All,
thanks much for the quick response & valuable comments.
i can't be as fast (or valuable), but i will digest the responses and
put it on the wiki - hopefully in the next month (sorry). then i'll
look into the internals, maybe starting w/ latex printing.
just some basic follow-up:
(1) regarding the subscripting:
(1a) Ondrej's output on my browser is:
In [5]: Symbol("F_x")
Out[5]: Fₓ
i.e., shows up as F^*, not F_x. maybe that is just a unicode(?)
problem on my browser.
(1b)in order to obtain subscripts in symbol/function names, should/
must the user include the underscore, or is either acceptable to you?
(e.g., x1=Symbol('x1') versus x1=Symbol('x_1'); in the former case,
the subscripting is magic(?!), and no superscripting is possible(?))
(2)do you want the wiki cookbook entries to be doctest-able or
otherwise in a form suitable for testing?
regards,
dean
On Apr 17, 8:23 am, "Ondrej Certik" <[EMAIL PROTECTED]> wrote:
> Hi Dean!
>
> first thanks a lot for doing this. Feel free to put it on our wiki.
> Some comments below:
>
> On Thu, Apr 17, 2008 at 5:03 PM, Kirill Smelkov
>
>
>
>
>
> <[EMAIL PROTECTED]> wrote:
>
> > 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.
>
> Yes, I think we need something like this. But I have no ideas here so
> far. Maybe something like:
>
> x = x(y)
>
> would create a function "x" of "y", but you could also work with "x"
> as a symbol.
>
>
>
>
>
>
>
> > 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
>
> We have this implemented already imho, just use the Derivative class:
>
> 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
>
> In [3]: Derivative(f(x)*g(x), x)
> Out[3]:
> d
> ──(f(x)*g(x))
> dx
>
>
>
>
>
> > > #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
>
> > ?
> > )
>
> Both. In Quantum Field Theory or General Relativity, we definitely
> need the second syntax. At least I prefer it. But the ascii art for
> this is not so sufficient. Why not to use unicode subscripts for "x"
> like this:
>
> In [5]: Symbol("F_x")
> Out[5]: Fₓ
>
> > All, what do you think?
>
> I think we should implement that. Dean, if you want to help here, feel
> free to ask us for guidance, we'll help you.
>
>
>
>
>
> > > #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.
>
> I think our latex printing needs some polishing -- I think Mateusz uses it?
>
> BTW the latex printing is easy to fix, just look into sympy/printing/latex.py.
>
> Ondrej- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
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