On 3/14/19 8:54 AM, kcrisman wrote:
Following up, does this computation make any sense? Presumably this
is the core issue.
That computation makes sense, it's the second integration that breaks:
(x,y) = var('x y')
z = sqrt(1-x^2-y^2)
print(z)
assume(abs(x)<1)
assume(abs(y)<1)
zint_y = z.integrate(y)
print('Integrating in y:')
print('int(z dy) = %s' % zint_y)
print('Taylor expansions:')
print(zint_y.taylor((x,0),(y,0),5))
zp = z.taylor((x,0),(y,0),4)
zpint_y = zp.integrate(y)
print(zpint_y)
print('Integrating in x')
zint_xy = zint_y.integrate(x)
print('int(z dx dy) = %s' % zint_xy)
print('Taylor expansions:')
print(zint_xy.taylor((x,0),(y,0),6))
zpint_xy = zpint_y.integrate(x)
print(zpint_xy)
Prints:
sqrt(-x^2 - y^2 + 1)
Integrating in y:
int(z dy) = -1/2*x^2*arcsin(2*y/sqrt(-4*x^2 + 4)) + 1/2*sqrt(-x^2 - y^2 + 1)*y
+ 1/2*arcsin(2*y/sqrt(-4*x^2 + 4))
Taylor expansions:
-1/8*x^4*y - 1/12*x^2*y^3 - 1/40*y^5 - 1/2*x^2*y - 1/6*y^3 + y
-1/8*x^4*y - 1/12*x^2*y^3 - 1/40*y^5 - 1/2*x^2*y - 1/6*y^3 + y
Integrating in x
int(z dx dy) = -1/4*(y^2*arcsin(2*x/sqrt(-4*y^2 + 4)) - sqrt(-x^2 - y^2 + 1)*x
- arcsin(2*x/sqrt(-4*y^2 + 4)))*y
Taylor expansions:
-1/80*x^5*y - 1/24*x^3*y^3 - 1/16*x*y^5 - 1/12*x^3*y - 1/4*x*y^3 + 1/2*x*y
-1/40*x^5*y - 1/36*x^3*y^3 - 1/40*x*y^5 - 1/6*x^3*y - 1/6*x*y^3 + x*y
--
Christopher Subich
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