With no explanation, label text_A→text_B with either "not_related" or "related".
text_A: From Here to Infirmary is the name of an album released by Alkaline Trio.
text_B: In Galois theory , a discipline within the field of abstract algebra , a resolvent for a permutation group G is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial p and has , roughly speaking , a rational root if and only if the Galois group of p is included in G .. Galois theory. Galois theory. abstract algebra. abstract algebra. permutation group. permutation group. polynomial. polynomial. rational. rational number. Galois group. Galois group. More exactly , if the Galois group is included in G , then the resolvent has a rational root , and the converse is true if the rational root is a simple root .. rational. rational number. Galois group. Galois group. simple root. simple root ( polynomial ). Resolvents were introduced by Joseph Louis Lagrange and systematically used by Evariste Galois .. Joseph Louis Lagrange. Joseph Louis Lagrange. Evariste Galois. Evariste Galois. Nowadays they are still a fundamental tool to compute Galois groups .. The simplest examples of resolvents are. where is the discriminant , which is a resolvent for the alternating group .. discriminant. discriminant. alternating group. alternating group. In the case of a cubic equation , this resolvent is sometimes called the quadratic resolvent ; its roots appear explicitly in the formulas for the roots of a cubic equation .. cubic equation. cubic equation. The cubic resolvent of a quartic equation , which is a resolvent for the dihedral group of 8 elements .. cubic resolvent. resolvent cubic. quartic equation. quartic function. dihedral group. dihedral group. The Cayley resolvent is a resolvent for the maximal resoluble Galois group in degree five .. Galois group. Galois group. Cayley resolvent. Quintic function#Solvable quintics. It is a polynomial of degree 6 .. polynomial. polynomial. These three resolvents have the property of being always separable , which means that , if they have a multiple root , then the polynomial p is not irreducible .. polynomial. polynomial. It is not known if there is an always separable resolvent for every group of permutations .. For every equation the roots may be expressed in terms of radicals and of a root of a resolvent for a resoluble group , because , the Galois group of the equation over the field generated by this root is resoluble .. Galois group. Galois group
not_related.