,')
:var('xLow,xUp')
:var('yLow,yUp')
:rNum=1
:
:#xLow=sqrt(4*y^2/(sqrt(2) - 2) + sqrt(2)/(sqrt(2) - 2) - 2/(sqrt(2) - 2))
:#xUp=y*sin(1/9*pi)/cos(1/9*pi)
:
:#yLow=0.379024477
:#yUp=0.921891033
:zLow=0
:zUp=sqrt(-x^2 - y^2 + 1)
:zInt=integrate(1,z,zLow,zUp)
:print(zInt)
:yIntegr=integrate(zInt,y,yLow,yUp,algorithm="giac")
:xIntegr=integrate(zInt,x,xLow,xUp,algorithm="giac")
:print("yIntegr : " , yIntegr)
:print("xIntegr : " , xIntegr)
:--
(x, y, z)
(xLow, xUp)
(yLow, yUp)
sqrt(-x^2 - y^2 + 1)
yIntegr :  1/2*x^2*arcsin(yLow/sqrt(-x^2 + 1)) - 1/2*x^2*arcsin(yUp/sqrt(-x^2 + 1)) - 1/2*sqrt(-x^2 - yLow^2 + 1)*yLow + 1/2*sqrt(-x^2 - yUp^2 + 1)*yUp - 1/2*arcsin(yLow/sqrt(-x^2 + 1)) + 1/2*arcsin(yUp/sqrt(-x^2 + 1))
xIntegr :  1/2*y^2*arcsin(xLow/sqrt(-y^2 + 1)) - 1/2*y^2*arcsin(xUp/sqrt(-y^2 + 1)) - 1/2*sqrt(-xLow^2 - y^2 + 1)*xLow + 1/2*sqrt(-xUp^2 - y^2 + 1)*xUp - 1/2*arcsin(xLow/sqrt(-y^2 + 1)) + 1/2*arcsin(xUp/sqrt(-y^2 + 1))


This may be Windows (and Cygwin)-specific. You should open an issue on its Github page.