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-- PHCpack interface for NAG4M2
-- used by ../NumericalAlgebraicGeometry.m2
-- needsPackage "PHCpack"
-- export {Xphc} -- a global variable
-- protect XphcRing;
toRingXphc = method()
toRingXphc (List,List) := (F,G) -> (
R := ring ideal (F|G);
Xphc := getSymbol "phcX";
XphcRing := (coefficientRing R)[Xphc_1..Xphc_(numgens R)];
M := map(XphcRing,R,gens XphcRing);
((M ideal F)_*, (M ideal G)_*)
)
toRingXphc List := F -> first toRingXphc(F,F)
fromRingXphc = method()
fromRingXphc (List,Ring) := (F,R) -> (
XphcRing := ring ideal F;
M := map(R,XphcRing,gens R);
(M ideal F)_*
)
solvePHCpack = method(TypicalValue => List)
solvePHCpack (List,HashTable) := List => (F,o) -> (
-- Anton: options are not used at the moment
PHCpack$solveSystem toRingXphc F
)
trackPHCpack = method(TypicalValue => List)
trackPHCpack (PolySystem, PolySystem, List, HashTable) := List => (S,T,sols,o) -> trackPHCpack(equations S, equations T, sols, o)
trackPHCpack (List,List,List,HashTable) := List => (S,T,sols,o) -> (
-- Anton: options are not used at the moment
--trackPaths(S,T,sols,PHCpack$gamma=>o.NAG$gamma,PHCpack$tDegree=>o.NAG$tDegree)
(T',S') := toRingXphc (T,S);
sols' := sols / (s-> if instance(s,AbstractPoint) then s else point {s});
trackPaths(T',S',sols',gamma=>o.NumericalAlgebraicGeometry$gamma,tDegree=>o.NumericalAlgebraicGeometry$tDegree,Verbose=>(DBG>0))
)
refinePHCpack = method(TypicalValue => List)
refinePHCpack (List,List,HashTable) := List => (T,sols,o) ->
refineSolutions(toRingXphc T, sols,
if o.Bits === infinity
then getDefault Precision
else ceiling(log(10,2)*o.Bits)
)
solveGenericSystemInTorus = method()
solveGenericSystemInTorus PolySystem := F -> solveGenericSystemInTorus equations F
solveGenericSystemInTorus List := F -> (
(vol,S,solsS) := mixedVolume(toRingXphc F, StartSystem=>true);
assert(vol==#solsS);
(fromRingXphc(S,ring ideal F), solsS)
)
numericalIrreducibleDecompositionPHCpack = (I,o) -> PHCpack$numericalIrreducibleDecomposition toRingXphc I_*
dismiss PHCpack
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