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# substitute(SimplicialComplex,PolynomialRing) -- change the ring of a simplicial complex

## Synopsis

• Function: substitute
• Usage:
substitute(Delta, R)
• Inputs:
• Delta, ,
• R, ,
• Outputs:

## Description

Given a polynomial ring $R$, with enough variables, we can create a simplicial complex identical to $\Delta$, defined over the ring $R$.

 i1 : S = ZZ/23[x,y,z,w]; i2 : Δ = simplexComplex(3,S) o2 = simplicialComplex | xyzw | o2 : SimplicialComplex i3 : R = ZZ/101[a,b,c,d,e]; i4 : Γ = substitute(Δ, R) o4 = simplicialComplex | abcd | o4 : SimplicialComplex

This method is a works by applying substitute(RingElement,Ring) to the facets of $\Delta$.

 i5 : code(substitute, SimplicialComplex, PolynomialRing) o5 = -- code for method: substitute(SimplicialComplex,PolynomialRing) /usr/local/share/Macaulay2/ SimplicialComplexes/Code.m2:671:77-679:71: --source code: substitute(SimplicialComplex, PolynomialRing) := SimplicialComplex => (D, R) -> ( if ideal D === ideal(1_(ring D)) then ( I := sub(ideal D, R); simplicialComplex monomialIdeal I ) else ( n := numgens ring D; simplicialComplex for F in facets D list sub(F, (vars R)_{0..n-1}) ) )