Hi, On Sat, Aug 14, 2010 at 04:26:46AM -0700, smichr wrote: > Can anyone tell me how to get (1+x+y+c*x+c*x*y)/(x+x*y) to give me > > c + (1+x+y)/(x+x*y) > > >>> Poly(1 + x + y + c*x + c*x*y).div(Poly(x+x*y)) > (Poly(0, x, y, c, domain='ZZ'), Poly(x*y*c + x*c + x + y + 1, x, y, c, > domain='ZZ')) >
In [1]: var('c')
Out[1]: c
In [2]: (1+x+y+c*x+c*x*y)/(x+x*y)
Out[2]:
1 + x + y + c⋅x + c⋅x⋅y
───────────────────────
x + x⋅y
If you want things to work out of the box then use ratsimp() from
polys11 branch:
In [3]: ratsimp(_)
Out[3]:
1 + x + y
c + ─────────
x + x⋅y
However, if you would like to use polynomial division then:
In [4]: p, q = _2.as_numer_denom()
In [5]: p
Out[5]: 1 + x + y + c⋅x + c⋅x⋅y
In [6]: q
Out[6]: x + x⋅y
In [7]: div(p, q, wrt=x)
Out[7]: (0, 1 + x + y + c⋅x + c⋅x⋅y)
In [8]: div(p, q, wrt=y)
Out[8]: (0, 1 + x + y + c⋅x + c⋅x⋅y)
In [9]: div(p, q, wrt=c)
Out[9]: (c, 1 + x + y)
This happens because div() uses recursive division algorithm, so,
depending on the order of variables, the results may differ (as
showed in [7]-[9]).
There exists also another, generalized division algorithm that
is implemented in reduced():
In [10]: reduced(p, [q])
Out[10]: ([c], 1 + x + y)
(which is, by the way, used in new ratsimp()).
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Mateusz
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