Effective calculations of the multiplicity of polynomial mappings

Effective calculations of the degree of ∗-covering

“…In summary, we can find effectively i 0 (f ) and deg 0 f (C n ) in (11). Hence the third number in (11) can be effectively determined.…”

“…In this Section we give effective method to calculate the number d(f ) in (11). Let I f be the ideal of the graph of the mapping f , i.e.…”

Multiplicity and Semicontinuity of the Łojasiewicz Exponent

“…The proof is based on an algorithm which allows us to effectively compute the multiplicity i 0 (f ) (Theorem 4, cf. [10]). As a corollary we get the above-mentioned semicontinuity theorem (Corollary 11).…”