@Mario: Thank you very much for the reply. I will have to go for this
option If I am unable to
fix `match()`
@Aaron: Sure.
Regards,
Thilina
On Mon, Sep 16, 2013 at 3:43 AM, Aaron Meurer <asmeu...@gmail.com> wrote:
> It's annoying to do this all the time, though. With dsolve and
> classify_ode, I ended up writing a bunch of custom matchers, but it's
> much less robust than using Wild() and match() when they work.
>
> Even for things that really do have to be algorithmically matched
> (e.g., the homogeneous_order hint in the ODE module), it would be
> better if it were done by passing a callable to Wild, rather than
> writing a custom matcher with some mix of Wilds and Python code.
>
> Thilina, regardless of what you do, can you make sure you open an
> issue for this bug (unless you fix it, then open a pull request).
>
> Aaron Meurer
>
> On Sun, Sep 15, 2013 at 3:17 PM, mario <mario.pern...@gmail.com> wrote:
> > It is easy to write a custom match; in the following example there is a
> > match for a quartic
> > form; it is easy to write additional conditions, like restriction to 3
> > variables, integer coefficients,
> > etc.
> >
> >>>> def match4(t):
> > ... "match a quartic form"
> > ... a = []
> > ... for xx in t.args:
> > ... f = Factors(xx).factors
> > ... c = 1
> > ... d = {}
> > ... tot_deg = 0
> > ... for k, v in f.items():
> > ... if k.is_number:
> > ... c = c*k**v
> > ... else:
> > ... d[k] = v
> > ... if not v.is_integer or v < 0:
> > ... return None
> > ... tot_deg += v
> > ... if tot_deg != 4:
> > ... return None
> > ... a.append((c, d))
> > ... return a
> > ...
> >>>> t = x**2*y**2 - 2*x**2*y*z + x**2*z**2 - 2*x*y**2*z - 2*x*y*z**2 +
> >>>> y**2*z**2
> >>>> match4(t)
> > [(1, {z: 2, y: 2}), (-2, {x: 1, z: 2, y: 1}), (1, {x: 2, z: 2}), (-2,
> {x: 1,
> > z: 1, y: 2}), (-2, {x: 2, z: 1, y: 1}), (1, {x: 2, y: 2})]
> >
> >
> >
> > On Sunday, September 15, 2013 8:13:29 PM UTC+2, Thilina Rathnayake wrote:
> >>
> >> Hi All,
> >>
> >> Addressing issue 4004, the equation after expanding can be written as
> >> below,
> >>
> >>> In [1]: t = (x*y + y*z + x*z)**2 - 4*x*y*z*(x + y + z)
> >>> In [2]: expand(t)
> >>> Out[2]:
> >>> 2 2 2 2 2 2 2 2 2
> >>> x ⋅y - 2⋅x ⋅y⋅z + x ⋅z - 2⋅x⋅y ⋅z - 2⋅x⋅y⋅z + y ⋅z
> >>
> >>
> >> This is of the form `X**2 + Y**2 + Z**2 - 2*X*Y - 2*Y*Z - 2*X*Z` with X
> =
> >> x*y, Y = y*z and
> >> Z = z*x. Latter can be solved by the Diophantine module for X, Y, Z and
> we
> >> can recover
> >> solutions for x, y and z.
> >>
> >> I tried to automate this process with Wild's and `match()` but couldn't
> >> do it. Given
> >> an expression, I tried to determine if it is in the form `ap**2 + bq**2
> +
> >> cr**2 + d*p*q + e*q*r + f*r*p`
> >> where a, b, c, d, e, f are Wilds trying to match Integers(used
> exclude=[x,
> >> y, z] while
> >> creating these) and p, q, r trying to match the variables.
> >>
> >> In[3]: _.match(a*p**2 + b*q**2 + c*r**2 + d*p*q + e*q*r + f*r*q)
> >>
> >> Above kept running forever. Is there a way to efficiently pattern match
> an
> >> expression
> >> so that we can decide whether it belongs to a particular form or not?
> >>
> >> Regards,
> >> Thilina.
> >>
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