New implementation of map_from_func with changed argument order

experimental/IntersectionTheory/src/IntersectionTheory.jl

@@ -4,7 +4,6 @@ using ..Oscar
 import Base: +, -, *, ^, ==, div, zero, one, parent
 import ..Oscar: AffAlgHom, Ring, MPolyDecRingElem, symmetric_power, exterior_power, pullback, canonical_bundle, graph, euler_characteristic, pullback
 import ..Oscar: basis, betti_numbers, chow_ring, codomain, degree, det, dim, domain, dual, gens, hilbert_polynomial, hom, integral, rank, signature, partitions, blow_up
-import ..Oscar.AbstractAlgebra.Generic: FunctionalMap
 import ..Oscar: pullback, pushforward, base, OO, product, compose, identity_map, map
 import ..Oscar: trivial_line_bundle
 import ..Oscar: intersection_matrix

experimental/IntersectionTheory/src/Main.jl

@@ -347,7 +347,7 @@ end
     map(X::AbstractVariety, Y::AbstractVariety, fˣ::Vector, fₓ = nothing; inclusion::Bool = false, symbol::String = "x")
 
 Return an abstract variety map `X` $\rightarrow$ `Y` by specifying the pullbacks of
-the generators of the Chow ring of `Y`. 
+the generators of the Chow ring of `Y`.
 
 !!! note
     The corresponding pushforward will be automatically computed in certain cases.
@@ -588,7 +588,7 @@ pushforward(f::AbstractVarietyMap, F::AbstractBundle) = AbstractBundle(f.codomai
 Return the identity map on `X`.
 """
 function identity_map(X::AbstractVariety)
-  AbstractVarietyMap(X, X, gens(X.ring), map_from_func(identity, X.ring, X.ring))
+  AbstractVarietyMap(X, X, gens(X.ring), MapFromFunc(X.ring, X.ring, identity))
 end
 
 @doc raw"""
@@ -602,7 +602,7 @@ function compose(f::AbstractVarietyMap, g::AbstractVarietyMap)
   Z = g.codomain
   gofₓ = nothing
   if isdefined(f, :pushforward) && isdefined(g, :pushforward)
-    gofₓ = map_from_func(g.pushforward ∘ f.pushforward, X.ring, Z.ring)
+    gofₓ = MapFromFunc(X.ring, Z.ring, g.pushforward ∘ f.pushforward)
   end
   gof = AbstractVarietyMap(X, Z, g.pullback * f.pullback, gofₓ)
   return gof
@@ -1051,7 +1051,7 @@ If `X` has been given a tangent bundle, return the dual bundle.
 julia> P2 = abstract_projective_space(2)
 AbstractVariety of dim 2
 
-julia> cotangent_bundle(P2) == dual(tangent_bundle(P2)) 
+julia> cotangent_bundle(P2) == dual(tangent_bundle(P2))
 true
 
 ```
@@ -1071,7 +1071,7 @@ AbstractVariety of dim 2
 julia> canonical_class(P2) == chern_class(cotangent_bundle(P2), 1)
 true
 
-julia> canonical_class(P2) 
+julia> canonical_class(P2)
 -3*h
 
 ```
@@ -1348,7 +1348,7 @@ end
 
 Return the product $X\times Y$. Alternatively, use `*`.
 
-!!! note 
+!!! note
     If both `X` and `Y` have been given a polarization, $X\times Y$ will be endowed with the polarization corresponding to the Segre embedding.
 
 ```jldoctest
@@ -1473,7 +1473,7 @@ end
     +(F::AbstractBundle, G::AbstractBundle)
     -(F::AbstractBundle, G::AbstractBundle)
     *(F::AbstractBundle, G::AbstractBundle)
-    
+
 Return `-F`, the sum `F` $+ \dots +$ `F` of `n` copies of `F`, `F` $+$ `G`, `F` $-$ `G`, and the tensor product of `F` and `G`, respectively.
 
 # Examples
@@ -1554,7 +1554,7 @@ end
 @doc raw"""
     symmetric_power(F::AbstractBundle, k::Int)
     symmetric_power(F::AbstractBundle, k::RingElement)
-    
+
 Return the `k`-th symmetric power of `F`. Here, `k` can contain parameters.
 """
 function symmetric_power(F::AbstractBundle, k::Int)
@@ -1665,7 +1665,7 @@ basis(X::AbstractVariety, k::Int) = basis(X)[k+1]
 @doc raw"""
     betti_numbers(X::AbstractVariety)
 
-Return the Betti numbers of the Chow ring of `X`. 
+Return the Betti numbers of the Chow ring of `X`.
 
 !!! note
     The Betti number of `X` in a given degree is the number of elements of `basis(X)` in that degree.
@@ -1787,7 +1787,7 @@ end
     intersection_matrix(X::AbstractVariety)
 
 If `b = vcat(basis(X)...)`, return `matrix([integral(bi*bj) for bi in b, bj in b])`.
-    
+
     intersection_matrix(a::Vector, b::Vector)
 
 Return `matrix([integral(ai*bj) for ai in a, bj in b])`.
@@ -2119,7 +2119,7 @@ function zero_locus_section(F::AbstractBundle; class::Bool=false)
     Z.O1 = Z(X.O1.f)
   end
   iₓ = x -> x.f * cZ
-  iₓ = map_from_func(iₓ, Z.ring, X.ring)
+  iₓ = MapFromFunc(Z.ring, X.ring, iₓ)
   @assert R isa MPolyQuoRing
   i = AbstractVarietyMap(Z, X, Z.(gens(base_ring(R))), iₓ)
   i.T = pullback(i, -F)
@@ -2424,9 +2424,9 @@ function projective_bundle(F::AbstractBundle; symbol::String = "z")
   X, r = F.parent, F.rank
   !(r isa Int) && error("expect rank to be an integer")
   R = X.ring
- 
+
   # construct the ring
-  
+
   w = vcat([1], gradings(R))
   R1, (z,), imgs_in_R1 = graded_polynomial_ring(X.base, [symbol], symbols(R); weights = w)
   if R isa MPolyQuoRing
@@ -2436,7 +2436,7 @@ function projective_bundle(F::AbstractBundle; symbol::String = "z")
   end
   pback = hom(PR, R1, imgs_in_R1)
   pfwd = hom(R1, R, pushfirst!(gens(R), R()))
-  
+
   # construct the relations
 
   rels = [sum(pback(chern_class(F, i).f) * z^(r-i) for i in 0:r)]
@@ -2445,19 +2445,19 @@ function projective_bundle(F::AbstractBundle; symbol::String = "z")
   end
   APF = quo(R1, ideal(rels))[1]
   z = APF(z)
-  
+
   # construct the abstract variety
-  
+
   PF = AbstractVariety(X.dim+r-1, APF)
   pₓ = x -> X(pfwd(div(simplify(x).f, simplify(PF(z^(r-1))).f)))
-  pₓ = map_from_func(pₓ, PF.ring, X.ring)
+  pₓ = MapFromFunc(PF.ring, X.ring, pₓ)
   p = AbstractVarietyMap(PF, X, PF.(imgs_in_R1), pₓ)
   if isdefined(X, :point)
     PF.point = p.pullback(X.point) * z^(r-1)
   end
   p.O1 = PF(z)
   PF.O1 = PF(z)
-  S = AbstractBundle(PF, 1, 1-z) 
+  S = AbstractBundle(PF, 1, 1-z)
   Q = pullback(p, F) - S
   p.T = dual(S)*Q
   if isdefined(X, :T)
@@ -2506,7 +2506,7 @@ end
 @doc raw"""
     abstract_grassmannian(k::Int, n::Int; base::Ring = QQ, symbol::String = "c")
 
-Return the abstract Grassmannian $\mathrm{G}(k, n)$ of `k`-dimensional subspaces of an 
+Return the abstract Grassmannian $\mathrm{G}(k, n)$ of `k`-dimensional subspaces of an
 `n`-dimensional vector space.
 
 !!! note
@@ -2544,7 +2544,7 @@ true
 ```
 """
 function abstract_grassmannian(k::Int, n::Int; base::Ring = QQ, symbol::String = "c")
-  @assert k < n 
+  @assert k < n
   d = k*(n-k)
   R, c = graded_polynomial_ring(base, symbol => 1:k; weights = 1:k)
   inv_c = sum((-sum(c))^i for i in 1:n) # this is c(Q) since c(S)⋅c(Q) = 1
@@ -2570,8 +2570,8 @@ end
     abstract_flag_variety(dims::Int...; base::Ring = QQ, symbol::String = "c")
     abstract_flag_variety(dims::Vector{Int}; base::Ring = QQ, symbol::String = "c")
 
-Given integers, say, $d_1, \dots, d_{k}, n$ with $0 < d_1 < \dots < d_{k} < n$ or a vector of such integers, 
-return the abstract flag variety $\mathrm{F}(d_1, \dots, d_{k}; n)$ of nested sequences of subspaces of 
+Given integers, say, $d_1, \dots, d_{k}, n$ with $0 < d_1 < \dots < d_{k} < n$ or a vector of such integers,
+return the abstract flag variety $\mathrm{F}(d_1, \dots, d_{k}; n)$ of nested sequences of subspaces of
 dimensions $d_1, \dots, d_{k}$ of an $n$-dimensional vector space.
 
 !!! note
@@ -2646,8 +2646,8 @@ end
     flag_bundle(F::AbstractBundle, dims::Int...; symbol::String = "c")
     flag_bundle(F::AbstractBundle, dims::Vector{Int}; symbol::String = "c")
 
-Given integers, say, $d_1, \dots, d_{k}, n$ with $0 < d_1 < \dots < d_{k} < n$ or a vector of such integers, 
-and given an abstract bundle $F$ of rank $n$, return the abstract flag bundle of nested sequences 
+Given integers, say, $d_1, \dots, d_{k}, n$ with $0 < d_1 < \dots < d_{k} < n$ or a vector of such integers,
+and given an abstract bundle $F$ of rank $n$, return the abstract flag bundle of nested sequences
 of subspaces of dimensions $d_1, \dots, d_{k}$ in the fibers of $F$.
 
 !!! note
@@ -2697,19 +2697,19 @@ end
 function flag_bundle(F::AbstractBundle, dims::Vector{Int}; symbol::String = "c")
   X, n = F.parent, F.rank
   !(n isa Int) && error("expect rank to be an integer")
-  
+
   # compute the ranks of successive subqotients and the relative dimension
-  
+
   if dims[end] < n # the last dim can be omitted
     dims = vcat(dims, [n])
   end
   l = length(dims)
   ranks = pushfirst!([dims[i+1]-dims[i] for i in 1:l-1], dims[1])
   @assert all(>(0), ranks) && dims[end] <= n
   d = sum(ranks[i] * sum(dims[end]-dims[i]) for i in 1:l-1)
-  
+
   # construct the ring
-  
+
   R = X.ring
   if R isa MPolyQuoRing
     PR = base_ring(R)
@@ -2722,9 +2722,9 @@ function flag_bundle(F::AbstractBundle, dims::Vector{Int}; symbol::String = "c")
   R1, gens_for_rels_R1, imgs_in_R1 = graded_polynomial_ring(X.base, syms, symbols(PR); weights = w)
   pback = hom(PR, R1, imgs_in_R1)
   pfwd = hom(R1, R, vcat(repeat([R()], n), gens(R)))
-  
+
   # compute the relations
-  
+
   c = [1+sum(gens_for_rels_R1[dims[i]+1:dims[i+1]]) for i in 1:l-1]
   pushfirst!(c, 1+sum(gens_for_rels_R1[1:dims[1]]))
   Rx, x = R1[:x]
@@ -2740,16 +2740,16 @@ function flag_bundle(F::AbstractBundle, dims::Vector{Int}; symbol::String = "c")
   c = AFl.(c)
 
   # construct the abstract_variety
-  
-  Fl = AbstractVariety(X.dim + d, AFl)  
+
+  Fl = AbstractVariety(X.dim + d, AFl)
   Fl.bundles = [AbstractBundle(Fl, r, ci) for (r,ci) in zip(ranks, c)]
   section = prod(top_chern_class(E)^sum(dims[i]) for (i, E) in enumerate(Fl.bundles[2:end]))
   if isdefined(X, :point)
     Fl.point = pback(X.point.f) * section
   end
   pˣ = Fl.(imgs_in_R1)
   pₓ = x -> (@warn("possibly wrong ans"); X(pfwd(div(simplify(x).f, simplify(section).f))))
-  pₓ = map_from_func(pₓ, Fl.ring, X.ring)
+  pₓ = MapFromFunc(Fl.ring, X.ring, pₓ)
   p = AbstractVarietyMap(Fl, X, pˣ, pₓ)
   p.O1 = simplify(sum((i-1)*chern_class(Fl.bundles[i], 1) for i in 1:l))
   Fl.O1 = p.O1

experimental/IntersectionTheory/src/Types.jl

@@ -124,11 +124,11 @@ mutable struct AbstractVarietyMap{V1 <: AbstractVarietyT, V2 <: AbstractVarietyT
   codomain::V2
   dim::Int
   pullback::AffAlgHom
-  pushforward::FunctionalMap
+  pushforward::MapFromFunc
   O1::MPolyDecRingOrQuoElem
   T::AbstractBundle{V1}
   function AbstractVarietyMap(X::V1, Y::V2, fˣ::AffAlgHom, fₓ=nothing) where {V1 <: AbstractVarietyT, V2 <: AbstractVarietyT}
-    if !(fₓ isa FunctionalMap) && isdefined(X, :point) && isdefined(Y, :point)
+    if !(fₓ isa MapFromFunc) && isdefined(X, :point) && isdefined(Y, :point)
       # pushforward can be deduced from pullback in the following cases
       # - explicitly specified (f is relatively algebraic)
       # - X is a point
@@ -141,7 +141,7 @@ mutable struct AbstractVarietyMap{V1 <: AbstractVarietyT, V2 <: AbstractVarietyT
         end;
         sum(integral(xi*fˣ(yi))*di for (i, xi) in zip(dim(Y):-1:0, x[dim(X)-dim(Y):dim(X)])
             if xi !=0 for (yi, di) in zip(basis(Y, i), dual_basis(Y, i))))
-      fₓ = map_from_func(fₓ, X.ring, Y.ring)
+      fₓ = MapFromFunc(X.ring, Y.ring, fₓ)
     end
     f = new{V1, V2}(X, Y, X.dim-Y.dim, fˣ)
     try
@@ -179,4 +179,3 @@ end
     return X
   end
 end
-

experimental/IntersectionTheory/src/blowup.jl

@@ -100,7 +100,7 @@
 
   # we construct E as the projective bundle PN of N, see [E-H, p 472]
 
-  E = projective_bundle(N) 
+  E = projective_bundle(N)
   AE, RE = E.ring, base_ring(E.ring)
   g = E.struct_map
   ζ = g.O1  # the first Chern class of O_E(1)
@@ -124,7 +124,7 @@
   degs = [degree(Int, Z(gs[i])) + 1 for i in 1:ngs]
   degsRX = [Int(degree(g)[1])  for g in gens(RX)]
   RBl, ev, xv = graded_polynomial_ring(X.base, syms, symbols(RX); weights = vcat(degs, degsRX))
-  
+
   RXtoRBl = hom(RX, RBl, xv) # fˣ on polynomial ring level
   jₓgˣ = x -> sum(ev .* RXtoRBl.(sect(x.f))) # AZ --> RBl
 
@@ -163,7 +163,7 @@
     rhs = sum([jₓgˣ(Z(gs[j]) * cN[k]) * (-ev[end])^(rN-k) for k in 1:rN])
     push!(Rels, lhs - rhs)
   end
- 
+
   Rels = minimal_generating_set(ideal(RBl, Rels)) ### TODO: make this an option?
   ABl, _ = quo(RBl, Rels)
   Bl = abstract_variety(X.dim, ABl)
@@ -175,15 +175,15 @@
   RBltoRX = hom(RBl, RX, vcat(repeat([RX()], ngs), gens(RX)))
   fₓ = x -> (xf = simplify(x).f;
 	     X(RBltoRX(xf));)
-  fₓ = map_from_func(fₓ, ABl, AX)
+  fₓ = MapFromFunc(ABl, AX, fₓ)
   f = AbstractVarietyMap(Bl, X, Bl.(xv), fₓ)
   Bl.struct_map = f
   if isdefined(X, :point) Bl.point = f.pullback(X.point) end
 
   # pullback of j
-  
+
   jˣ = vcat([-ζ * g.pullback(Z(xi)) for xi in gs], [g.pullback(i.pullback(f)) for f in gens(AX)])
-  
+
   # pushforward of j: write as a polynomial in ζ, and compute term by term
 
   REtoRZ = hom(RE, RZ, pushfirst!(gens(RZ), RZ()))
@@ -195,7 +195,7 @@
 	      xf -= q * ζ.f^k
 	    end;
 	    Bl(ans))
-  jₓ = map_from_func(jₓ, AE, AX)
+  jₓ = MapFromFunc(AE, ABl, jₓ)
   j = AbstractVarietyMap(E, Bl, jˣ, jₓ)
 
   # the normal bundle of E in Bl is O(-1)
@@ -339,15 +339,15 @@
   X⁺ = abstract_variety(X.dim, AX⁺)
 
   set_attribute!(X⁺, :description => "$X")
-  fₓ = map_from_func(x -> error("not defined"), X⁺.ring, X.ring)  # TODO check this
+  fₓ = MapFromFunc(X⁺.ring, X.ring, x -> error("not defined"))  # TODO check this
   f = AbstractVarietyMap(X⁺, X, X⁺.(xv), fₓ)
   X⁺.struct_map = f
   X⁺.T = pullback(f, X.T)
   f.T = AbstractBundle(X⁺, X⁺(0)) # there is no relative tangent bundle
   X⁺.point = f.pullback(X.point)
   if isdefined(X, :O1) X⁺.O1 = f.pullback(X.O1) end
   jˣ = vcat(Z.(gs) .* c, [i.pullback(f) for f in gens(AX)])
-  j_ = map_from_func(x -> X⁺(jₓ(x)), Z.ring, X⁺.ring)
+  j_ = MapFromFunc(Z.ring, X⁺.ring, x -> X⁺(jₓ(x)))
   j = AbstractVarietyMap(Z, X⁺, jˣ, j_)
   return j
 end