The ring $R$ must be a ring of probability distributions on $n$ random variables created using markovRing. The integer $i$ must be in the range from 1 to $n$.
Let $p_{u_1,u_2,\dots, +,\dots,u_n}$ denote the linear form $p_{u_1,u_2,\dots, 1,\dots,u_n} + \dots + p_{u_1,u_2,\dots, d_i,\dots,u_n}$, where $d_i$ is the number of states of random variable $X_i$.
The method marginMap returns a ring map $F : R \to R$ such that after applying $F$, the indeterminate $p_{u_1,u_2,\dots,1,\dots,u_n}$ refers to $ p_{u_1,u_2,\dots, +,\dots,u_n}$, where the '1' and the '$+$' are in the $i$th spot.
Further $F$ is the identity on all other indeterminates, that is, $ F(p_{u_1,u_2,\dots, j,\dots,u_n}) = p_{u_1,u_2,\dots, j,\dots,u_n} $, for all $j\geq 2$.
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This linear transformation simplifies ideals and/or polynomials involving $ p_{u_1,u_2,..., +,...,u_n} $. Sometimes, the resulting ideals are toric ideals as the example below shows. For more details see the paper "Algebraic Geometry of Bayesian Networks" by Garcia, Stillman, and Sturmfels.
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The object marginMap is a method function.