The following code may be useful -
def square_root_of_expr(expr):
"""
If expression is product of even powers then every power is divided
by two and the product is returned. If some terms in product are
not even powers the sqrt of the absolute value of the expression is
returned. If the expression is a number the sqrt of the absolute
value of the number is returned.
"""
if expr.is_number:
if expr > 0:
return sqrt(expr)
else:
return sqrt(-expr)
else:
expr = trigsimp(expr)
coef, pow_lst = sqf_list(expr)
if coef != S.One:
if coef.is_number:
coef = square_root_of_expr(coef)
else:
coef = sqrt(abs(coef)) # Product coefficient not a number
for p in pow_lst:
f, n = p
if n % 2 != 0:
return sqrt(abs(expr)) # Product not all even powers
else:
coef *= f ** (n / S(2)) # Positive sqrt of the square
of an expression
return coef
On 12/22/22 5:34 PM, Chris Smith wrote:
If you want to ignore `Abs`, replace it: `expr.replace(Abs, Id)`
/c
On Wednesday, December 21, 2022 at 10:13:22 PM UTC-6
arthur...@gmail.com wrote:
Staffan,
Just a guess, but sin(phi) goes negative even for positive values
of phi. You’d have limit the range to 0 <= phi <= pi.
— Arthur
On Mon, Dec 19, 2022 at 1:41 PM Staffan Lundberg
<drstaffan...@gmail.com> wrote:
I am working with curvilinear coordinates, especiallt how to
determine scale factors for spherical coordinates and how to
express the unit vectors i terms of i, j, k (cartesian base
vectors). I submit some code
#
# curvilinear.py
#from sympy import *
x, y, z = symbols("x y z")
rho= symbols("rho",positive=True,real=True)
theta = symbols("theta",positive=True,real=True)
phi = symbols("phi",positive=True,real=True)
# spherical coord
x=rho*sin(phi)*cos(theta)
y=rho*sin(phi)*sin(theta)
z=rho*cos(phi)
A=Matrix([[x],[y],[z]])
r=A
dr=diff(r,rho)
hr=dr.norm()
hr=simplify(hr)
dphi=diff(r,phi)
hphi=dphi.norm()
hphi=simplify(hphi)
dtheta=diff(r,theta)
htheta=dtheta.norm()
htheta=simplify(htheta)
r_hat=dr/hr
fi_hat=dphi/hphi
th_hat=dtheta/htheta
print(fi_hat)
print(th_hat)
print(r_hat)
#
#
Problems with th_hat. Despite telling sympy that phi is
positive, I get
Abs(sin(phi)) instead of sin(phi). Thus python does not
cancel the factor sin(phi).
Has anyone some hints how to solve this issue. Maybe a bug in
sympy?
/Staffan L
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