I confirm the bug on 8.9.beta5. It is most probably a bug in Pynac. Note
that if you multiply by 2 it "works"
sage: (2*num).factor()
(16*r^6 - 32*r^4*x^2 + 16*r^2*x^4 + 32*r^4*y^2 + 32*r^2*x^2*y^2 +
16*r^2*y^4 + 80*r^2*x^2 + 16*x^4 + 16*r^2*y^2 + 32*x^2*y^2 + 16*y^4 -
16*x^2 - 16*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
Le 24/07/2019 à 13:31, 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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