Let $R$ be the polynomial ring $R=k[x_0,...,x_r]$ and $I$ be the homogeneous ideal $I=(f_0,f_1,...,f_s)$ where $deg(f_i)=d$. We compute the degree of the rational map $\mathbb{F}: \mathbb{P}^r \to \mathbb{P}^s$ defined by $$ (x_0: ... :x_r) \to (f_0(x_0,...,x_r), f_1(x_0,...,x_r), ..... , f_s(x_0,...,x_r)). $$ Using certain Hilbert functions the degree of the map is bounded (see Theorem 3.22 in Degree and birationality of multi-graded rational maps).
The following example is a rational map without base points:
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In the following examples we play with the relations of the Hilbert-Burch presentation and the degree of $\mathbb{F}$ (see Proposition 5.2 and Theorem 5.12):
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To call the method "degreeOfMap(I)", the ideal $I$ should be in a single graded polynomial ring and dim(R/I) <= 1.
The object upperBoundDegreeSingleGraded is a method function.