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<https://code.google.com/p/sympy/issues/detail?id=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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