# Revision history [back]

Hi,

You should avoid using the symbolic ring for computations with polynomials (it is slow and most of the time the answer is wrong). Here is a way to solve your question. You want to solve the following system

$25/4q^6?75q^5+525/2q^4?400q^3+300q^2?120q+20 = 0$ $?175/8q^6+525/2q^5?3675/4q^4+1400q^3?1050q^2+420q?70 = 0$

...

$(5/16q^6?15/4q^5+45/4q^4?10q^3) = -1$

You can enter each of these polynomials into Sage:

sage: R.<q> = PolynomialRing(QQ,'q')
sage: P7 = (5*q^6 - 60*q^5 + 210*q^4 - 320*q^3 + 240*q^2 - 96*q + 16)
sage: P5 = (85*q^6 - 1020*q^5 + 3540*q^4 - 5280*q^3 + 3800*q^2 - 1440*q + 224)
...
sage: P1 = (q^6 - 12*q^5 + 36*q^4 - 32*q^3)


Now, if there is a common solution there is a common irreducible factor to P7, P6, P5, P4, P3, P2 and P1-1. But as you can check there is no, even between P7 and P5:

sage: P7.factor()
(5) * (q^6 - 12*q^5 + 42*q^4 - 64*q^3 + 48*q^2 - 96/5*q + 16/5)
sage: P5.factor()
(85) * (q^6 - 12*q^5 + 708/17*q^4 - 1056/17*q^3 + 760/17*q^2 - 288/17*q + 224/85)


So, there is no q for this polynomial.

V.

Hi,

You should avoid using the symbolic ring for computations with polynomials (it is slow and most of the time the answer is wrong). Here is a way to solve your question. You want to solve the following system

$25/4q^6?75q^5+525/2q^4?400q^3+300q^2?120q+20$25/4q^6-75q^5+525/2q^4-400q^3+300q^2-120q+20 = 0?175/8q^6+525/2q^5?3675/4q^4+1400q^3?1050q^2+420q?70 $175/8q^6-525/2q^5+3675/4q^4-1400q^3+1050q^2-420q+70 = 0$

...

$(5/16q^6?15/4q^5+45/4q^4?10q^3)$(5/16q^6-15/4q^5+45/4q^4-10q^3) = -1\$

You can enter each of these polynomials into Sage:

sage: R.<q> = PolynomialRing(QQ,'q')
sage: P7 = (5*q^6 - 60*q^5 + 210*q^4 - 320*q^3 + 240*q^2 - 96*q + 16)
sage: P5 = (85*q^6 - 1020*q^5 + 3540*q^4 - 5280*q^3 + 3800*q^2 - 1440*q + 224)
...
sage: P1 = (q^6 - 12*q^5 + 36*q^4 - 32*q^3)


Now, if there is a common solution there is a common irreducible factor to P7, P6, P5, P4, P3, P2 and P1-1. But as you can check there is no, even between P7 and P5:

sage: P7.factor()
(5) * (q^6 - 12*q^5 + 42*q^4 - 64*q^3 + 48*q^2 - 96/5*q + 16/5)
sage: P5.factor()
(85) * (q^6 - 12*q^5 + 708/17*q^4 - 1056/17*q^3 + 760/17*q^2 - 288/17*q + 224/85)


So, there is no q for this polynomial.

V.