Hi Oscar,
thanks for the quick reply. Yes, I can simplify, but with a warning
"Simplification is not a well-defined term". I have written a smaller script to
reproduce the issue.
By the way, this is not urgent; I have achieved my first goal already
(reproduce and understand the original paper), all calculations up to here can
be done by hand, and I have learned the basics of how to use SymPy. Now, I have
started with the hard part (extend the original work), and don't need the
derivatives for that.
import sympy
from sympy import symbols, latex, Eq, Derivative
from sympy import I, simplify
nu = symbols('\\nu')
tau = symbols('\\tau')
v, u, s = symbols('v u s')
eqX1 = 2*nu*Derivative(I*(s - u)/2, tau)
print('eqX1:')
print(eqX1)
print(latex(eqX1))
eqX2 = eqX1.simplify()
print('eqX2 = simplification of eqX1:')
print(eqX2)
print(latex(eqX2))
# The rest can be ignored
eqTest1 = Eq(nu**2*Derivative(s/2 + u/2, (tau, 2)) - 2*nu*Derivative(I*(s -
u)/2, tau) - 3*s/2 - 3*u/2 + I*(nu**2*Derivative(I*(s - u)/2, (tau, 2)) +
2*nu*Derivative(s/2 + u/2, tau) + I*(s - u)/(2*(s*u)**(3/2))) + (s/2 +
u/2)/(s*u)**(3/2), 0)
print('eqTest1:')
print(eqTest1)
print(latex(eqTest1))
eqTest2 = eqTest1.simplify()
print('eqTest2 = simplification of eqTest1:')
print(eqTest2)
print(latex(eqTest2))
Tom
(Dr. Thomas S. Ligon)
thomassli...@gmail.com
Frohnloher Str. 6a
81475 Muenchen
Germany
Tel. +49(89)74575075
-----Original Message-----
From: sympy@googlegroups.com <sympy@googlegroups.com> On Behalf Of Oscar
Benjamin
Sent: Thursday, December 26, 2019 10:12 PM
To: sympy <sympy@googlegroups.com>
Subject: Re: [sympy] simplify loses derivatives
Can you simplify this a bit? That's a lot of code but presumably there is a
smaller part that shows the problem. Is this it?
In [4]: simplify(Derivative(sin(x), x))
Out[4]: cos(x)
On Thu, 26 Dec 2019 at 20:05, <thomassli...@gmail.com> wrote:
>
> It looks to me like “simplify” has lost all derivatives. As you might guess
> from the code snippet, this was working earlier, but I don’t know what broke
> it, and I have made some modifications since then. I am using Python 3.7 and
> SymPy 1.5.
>
>
>
> Here is a code snippet:
>
> eq27 = Eq(eq24.lhs + I*eq25.lhs, 0)
>
> print('eq27 after creation:')
>
> print(eq27)
>
> print(latex(eq27))
>
> eq28 = Eq(eq24.lhs - I*eq25.lhs, 0)
>
> eq27 = eq27.simplify()
>
> print('eq27 after simplify 1:')
>
> print(eq27)
>
> print(latex(eq27))
>
> eq28 = eq28.simplify()
>
> eq27 = eq27.subs(Derivative(s/2 + u/2, tau, 2), Derivative(s, tau,
> 2)/2 + Derivative(u, tau, 2)/2)
>
> eq27 = eq27.subs(Derivative(I*s/2 - I*u/2, tau, 2), I*Derivative(s,
> tau, 2)/2 - I*Derivative(u, tau, 2)/2)
>
> eq28 = eq28.subs(Derivative(s/2 + u/2, tau, 2), Derivative(s, tau,
> 2)/2 + Derivative(u, tau, 2)/2)
>
> eq28 = eq28.subs(Derivative(I*s/2 - I*u/2, tau, 2), I*Derivative(s,
> tau, 2)/2 - I*Derivative(u, tau, 2)/2)
>
> eq27 = eq27.subs(Derivative(s/2 + u/2, tau), Derivative(s,
> tau)/2+Derivative(u, tau)/2)
>
> eq27 = eq27.subs(Derivative(I*s/2 - I*u/2, tau), I*Derivative(s,
> tau)/2-I*Derivative(u, tau)/2)
>
> eq28 = eq28.subs(Derivative(s/2 + u/2, tau), Derivative(s,
> tau)/2+Derivative(u, tau)/2)
>
> eq28 = eq28.subs(Derivative(I*s/2 - I*u/2, tau), I*Derivative(s,
> tau)/2-I*Derivative(u, tau)/2)
>
> eq27 = eq27.simplify()
>
> print('eq27 after simplify 2:')
>
> print(eq27)
>
> print(latex(eq27))
>
> eq28 = eq28.simplify()
>
> eq29 = eq26
>
> eq29 = eq29.subs(-I*(-s + u)/2, I*s/2 - I*u/2)
>
> eq29 = eq29.subs(Derivative(s/2 + u/2, tau), Derivative(s,
> tau)/2+Derivative(u, tau)/2)
>
> eq29 = eq29.subs(Derivative(I*s/2 - I*u/2, tau), I*Derivative(s,
> tau)/2-I*Derivative(u, tau)/2)
>
> eq29 = eq29.subs((I*Derivative(s, tau)/2 - I*Derivative(u, tau)/2)**2,
> -Derivative(s, tau)**2/4 + Derivative(s, tau)*Derivative(u, tau)/2 -
> Derivative(u, tau)**2/4)
>
> eq29 = eq29.subs((Derivative(s, tau)/2 + Derivative(u, tau)/2)**2,
> Derivative(s, tau)**2/4 + Derivative(s, tau)*Derivative(u, tau)/2 +
> Derivative(u, tau)**2/4)
>
> eq29 = eq29.simplify()
>
> eq29 = eq29.subs(3*s**2/8 + 3*s*u/4 + 3*u**2/8, 3*(s + u )**2/8)
>
> print('eq27:')
>
> print(eq27)
>
> print(latex(eq27))
>
> print('eq28:')
>
> print(eq28)
>
> print(latex(eq28))
>
> print('eq29:')
>
> print(eq29)
>
> print(latex(eq29))
>
>
>
> …and here is a piece of the output:
>
> eq24:
>
> Eq(\nu**2*Derivative(x, (\tau, 2)) - 2*\nu*Derivative(y, \tau) - 3*x +
> x/r**3, 0)
>
> \nu^{2} \frac{d^{2}}{d \tau^{2}} x - 2 \nu \frac{d}{d \tau} y - 3 x +
> \frac{x}{r^{3}} = 0
>
> eq25:
>
> Eq(\nu**2*Derivative(y, (\tau, 2)) + 2*\nu*Derivative(x, \tau) +
> y/r**3, 0)
>
> \nu^{2} \frac{d^{2}}{d \tau^{2}} y + 2 \nu \frac{d}{d \tau} x +
> \frac{y}{r^{3}} = 0
>
> eq26:
>
> Eq(-\nu**2*Derivative(x, \tau)**2/2 - \nu**2*Derivative(y, \tau)**2/2
> + 3*x**2/2 + 1/r, C)
>
> - \frac{\nu^{2} \left(\frac{d}{d \tau} x\right)^{2}}{2} -
> \frac{\nu^{2} \left(\frac{d}{d \tau} y\right)^{2}}{2} + \frac{3
> x^{2}}{2} + \frac{1}{r} = C
>
> eq24:
>
> Eq(\nu**2*Derivative(s/2 + u/2, (\tau, 2)) - 2*\nu*Derivative(I*(s -
> u)/2, \tau) - 3*s/2 - 3*u/2 + (s/2 + u/2)/(s*u)**(3/2), 0)
>
> \nu^{2} \frac{\partial^{2}}{\partial \tau^{2}} \left(\frac{s}{2} +
> \frac{u}{2}\right) - 2 \nu \frac{\partial}{\partial \tau} \frac{i
> \left(s - u\right)}{2} - \frac{3 s}{2} - \frac{3 u}{2} +
> \frac{\frac{s}{2} + \frac{u}{2}}{\left(s u\right)^{\frac{3}{2}}} = 0
>
> eq25:
>
> Eq(\nu**2*Derivative(I*(s - u)/2, (\tau, 2)) + 2*\nu*Derivative(s/2 +
> u/2, \tau) + I*(s - u)/(2*(s*u)**(3/2)), 0)
>
> \nu^{2} \frac{\partial^{2}}{\partial \tau^{2}} \frac{i \left(s -
> u\right)}{2} + 2 \nu \frac{\partial}{\partial \tau} \left(\frac{s}{2}
> + \frac{u}{2}\right) + \frac{i \left(s - u\right)}{2 \left(s
> u\right)^{\frac{3}{2}}} = 0
>
> eq26:
>
> Eq(-\nu**2*Derivative(I*(s - u)/2, \tau)**2/2 - \nu**2*Derivative(s/2
> + u/2, \tau)**2/2 + 3*(s/2 + u/2)**2/2 + 1/sqrt(s*u), C)
>
> - \frac{\nu^{2} \left(\frac{\partial}{\partial \tau} \frac{i \left(s -
> u\right)}{2}\right)^{2}}{2} - \frac{\nu^{2}
> \left(\frac{\partial}{\partial \tau} \left(\frac{s}{2} +
> \frac{u}{2}\right)\right)^{2}}{2} + \frac{3 \left(\frac{s}{2} +
> \frac{u}{2}\right)^{2}}{2} + \frac{1}{\sqrt{s u}} = C
>
> Loaded '__main__'
>
> Loaded 'runpy'
>
> eq27 after creation:
>
> Eq(\nu**2*Derivative(s/2 + u/2, (\tau, 2)) - 2*\nu*Derivative(I*(s -
> u)/2, \tau) - 3*s/2 - 3*u/2 + I*(\nu**2*Derivative(I*(s - u)/2, (\tau,
> 2)) + 2*\nu*Derivative(s/2 + u/2, \tau) + I*(s - u)/(2*(s*u)**(3/2)))
> + (s/2 + u/2)/(s*u)**(3/2), 0)
>
> \nu^{2} \frac{\partial^{2}}{\partial \tau^{2}} \left(\frac{s}{2} +
> \frac{u}{2}\right) - 2 \nu \frac{\partial}{\partial \tau} \frac{i
> \left(s - u\right)}{2} - \frac{3 s}{2} - \frac{3 u}{2} + i
> \left(\nu^{2} \frac{\partial^{2}}{\partial \tau^{2}} \frac{i \left(s -
> u\right)}{2} + 2 \nu \frac{\partial}{\partial \tau} \left(\frac{s}{2}
> + \frac{u}{2}\right) + \frac{i \left(s - u\right)}{2 \left(s
> u\right)^{\frac{3}{2}}}\right) + \frac{\frac{s}{2} +
> \frac{u}{2}}{\left(s u\right)^{\frac{3}{2}}} = 0
>
> eq27 after simplify 1:
>
> Eq(3*s/2 + 3*u/2 - u/(s*u)**(3/2), 0)
>
> \frac{3 s}{2} + \frac{3 u}{2} - \frac{u}{\left(s
> u\right)^{\frac{3}{2}}} = 0
>
> eq27 after simplify 2:
>
> Eq(3*s/2 + 3*u/2 - u/(s*u)**(3/2), 0)
>
> \frac{3 s}{2} + \frac{3 u}{2} - \frac{u}{\left(s
> u\right)^{\frac{3}{2}}} = 0
>
> eq27:
>
> Eq(3*s/2 + 3*u/2 - u/(s*u)**(3/2), 0)
>
> \frac{3 s}{2} + \frac{3 u}{2} - \frac{u}{\left(s
> u\right)^{\frac{3}{2}}} = 0
>
> eq28:
>
> Eq(3*s/2 - s/(s*u)**(3/2) + 3*u/2, 0)
>
> \frac{3 s}{2} - \frac{s}{\left(s u\right)^{\frac{3}{2}}} + \frac{3
> u}{2} = 0
>
> eq29:
>
> Eq(C, (3*sqrt(s*u)*(s + u)**2 + 8)/(8*sqrt(s*u)))
>
> C = \frac{3 \sqrt{s u} \left(s + u\right)^{2} + 8}{8 \sqrt{s u}}
>
>
>
> Finally, I have pasted the LaTeX output into a Word document to make them
> more readable. (I know that Jupyter is a great tool for this, but Word is a
> quick and easy way for me to do it.) In case someone doesn’t have Word, I
> have included a pdf version.
>
>
>
> Tom
>
> (Dr. Thomas S. Ligon)
>
> thomassli...@gmail.com
>
> Frohnloher Str. 6a
> 81475 Muenchen
> Germany
> Tel. +49(89)74575075
>
>
>
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