Hi Thomas, You need to declare what is a function of what in your expressions. Unrelated symbols are assumed to have no relationship so that differentiating one wrt another is like differentiating a constant:
In [1]: x = Symbol('x') In [2]: y = Symbol('y') In [3]: Derivative(x**2, x) Out[3]: d ⎛ 2⎞ ──⎝x ⎠ dx In [4]: Derivative(x**2, x).doit() Out[4]: 2⋅x In [5]: simplify(Derivative(x**2, x)) Out[5]: 2⋅x In [6]: Derivative(y**2, x) Out[6]: d ⎛ 2⎞ ──⎝y ⎠ dx In [7]: Derivative(y**2, x).doit() Out[7]: 0 In [8]: simplify(Derivative(y**2, x)) Out[8]: 0 If you want `Derivative` to understand that something depends on x then it needs to be a function of x. You clarify this by using Function rather than Symbol: In [9]: f = Function('f') In [10]: Derivative(f(x)**2, x) Out[10]: d ⎛ 2 ⎞ ──⎝f (x)⎠ dx In [11]: Derivative(f(x)**2, x).doit() Out[11]: d 2⋅f(x)⋅──(f(x)) dx In [12]: simplify(Derivative(f(x)**2, x)) Out[12]: d 2⋅f(x)⋅──(f(x)) dx -- Oscar On Fri, 27 Dec 2019 at 09:33, <thomassli...@gmail.com> wrote: > > 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 > > > > > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to sympy+unsubscr...@googlegroups.com. > > To view this discussion on the web visit > > https://groups.google.com/d/msgid/sympy/001301d5bc27%24c66b39c0%245341ad40%24%40gmail.com. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxQ8Lv1kx3M06tCU-iiOJTQbSt17y4dXUu4_U1Ju6s7DUA%40mail.gmail.com. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/000c01d5bc98%24ba958670%242fc09350%24%40gmail.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHVvXxThsWOF0qd90FCU84jehh-ziPnoXPJDBqBARrsGei_eaA%40mail.gmail.com.