got Strategy=>factor working on getRoots no real speed difference though

NumberFields/KarlsTestingFile.m2

@@ -53,6 +53,9 @@ restart
 
 loadPackage "NumberFields"
 S = QQ[a,b,c]/ideal(a^3-2, a^2+a*b+b^2, sum(apply(11, t->c^t)))
+Ss = S[x]
+f = x^3-2
+time getRoots(f, Strategy=>decompose)
 T = QQ[a,b]/ideal(a^3-2, a^2+a*b+b^2)
 psi = map(S, T)
 R = time numberField(S)

NumberFields/NumberFields.m2

@@ -700,15 +700,30 @@ inverseNumberFieldAutomorphism(RingMap) := opts -> (phi1) -> (
  outputMap 
 )
 
+--given a polynomial f in K[x] and a map K -> L, this forms the image of f in L[x].
+polynomialFieldChange = method(Options => {});
+polynomialFieldChange(RingElement, RingMap) := opts -> (f1,psi1) -> (
+ coeffRing := coefficientRing ring f1;
+ oldVars := gens ring f1;
+ (myVars, myCoeffs) := coefficients f1;
+ error "This is not finished yet.";
+)
 
 getRoots = method(Options =>{Strategy=>decompose});
 getRoots(RingElement) := opts -> (f) -> (
  R := ring f;
+ linearTerms := {};
+ local i;
+ local newLinTerm;
+ local newCoeffs;
+ local newCoeffs2;
+ local newVars;
+ local newVars2;
  if #(gens R) != 1 then error "getRoots: expected a polynomial in a single variable";
  if opts.Strategy === decompose then (
  (S,M, MInv) := (flattenRing (R,Result=>3));
  primeFactors := decompose ideal M(f);
- linearTerms := {};
+
  for i from 0 to ((length primeFactors)-1) do(
  if (degree primeFactors#i_0)#0 == 1 then (
  linearTerms = append(linearTerms, (gens R)_0 - MInv(primeFactors#i_0));
@@ -719,10 +734,28 @@ getRoots(RingElement) := opts -> (f) -> (
  else if (opts.Strategy === factor) then (
  K1 := ((flattenRing(coefficientRing R))#0);
  (K2a, psi1) := simpleExt(K1);
- R2 := K2a[gens R];
- --todo this needs to be written.
+ psi2 := inverse psi1; --this is slow, it would be nice if it was faster
+ (myVars, myCoeffs) := coefficients f;
+ K2 := toField K2a;
+ R2 := K2[gens R];
+ myVars2 := sub(myVars, R2);
+ myCoeffs2 := sub(psi2(sub(myCoeffs, K1)), R2);
+ newf := first first entries (myVars2*myCoeffs2);
+ tempTerms := factor newf;
+ i = 0;
+ while i < #tempTerms do (
+ if ((degree (tempTerms#i#0))#0 == 1) then (
+ (newVars, newCoeffs) = coefficients tempTerms#i#0;
+ newVars2 = sub(newVars, R);
+ newCoeffs2 = psi1(sub(newCoeffs, K2a));
+ linearTerms = append(linearTerms, (gens R)_0 - (entries(newVars2*newCoeffs2))#0#0);
+ );
+ i = i+1;
+ );
+ return linearTerms;
+ --todo this needs to be written.newf
  --we should first find a way to 
- error "getRoots:strategy=>factor not implemented yet";
+ --error "getRoots:strategy=>factor not implemented yet";
  )
  else (
  error "getRoots: not a valid strategy";