how to calculate the polynomial map for a system of  polynomials

assume system of polynomial is in terms of a,b,c

how to find polynomial map

(r - something in terms of a,b,c)

(u - something in terms of a,b,c)

(v - something in terms of a,b,c)

i use normaliser's example's code in maple help file

generators is [50] originally, then i calculated again , it become [51], [52], [53] , i do not know whether virus change my library

https://drive.google.com/file/d/0Bxs_ao6uuBDUb1VzaWQwQlBYLWs/view?usp=sharing

then i use another computer to calculate, the result is [50]

then i further calculate subgroup got error below

with(GroupTheory):
with(group):
G := AlternatingGroup(5);
IsFinite(G);
GroupOrder(G);
spg := SylowSubgroup(5, G);
IsAbelian(spg);
Elements(spg);
lprint(%);
H := Subgroup(Elements(G), spg);
N := Normaliser(G, spg);
#N := Normaliser(spg, G);
Elements(N);
lprint(%);
Elements(G);
H2 := Subgroup({[[5,2],[3,4]]}, G);
H2 := Subgroup(Elements(G), G);
elements2 := convert(Elements(G), 'list');
generators := map(ListTools:-Search, [Perm([[1,2,3]])], elements2);
H2 := Subgroup(generators, G);

H2 := Subgroup(Perm([generators]), G);
Error, invalid input: GroupTheory:-Subgroup expects its 1st argument, generators, to be of type {list, set, identical(undefined)}, but received module () local cycles, p, d, work; option object; end module
H2 := Subgroup(generators, G);
Error, (in Perm:-normalform) invalid input: map expects 2 or more arguments, but received 1

SubgroupMembership(H2, G);

of homomorphism from permutation group 1 to permutation group?

g1 = PermutationGroup([[(2, 3), (4, 5)]])
g2 = PermutationGroup([[(1, 5), (3, 4)]])

ker(hom(g1, g2))

how to calculate the kernel of homomorphism from permutation group 1 to permutation group 2 in maple

and how to prove this make x and y are conjugate by an element of  N?

with(GroupTheory):
with(group):
G := AlternatingGroup(3);

IsFinite(G);

GroupOrder(G);

spg := SylowSubgroup(3, G);

IsAbelian(spg);

Elements(spg);
lprint(%);

H := Subgroup(G, spg);
got error, invalid input here,

GroupTheory:-SylowSubgroup(3, module () local labels, minSupp,

maxSupp, suppSize, AtkinsonsAlgorithm, IsSimpleGroupOrder,

doDerivedSeries, doLowerCentralSeries, Intersection2,

RightCosetRepresentatives, LeftCosetRepresentatives, PRA,

`Giant?`, `Even?`, doStab1, doStab, CycleIndexMonomial;

export generator_list, n, supergroup, Sylows, pCores,

ModulePrint, ModuleDeconstruct, Generators, Orbit, Orbits,

IsTransitive, Transitivity, IsPrimitive, GroupOrder,

Elements, IsAbelian, IsElementary, IsSimple, ConjugacyClass,

ConjugacyClasses, CayleyTable, Centre, DerivedSubgroup,

IsPerfect, DerivedSeries, LowerCentralSeries, NilpotencyClass\

, IsNilpotent, doUpperCentralSeries, UpperCentralSeries,

SylowSubgroup, IsSubgroup, IsNormal, Core, NormalClosure,

Normaliser, Conjugator, AreConjugate, Centraliser,

Intersection, `intersect`, LeftCoset, RightCoset,

RightCosets, LeftCosets, Factor, RandomElement, IsAlternating\

, IsSymmetric, PCore, FittingSubgroup, FrattiniSubgroup,

MatrixRepresentation, Stabiliser, CycleIndexPolynomial,

properties; option object; end module)
Error, invalid input: GroupTheory:-Subgroup expects its 1st argument, generators, to be of type {list, set, identical(undefined)}, but received module () local labels, minSupp, maxSupp, suppSize, AtkinsonsAlgorithm, IsSimpleGroupOrder, doDerivedSeries, doLowerCentralSeries, Intersection2, RightCosetRepresentatives, LeftCosetRepresentatives, PRA, `Giant?`, `Even?`, doStab1, doStab, CycleIndexMonomial; export generator_list, n, supergroup, Sylows, pCores, ModulePrint, ModuleDeconstruct, Generators, Orbit, Orbits, IsTransitive, Transitivity, IsPrimitive, GroupOrder, Elements, IsAbelian, IsElementary, IsSimple, ConjugacyClass, ConjugacyClasses, ...

N := Normaliser(G, spg);

H2 := Subgroup(G, G);

how to find the subgroup G which is finite group here?

elist := Elements(H2);
AreConjugate(elist[1], elist[2], N);

originally x and y are not conjugate,

how to prove this make x and y are conjugate by an element of  N if spg is abelian

where x and y are elements of H2 which is subgroup of G, which is finite group

i guess find subgroup with following command, however, normaliser N can not

make elements of x and y conjugate

H2 := Subgroup(Elements(G), G);
elist := Elements(H2);
AreConjugate(elist[2], elist[3], N); #N*elist[1]*N^(-1) = elist[2]

but it is false,

i use G := AlternatingGroup(5); it is true,

does it mean that this theorem is not for all cases?

how to do differentiation of an ideal in maple?

availables variables : a,b,c

case 1 : all are independent variebles, a,b,c

case 2 : only one independent variable, a

case 3: only one dependent variable a

i find this, but i do not know respect to which variable when differentiate an ideal which has 3 variables and 3 equations

http://www.maplesoft.com/support/help/maple/view.aspx?path=DifferentialAlgebra%2fTools%2fDifferentiate