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 <[email protected]> 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. >> > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
