On Mon, Feb 19, 2018 at 6:12 AM, mohab meshref <mohabe1...@gmail.com> wrote: > so i am implementing a simple chain rule differentiation , given two > functions m2 , m > with: > > m2 = r0**2 + r1**2 + r2**2 > > m= m2**(0.5) > > i want to get the differentiation of (m wrt r0), so i calculate: diff(m wrt > m2) * diff (m2 wrt r0). > > expected output: > r0 * m2**(-0.5). > > sympy output: > 1.0*r0*m2(r0**2 + r1**2 + r2**2)**(-0.5)*Subs(Derivative(m(_xi_1), _xi_1), > (_xi_1,), (m2(r0**2 + r1**2 + r2**2)**0.5,))*Subs(Derivative(m2(_xi_1), > _xi_1), (_xi_1,), (r0**2 + r1**2 + r2**2,)) > > --------------------------------------------------------------- > > first thing i want to know is why instead of writing just m2 it has to write > this (m2(r0**2 + r1**2 + r2**2)) ?
This is the expression in question. Note that SymPy has no idea what you called your Python variables. See http://docs.sympy.org/latest/tutorial/gotchas.html > second, why is this term (Subs(Derivative(m(_xi_1), _xi_1), (_xi_1,), > (m2(r0**2 + r1**2 + r2**2)**0.5,))*Subs(Derivative(m2(_xi_1), _xi_1), > (_xi_1,), (r0**2 + r1**2 + r2**2,))) here? > and what does it actually means? This represents the derivative of the function evaluated at that point, which is needed for the chain rule. This is the only way SymPy has to represent something like f'(a) when 'a' is something more complicated than a single variable. It is perhaps clearer to see what it is if you use pprint() on the output: -0.5⎛ 2 2 2⎞ ⎛ d ⎞│ ⎛ d ⎞│ 1.0⋅r₀⋅m₂ ⎝r₀ + r₁ + r₂ ⎠⋅⎜───(m(ξ₁))⎟│ 0.5⎛ 2 2 2⎞⋅⎜───(m₂(ξ₁))⎟│ 2 2 2 ⎝dξ₁ ⎠│ξ₁=m₂ ⎝r₀ + r₁ + r₂ ⎠ ⎝dξ₁ ⎠│ξ₁=r₀ + r₁ + r₂ Aaron Meurer > > Here's my code: > > import sympy as sp > > r0, r1, r2, t0 = sp.symbols( > "r0,r1,r2,t0", real=True) > > m2, m = sp.symbols('m2, m', cls=sp.Function) > > m2 = m2(r0**2 + r1**2 + r2**2) > > m = m(m2 ** (0.5)) > > dm2r0 = sp.Derivative(m2,r0) > > dmm2 = sp.Derivative(m,m2) > > dmr0 = dmm2 * dm2r0 > > print("dmr0:\n"+str(dmr0.doit())+"\n\n") > > -- > 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 post to this group, send email to sympy@googlegroups.com. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/56251b73-da56-4938-a250-1c91d1cdad07%40googlegroups.com. > For more options, visit https://groups.google.com/d/optout. -- 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 post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6%2BT9r9PSCbkaePxrgBy0Ktb3vBU0UqMXzLTOQGFnPMxxA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
