Possible workaround:
sage: num
-1/2*(12*r^4*x + 4*r^2*x^3 + 4*r^2*x*y^2 - 4*r^2*x + 4*x^3 +
4*x*y^2)^2/(r^6 + 6*r^4*x^2 + r^2*x^4 + 2*r^4*y^2 + 2*r^2*x^2*y^2 + r^2*y^4
- 2*r^2*x^2 + x^4 + 2*r^2*y^2 + 2*x^2*y^2 + y^4)^2 - 1/2*(4*r^4*y +
4*r^2*x^2*y + 4*r^2*y^3 + 4*r^2*y + 4*x^2*y + 4*y^3)^2/(r^6 + 6*r^4*x^2 +
r^2*x^4 + 2*r^4*y^2 + 2*r^2*x^2*y^2 + r^2*y^4 - 2*r^2*x^2 + x^4 + 2*r^2*y^2
+ 2*x^2*y^2 + y^4)^2 + 1/2*(12*r^4 + 12*r^2*x^2 + 4*r^2*y^2 - 4*r^2 +
12*x^2 + 4*y^2)/(r^6 + 6*r^4*x^2 + r^2*x^4 + 2*r^4*y^2 + 2*r^2*x^2*y^2 +
r^2*y^4 - 2*r^2*x^2 + x^4 + 2*r^2*y^2 + 2*x^2*y^2 + y^4) + 1/2*(4*r^4 +
4*r^2*x^2 + 12*r^2*y^2 + 4*r^2 + 4*x^2 + 12*y^2)/(r^6 + 6*r^4*x^2 + r^2*x^4
+ 2*r^4*y^2 + 2*r^2*x^2*y^2 + r^2*y^4 - 2*r^2*x^2 + x^4 + 2*r^2*y^2 +
2*x^2*y^2 + y^4)
sage: num.maxima_methods().factor()
8*(r^6 - 2*r^4*x^2 + r^2*x^4 + 2*r^4*y^2 + 2*r^2*x^2*y^2 + r^2*y^4 +
5*r^2*x^2 + x^4 + r^2*y^2 + 2*x^2*y^2 + y^4 - x^2 - y^2)*r^4/(r^6 +
6*r^4*x^2 + r^2*x^4 + 2*r^4*y^2 + 2*r^2*x^2*y^2 + r^2*y^4 - 2*r^2*x^2 + x^4
+ 2*r^2*y^2 + 2*x^2*y^2 + y^4)^2
HTH,
Le mercredi 24 juillet 2019 13:31:08 UTC+2, Enrique Artal a écrit :
>
> I have encountered a problem with factor in SR which can be avoided but it
> shows a problem. If I run this code:
>
> var('t',domain='complex')
> var('r,x,y',domain='real')
> h= r^6+r^4*t^2 + 4*r^4*t*conjugate(t) + r^4*conjugate(t)^2 +
> r^2*t^2*conjugate(t)^2 - r^2*t^2 - r^2*conjugate(t)^2 + t^2*conjugate(t)^2
> H=h(t=x+I*y).factor()
>
> num=1/2*(H.derivative(x)/H).derivative(x)+1/2*(H.derivative(y)/H).derivative(y)
> num.factor()
>
> I get the following error
>
> ---------------------------------------------------------------------------ValueError
> Traceback (most recent call
> last)<ipython-input-1-bfb20671ab22> in <module>() 6
> H=h(t=x+I*y).factor() 7
> num=Integer(1)/Integer(2)*(H.derivative(x)/H).derivative(x)+Integer(1)/Integer(2)*(H.derivative(y)/H).derivative(y)---->
> 8 num.factor()
> /home/artal/sage/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx
> in sage.symbolic.expression.Expression.factor
> (build/cythonized/sage/symbolic/expression.cpp:57759)() 11107 cdef
> GEx x 11108 cdef bint b> 11109 if dontfactor or not
> self.is_rational_expression(): 11110 m = self._maxima_() 11111
> name = m.name()
> /home/artal/sage/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx
> in sage.symbolic.expression.Expression.is_rational_expression
> (build/cythonized/sage/symbolic/expression.cpp:15368)() 2030
> False 2031 """-> 2032 return all(part.is_polynomial(v)
> 2033 for part in (self.numerator(), self.denominator())
> 2034 for v in part.variables())
> /home/artal/sage/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx
> in genexpr (build/cythonized/sage/symbolic/expression.cpp:15110)() 2031
> """ 2032 return all(part.is_polynomial(v)-> 2033
> for part in (self.numerator(), self.denominator()) 2034
> for v in part.variables()) 2035
> /home/artal/sage/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx
> in sage.symbolic.expression.Expression.numerator
> (build/cythonized/sage/symbolic/expression.cpp:48252)() 9377
> sig_on() 9378 try:-> 9379 ex =
> self._gobj.numer() 9380 finally: 9381
> sig_off()
> ValueError: divide: arguments must be polynomials over the rationals
>
>
> This error does not happen if I erase some terms of h; and some times it
> gives the error only if I did not restart the jupyter notebook. Any ideas?
> Enrique.
>
>
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