Hi fred2 (what is your name, btw)!
On Wed, Apr 16, 2008 at 10:36:46PM -0700, fred2 wrote:
> Hello sympy experts,
I'm not an expert, but I'll try to answer some questions.
> Thanks for making sympy available. it looks like a great package. i figured i
> would put together a cookbook page for wiki/Cookbook on how to define and
> manipulate differential equations as i learned sympy. however, after a bit
> of testing, i am not sure whether all features for this type of application
> are supported.
Indeed, for some problems we don't have all features ready, but SymPy is
developed with the idea that it should be easily extendable.
> the attached file is just an (incomplete) commented script that shows some of
> the questions a user may have, with some possible answers (but definitely
> lacking references into the documentation, as it is). it needs some expert
> inputs in order to be useful.
> also, if you think another package currently would be more suitable than
> sympy, let me know and i'll try to make this more of a rosetta stone for a
> new user to help explain what features are/aren't available or supported for
> this application.
Thanks for doing this!
I don't usually work with pde, but at least one of your question is
answered now:
> #Q2b: ok, but the (pprint,latex) display of the differential operator does
> not have a subscript (e.g., pprint displays as dx1, not dx_1)?
> #A2b: [expected feature? or possible bug?]
Yes, this was a bug, it is fixed now in hg version of SymPy
In [1]: t=Symbol('t'); x1=Symbol('x1'); x2=Symbol('x2')
In [2]: rho=Function('rho')(t,x1,x2) #dep vars
In [3]: rho.diff(x1)
Out[3]:
d
───(ρ(t, x₁, x₂))
dx₁
----
As to your other questions, below are my thoughs. I'm sure other SymPy
developers would want to add their comments too.
> #e.g., the continuity equation for a compressible gas (unsteady + 2 spatial
> dimensions)
> t,x,y=symbols('txy') #indep vars
> rho=Function('rho')(t,x,y) #dep vars
> u=Function('u')(t,x,y)
> v=Function('v')(t,x,y)
> cont = rho.diff(t) + (rho*u).diff(x) + (rho*v).diff(y)
>
> #Q1b: ok, but (pprint,print,latex) cont explicitly displays the independent
> vars - how do i hide them?
> #A1b: [unknown]
I think we don't have support for this yet.
Maybe we just need to extend the concept of variable and introduce
variables dependencies.
Suggestions welcome!
> #Q1c: ok, but (pprint,print,latex) cont simplifies the differential terms
> [e.g., d(rho u) becomes rho*du + u*drho]; how do i retain d(rho u) (i.e.,
> "conservative form")?
> #A1c: [unknown. Expand 'basic' is the default. does expand() apply to diff or
> algebraic terms? does expand(basic=False) apply only to alg. terms?. can
> expand() be turned off at the point of Function definition? can expand() be
> turned off globally?]
This is not related to pprint or latex.
The point here is that diff expands product via (uv)' = u'v + uv' rule
In [1]: g = Function('g')
In [2]: diff(f(x)*g(x), x)
Out[2]:
d d
f(x)*──(g(x)) + g(x)*──(f(x))
dx dx
I think diff should not automatically expand products, so could you
please create an issues for this?
http://code.google.com/p/sympy/issues/entry
> #Q1d: when diff operates on a multi-variate function, should d/dx display in
> pprint like (the ascii form of) \partial / \partial x?
> #A1d: [unknown. maybe not possible under ~pprint?]
I agree we should use partial derivative symbols, just because
semantically
diff(f(x,y), x)
means
∂
──(f(x, y))
∂x
i.e. partial derivative
(also, maybe we should simplify it more, e.g.
∂ f(x, y)
x
?
)
All, what do you think?
> #Q2: can i use subscripted variables instead of x,y,z, etc.?
> #A2: yes. subscripting is defined implicitly(?) via Symbol(); you cannot use
> symbols()[?].
Yes, implicitely indexed symbols gets subscripts and superscripts when
pprinted
In [1]: Symbol('Y^+_00')
Out[1]: Y⁺₀₀
But this is only some kind of eye-candy, nothing more.
What we really need is to support array, or better tensors.
http://code.google.com/p/sympy/issues/detail?id=16
Comments, Suggestions, Patches -- all welcome!
> #Q3: subscripting is just a way to indicate vectors/tensors. i have the
> equation written in vector form. can i define vector variables (e.g., the
> tuple (x1,x2), and have sympy do all the work (e.g., apply a gradient
> differential operator)? these features would be similar to macsyma's tensor
> package, e.g., contvec = rho_{,t} + (rho u_i)_{,i}.
> #A3: [unknown; see also: matrix; a matrix can contain symbols]
See above about tensors.
>Q4: what do i need in a latex/tex file to make use of the output of latex()?
>e.g., latex(cont) has (Undefined) control sequences like \operatorname{rho}.
>A4: [unknown]
Unfortunately we have to wait what others will say -- at present I'm not
using latex printing.
> thanks in advance for any comments / corrections,
Thanks again for your effort and your interest to SymPy!
Please feel free to ask more questions and discuss things on this list
and in the issues.
> dean
Ah, now I see - you are Dean :)
--
Всего хорошего, Кирилл.
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