Add zero_basis (#377)

* Add zero_basis

* Fix format

Author: blegat

docs/src/tutorials/Extension/certificate.jl

@@ -99,7 +99,7 @@ model = SOSModel(solver)
 @variable(model, α)
 @objective(model, Max, α)
 basis = MB.FullBasis{MB.Monomial,typeof(x * y)}()
-ideal_certificate = SOSC.Newton(SOSCone(), basis, tuple())
+ideal_certificate = SOSC.Newton(SOSCone(), basis, basis, tuple())
 certificate = Schmüdgen(ideal_certificate, SOSCone(), basis, maxdegree(p))
 @constraint(model, c, p >= α, domain = S, certificate = certificate)
 optimize!(model)

src/Bridges/Constraint/sos_polynomial.jl

@@ -75,7 +75,7 @@ function MOI.Bridges.Constraint.bridge_constraint(
     gram_bases = [gram_basis]
     weights = [MB.constant_algebra_element(typeof(SA.basis(poly)), T)]
     flat_gram_bases, flat_weights, flat_indices = _flatten(gram_bases, weights)
-    new_basis = SOS.Certificate.reduced_basis(
+    new_basis = SOS.Certificate.zero_basis(
         set.certificate,
         MB.explicit_basis(poly),
         domain,
@@ -117,14 +117,14 @@ function MOI.Bridges.Constraint.concrete_bridge_type(
     M = SOS.matrix_cone_type(CT)
     W = SOS.Certificate._weight_type(T, BT)
     B = MA.promote_operation(
-        SOS.Certificate.reduced_basis,
+        SOS.Certificate.zero_basis,
         CT,
         BT,
         SemialgebraicSets.similar_type(DT, T),
         Vector{BT},
         Vector{W},
     )
-    G = SOS.Certificate.gram_basis_type(CT)
+    G = MA.promote_operation(SOS.Certificate.gram_basis, CT)
     return SOSPolynomialBridge{T,F,DT,M,BT,B,_eltype(G),CT,W}
 end
 

src/Certificate/Certificate.jl

@@ -28,11 +28,9 @@ const Index = Union{PreorderIndex,IdealIndex}
 
 abstract type Attribute end
 
-# For get
 function cone end
+function zero_basis end
 function gram_basis end
-# FIXME currently, this returns `MB.MonomialBasis` instead of `MB.MonomialBasis{MT, MVT}`
-function gram_basis_type end
 function reduced_polynomial end
 function ideal_certificate end
 function preprocessed_domain end

src/Certificate/Sparsity/ideal.jl

@@ -14,24 +14,52 @@ struct Ideal{S<:Pattern,C<:SumOfSquares.Certificate.AbstractIdealCertificate} <:
     certificate::C
 end
 
-function Ideal(sp::Variable, basis, cone, maxdegree::Nothing, newton_polytope)
+function Ideal(
+    sp::Variable,
+    gram_basis,
+    zero_basis,
+    cone,
+    maxdegree::Nothing,
+    newton_polytope,
+)
     return error(
         "`maxdegree` cannot be `nothing` when `sparsity` is `Sparsity.Variable`.",
     )
 end
-function Ideal(sp::Variable, basis, cone, maxdegree::Integer, newton_polytope)
-    return Ideal(sp, SumOfSquares.Certificate.MaxDegree(cone, basis, maxdegree))
+function Ideal(
+    sp::Variable,
+    gram_basis,
+    zero_basis,
+    cone,
+    maxdegree::Integer,
+    newton_polytope,
+)
+    return Ideal(
+        sp,
+        SumOfSquares.Certificate.MaxDegree(
+            cone,
+            gram_basis,
+            zero_basis,
+            maxdegree,
+        ),
+    )
 end
 function Ideal(
     sp::Union{Monomial,SignSymmetry},
-    basis,
+    gram_basis,
+    zero_basis,
     cone,
     maxdegree,
     newton_polytope,
 )
     return Ideal(
         sp,
-        SumOfSquares.Certificate.Newton(cone, basis, newton_polytope),
+        SumOfSquares.Certificate.Newton(
+            cone,
+            gram_basis,
+            zero_basis,
+            newton_polytope,
+        ),
     )
 end
 
@@ -44,7 +72,7 @@ function sparsity(
     H, cliques = chordal_csp_graph(basis, SemialgebraicSets.FullSpace())
     return map(cliques) do clique
         return SumOfSquares.Certificate.maxdegree_gram_basis(
-            certificate.basis,
+            certificate.gram_basis,
             clique,
             certificate.maxdegree,
         )
@@ -71,10 +99,11 @@ end
 function SumOfSquares.Certificate.gram_basis(certificate::Ideal, poly)
     return sparsity(poly, certificate.sparsity, certificate.certificate)
 end
-function SumOfSquares.Certificate.gram_basis_type(
+function MA.promote_operation(
+    ::typeof(SumOfSquares.Certificate.gram_basis),
     ::Type{Ideal{S,C}},
 ) where {S,C}
-    return Vector{SumOfSquares.Certificate.gram_basis_type(C)}
+    return Vector{MA.promote_operation(SumOfSquares.Certificate.gram_basis, C)}
 end
 function SumOfSquares.Certificate.reduced_polynomial(
     certificate::Ideal,
@@ -87,14 +116,14 @@ function SumOfSquares.Certificate.reduced_polynomial(
         domain,
     )
 end
-function SumOfSquares.Certificate.reduced_basis(
+function SumOfSquares.Certificate.zero_basis(
     certificate::Ideal,
     basis,
     domain,
     gram_bases,
     weights,
 )
-    return SumOfSquares.Certificate.reduced_basis(
+    return SumOfSquares.Certificate.zero_basis(
         certificate.certificate,
         basis,
         domain,
@@ -103,15 +132,15 @@ function SumOfSquares.Certificate.reduced_basis(
     )
 end
 function MA.promote_operation(
-    ::typeof(SumOfSquares.Certificate.reduced_basis),
+    ::typeof(SumOfSquares.Certificate.zero_basis),
     ::Type{Ideal{S,C}},
     ::Type{B},
     ::Type{D},
     ::Type{G},
     ::Type{W},
 ) where {S,C,B,D,G,W}
     return MA.promote_operation(
-        SumOfSquares.Certificate.reduced_basis,
+        SumOfSquares.Certificate.zero_basis,
         C,
         B,
         D,
@@ -129,8 +158,10 @@ end
 function SumOfSquares.Certificate.zero_basis(certificate::Ideal)
     return SumOfSquares.Certificate.zero_basis(certificate.certificate)
 end
-function SumOfSquares.Certificate.zero_basis_type(
+
+function MA.promote_operation(
+    b::typeof(SumOfSquares.Certificate.zero_basis),
     ::Type{Ideal{S,C}},
 ) where {S,C}
-    return SumOfSquares.Certificate.zero_basis_type(C)
+    return MA.promote_operation(b, C)
 end

src/Certificate/Sparsity/variable.jl

@@ -57,7 +57,7 @@ function sparsity(
     function bases(q)
         return [
             SumOfSquares.Certificate.maxdegree_gram_basis(
-                certificate.multipliers_certificate.basis,
+                certificate.multipliers_certificate.gram_basis,
                 clique,
                 SumOfSquares.Certificate.multiplier_maxdegree(
                     certificate.maxdegree,

src/Certificate/Symmetry/wedderburn.jl

@@ -75,10 +75,18 @@ end
 function SumOfSquares.matrix_cone_type(::Type{<:Ideal{C}}) where {C}
     return SumOfSquares.matrix_cone_type(C)
 end
-function SumOfSquares.Certificate.gram_basis_type(::Type{<:Ideal})
+function MA.promote_operation(
+    ::typeof(SumOfSquares.Certificate.gram_basis),
+    ::Type{<:Ideal},
+)
     return Vector{Vector{MB.FixedPolynomialBasis}}
 end
-SumOfSquares.Certificate.zero_basis_type(::Type{<:Ideal}) = MB.Monomial
+function MA.promote_operation(
+    ::typeof(SumOfSquares.Certificate.zero_basis),
+    ::Type{<:Ideal},
+)
+    return MB.Monomial
+end
 SumOfSquares.Certificate.zero_basis(::Ideal) = MB.Monomial
 function SumOfSquares.Certificate.reduced_polynomial(
     certificate::Ideal,
@@ -91,14 +99,14 @@ function SumOfSquares.Certificate.reduced_polynomial(
         domain,
     )
 end
-function SumOfSquares.Certificate.reduced_basis(
+function SumOfSquares.Certificate.zero_basis(
     certificate::Ideal,
     basis,
     domain,
     gram_bases,
     weights,
 )
-    return SumOfSquares.Certificate.reduced_basis(
+    return SumOfSquares.Certificate.zero_basis(
         certificate.certificate,
         basis,
         domain,
@@ -107,15 +115,15 @@ function SumOfSquares.Certificate.reduced_basis(
     )
 end
 function MA.promote_operation(
-    ::typeof(SumOfSquares.Certificate.reduced_basis),
+    ::typeof(SumOfSquares.Certificate.zero_basis),
     ::Type{Ideal{S,C}},
     ::Type{B},
     ::Type{D},
     ::Type{G},
     ::Type{W},
 ) where {S,C,B,D,G,W}
     return MA.promote_operation(
-        SumOfSquares.Certificate.reduced_basis,
+        SumOfSquares.Certificate.zero_basis,
         C,
         B,
         D,