Comment #13 on issue 3742 by matt...@gmail.com: rref very slow
http://code.google.com/p/sympy/issues/detail?id=3742
In [1]: from sympy.polys.solvers import RawMatrix
In [2]: from sympy.polys.fields import vfield
In [3]: var("a_(1:5)(1:5)")
Out[3]: (a₁₁, a₁₂, a₁₃, a₁₄, a₂₁, a₂₂, a₂₃, a₂₄, a₃₁, a₃₂, a₃₃, a₃₄, a₄₁,
a₄₂, a₄₃, a₄₄)
In [4]: M = Matrix([[a_11*a_12, a_21*a_22, 1], [a_31*a_32, a_41*a_42, 0]])
In [5]: M
Out[5]:
⎡a₁₁⋅a₁₂ a₂₁⋅a₂₂ 1⎤
⎢ ⎥
⎣a₃₁⋅a₃₂ a₄₁⋅a₄₂ 0⎦
In [6]: M.applyfunc(type)
Out[6]:
⎡<class 'sympy.core.mul.Mul'> <class 'sympy.core.mul.Mul'>
<class 'sympy.core.numbers.One'> ⎤
⎢
⎥
⎣<class 'sympy.core.mul.Mul'> <class 'sympy.core.mul.Mul'>
<class 'sympy.core.numbers.Zero'>⎦
In [7]: F = vfield("a_(1:5)(1:5)", ZZ)
In [8]: N = RawMatrix(M.rows, M.cols, map(F.to_domain().convert, M))
In [9]: N
Out[9]:
⎡a_11*a_12 a_21*a_22 1⎤
⎢ ⎥
⎣a_31*a_32 a_41*a_42 0⎦
In [10]: N.applyfunc(type)
Out[10]:
⎡<class 'sympy.polys.fields.FracElement'>
<class 'sympy.polys.fields.FracElement'>
<class 'sympy.polys.fields.FracElement'>⎤
⎢
⎥
⎣<class 'sympy.polys.fields.FracElement'>
<class 'sympy.polys.fields.FracElement'>
<class 'sympy.polys.fields.FracElement'>⎦
This is verbose to show you how to check if conversions went OK. The
conversion happens in [8]. Note that step [7] overrides a_ij defined with
var(). If you don't want that, use F = field("a_(1:5)(1:5)", ZZ)[0] or F, _
= xfield("a_(1:5)(1:5)", ZZ). What we show you here is all experimental
code, so be warned that things will most likely work differently in the
final version (and will be much simpler to use).
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