Algebraic number theory studies algebraic number fields. Algebraic curves are the curves considered in algebraic geometry. Solving differential equations is not like solving algebraic equations. Irreducible polynomials appear naturally in the study of polynomial factorization and algebraic field extensions. Chain complexes arise in abundance in algebra and algebraic topology. Themes common to all kinds of algebraic structures are studied in universal algebra. Infinite complexes are a technical tool basic in algebraic topology. Critical points are fundamental for studying the topology of manifolds and real algebraic varieties. Let formula 144 be an eigenvalue of formula 1 of algebraic multiplicity formula 146. Let formula 70 be an eigenvalue of formula 2 of algebraic multiplicity formula 72. There are numerous machines built for computing the cohomology of algebraic varieties. Examples of algebraic integers are , and . They can be solved by algebraic or numerical methods. A version of Euler characteristic used in algebraic geometry is as follows. Jurjen Koksma in 1939 proposed another classification based on approximation by algebraic numbers.