trac 17251 adding a doctest for factorisation of polynomials

Author: Frédéric Chapoton

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -4315,6 +4315,13 @@ cdef class MPolynomial_libsingular(MPolynomial):
             sage: f = 248301045*a^2*r^10*n^2*o^10+570807000*a^2*r^9*n*o^9-137945025*a^2*r^8*n^2*o^8+328050000*a^2*r^8*o^8-253692000*a^2*r^7*n*o^7+30654450*a^2*r^6*n^2*o^6-109350000*a^2*r^6*o^6+42282000*a^2*r^5*n*o^5-3406050*a^2*r^4*n^2*o^4-22457088*a*r^2*v*n^2*o^6+12150000*a^2*r^4*o^4-3132000*a^2*r^3*n*o^3+189225*a^2*r^2*n^2*o^2+2495232*a*v*n^2*o^4-450000*a^2*r^2*o^2+87000*a^2*r*n*o-4205*a^2*n^2
             sage: len(factor(f))
             4
+
+        Test for :trac:`17251`::
+
+            sage: R.<z,a,b> = PolynomialRing(QQ)
+            sage: N = -a^4*z^8 + 2*a^2*b^2*z^8 - b^4*z^8 - 16*a^3*b*z^7 + 16*a*b^3*z^7 + 28*a^4*z^6 - 56*a^2*b^2*z^6 + 28*b^4*z^6 + 112*a^3*b*z^5 - 112*a*b^3*z^5 - 70*a^4*z^4 + 140*a^2*b^2*z^4 - 70*b^4*z^4 - 112*a^3*b*z^3 + 112*a*b^3*z^3 + 28*a^4*z^2 - 56*a^2*b^2*z^2 + 28*b^4*z^2 + 16*a^3*b*z - 16*a*b^3*z - a^4 + 2*a^2*b^2 - b^4
+            sage: N.factor()
+            (-1) * (-a + b) * (a + b) * (-z^4*a + z^4*b - 4*z^3*a - 4*z^3*b + 6*z^2*a - 6*z^2*b + 4*z*a + 4*z*b - a + b) * (z^4*a + z^4*b - 4*z^3*a + 4*z^3*b - 6*z^2*a - 6*z^2*b + 4*z*a - 4*z*b + a + b)
         """
         cdef ring *_ring = self._parent_ring
         cdef poly *ptemp