with(GroupTheory):
G := Group({[[1, 2]], [[3, 4]]});
Orbit(G);
G := Group({[[1, 2], [3, 4]]});
Orbit(G);

GroupTheory:-PermutationGroup(

{module () local cycles, p, d, work; option object; end module,

module () local cycles, p, d, work; option object; end module},

degree = 4)
Error, invalid input: GroupTheory:-Orbit expects its 1st argument, point, to be of type posint, 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, CayleyTable, Centre, DerivedSubgrou...
GroupTheory:-PermutationGroup(

{module () local cycles, p, d, work; option object; end module},

degree = 4)
Error, invalid input: GroupTheory:-Orbit expects its 1st argument, point, to be of type posint, 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, CayleyTable, Centre, DerivedSubgrou...

how to calculate Ferrari resolvent of x^4-c1*x^3+c2*x^2-c3*x+c4

for the questions below

you can use A,B,C as single varible or matrix form if needed

you can use A,B,C as single varible or matrix form if needed

1.how to calculate AA1, AA2 and B2 in terms of A,B,C?

2.how to calculate A,B,C in terms of AA1, AA2 and B2 ?

xrestart;

with(LinearAlgebra):
A := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);
B := Matrix([[b1,b2,b3],[b4,b5,b6],[b7,b8,b9]]);
C := Matrix([[c1,c2,c3],[c4,c5,c6],[c7,c8,c9]]);
#AA1,AA2, C:=seq(Matrix(3, symbol=i), i=[a,b,c]);
#AA1 := Matrix([[aaa1,0,0],[0,aaa1,0],[0,0,aaa1]]);
#AA2 := Matrix([[aab1,0,0],[0,aab1,0],[0,0,aab1]]);
#B2 := Matrix([[aabb1,0,0],[0,aabb1,0],[0,0,aabb1]]);
AA1 := Matrix([[aaa1,aaa2,aaa3],[aaa4,aaa5,aaa6],[aaa7,aaa8,aaa9]]);
AA2 := Matrix([[aab1,aab2,aab3],[aab4,aab5,aab6],[aab7,aab8,aab9]]);
B2 := Matrix([[aabb1,aabb2,aabb3],[aabb4,aabb5,aabb6],[aabb7,aabb8,aabb9]]);
eq2 := C.A+C.B;
eq3 := C.B+C;
eq4 := B+C.A;
ABC := fsolve(map(t->Equate(op(t))[], [eq2=AA1,eq3=AA2,eq4=B2]));

I was using Maple18 for the Ideal Membership Problem. While checking it I got the following error

Error, (in F4:-GroebnerBasis) argument `[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-48,-48,48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]/A1[119295][119295]` is incorrect or out of order

Please tell me, how can I resolve this error ?.

Thank You.

do not know why Basis got error in this case.

how to calculate this Basis?

with(LinearAlgebra):
prej := Matrix([[diff(eq2,a),diff(eq2,b),diff(eq2,c)],[diff(eq3,a),diff(eq3,b),diff(eq3,c)],[diff(eq4,a),diff(eq4,b),diff(eq4,c)]]);
jaco := Determinant(prej);
jaco := -a*b*c^2+c^2;
g3 := [diff(jaco,a),diff(jaco,b),diff(jaco,c)];
K := [r-g3[1],u-g3[2],v-g3[3]];
G := Basis(K, 'tord', degrevlex(r,u,v));

Error, (in LinearAlgebra:-Basis) invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, {list(Vector), set(Vector)}} but received [b*c^2+r, a*c^2+u, 2*a*b*c-2*c+v]

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);

Hi everyone!

I tried to plot the solution of the following ode, but I only got the message error:

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

(file attached)

Problem.mw

https://dl.dropboxusercontent.com/u/66502600/Problem.mw

Please, help me!

Thank you so much!

How I can sketch the helix with parametric equations x=2cost  y=sint  z=t  and the line with parameric equation x=-2t  y=1  z=(pi/2)+t   on a three-dimensional coordinate system?

How I can graph parabolic cylinder y=x^2 and elipsoid x^2+4y^2+4z^2=16 on a three-dimensional coordinate system?

I faced a very large eigenproblem during my research. The square matrix under consideration is of size more than 2^30 times 2^30. I have tried to deal with this problem by the QR algorithm with double implicit shift (more precisely, the Francis double step QR algorithm). I'm a very beginner of programming, but I tried as follows:

--------------------------------------------------------------------------------------------------

A := Matrix([[7, 3, 4, -11, -9, -2], [-6, 4, -5, 7, 1, 12], [-1, -9, 2, 2, 9, 1], [-8, 0, -1, 5, 0, 8], [-4, 3, -5, 7, 2, 10], [6, 1, 4, -11, -7, -1]]):
H := HessenbergForm(A):
p:=6:  
for p while p>2 do: 
q:=p-1: 
s:=H(q,q)+H(p,p):  
t:=H(q,q)*H(p,p)-H(q,p)*H(p,q): 
x:=(H(1,1))^(2)+H(1,2)*H(2,1)-s*H(1,1)+t: 
y:=H(2,1)*(H(1,1)+H(2,2)-s): 
z:=H(2,1)*H(3,2): 
for k from 0 to p-3 do:  
V:=Vector([x,y,z]):   
P:=Transpose(HouseholderMatrix(1/(Norm(V+exp(argument(V(1))*I)*Norm(V,2)*Vector(3,shape=unit[1]),2))*(V+exp(argument(V(1))*I)*Norm(V,2)*Vector(3,shape=unit[1])))):   
r:=max(1,k):
H[k+1..k+3,r..6]:=MatrixMatrixMultiply(Transpose(P),SubMatrix(H,[k+1..k+3],[r..6])):  
r:=min(k+4,6):
H[1..r,k+1..k+3]:=MatrixMatrixMultiply(SubMatrix(H,[1..r],[k+1..k+3]),P):   
x:=H(k+2,k+1):
y:=H(k+3,k+1):   
if k<3 then z:=H(k+4,k+1):   
end if: 
od: 
P:=GivensRotationMatrix(Vector([x,y]),1,2): 
H[q..p,p-2..6]:=MatrixMatrixMultiply(Transpose(P),SubMatrix(H,[q..p],[p-2..6])): 
H[1..p,p-1,p]:=MatrixMatrixMultiply(SubMatrix(H,[1..p],[p-1,p]),P): 
if abs(H(p,q))<10^(-20)*(abs(H(q,q))+abs(H(p,p))) then    H(p,q):=0: p:=p-1:q=p-1:  
elif abs(H(p-1,q-1))<10^(-20)*(abs(H(q-1,q-1))+abs(H(q,q))) then    H(p-1,q-1):=0: p:=p-2:q:=p-1:  
end if:  od:
--------------------------------------------------------------------------------------------------

It seemed that replacing 0 in a Hessenberg matrix by a non-zero element is not allowed. How can I remedy this?

Plus, can anyone tell me the problem of the above thing(it's not really a programming...;( ), please?

I would also appreciate it if someone let me know a better idea for a huge eigenproblem.

Thanks in advance.

Let's say I've got somehow a result of the product:

as series expression and I want to factor out the series of

in order to get

How can I do that with Maple?

There has been a spate of Questions posted in the past week about computing eigenvalues. Invariably, the Questioners have computed some eigenvalues by applying fsolve to a characteristic polynomial obtained from a floating-point matrix via LinearAlgebra:-Determinant. They are then surprised when various tests show that these eigenvalues are not correct. In the following worksheet, I show that the eigenvalues computed by the fsolve@Determinant method (when applied to a floating-point matrix) are 100% garbage for dense matrices larger than about Digits x Digits. The reason for this is that computing the determinant introduces too much round-off error into the coefficients of the characteristic polynomial. The best way to compute the eigenvalues is to use LinearAlgebra:-Eigenvalues or LinearAlgebra:-Eigenvectors. Furthermore, very accurate results can be obtained without increasing Digits.

Download Eigenvalues.mw

I have some preferences for viewing. Specially, I prefer atomic variables to be showed with a different color. So I check mark the related option for this in the view menu. But every time I close and reopen the Maple, it just restore my setting for atomic variables. Suprisingly, this does not happen for other viewing options in the view menu! What should I do? Why is it like this?

Hi,

I was wondering how to go about plotting a Fourier Tranform in Maple.

My assignment is to plot a simple harmonic equation as a Fourier transform, depicting amplitude against fequency.

I've been given: x'' + w^2 x = 0

And want to obtain both the f(x) = a0 sin(wt) + b0cos(wt) form, and a graph of the the amplitude (c^2 =a0^2 + b0^2) against frequency.

I know how to do this on paper but not in Maple, so any help with line commands and layout would be very much appreciated.

Thanks

Hi,

I have an issue calculating an electronics circuit with Maple, using units. I have a current source that I know, and I want to determin the voltage in a capacitor by solving an ODE (except that the current source is defined piecewise). And to make sure I have all the units and scales right, I use the standard unit package. All my variables have their units defined.

Except that Maple doesn't want to solve the equation. It seems to me that it assumes that the function I am trying to solve is unitless, and therefore refuses to solve. 

V__out := 3*Unit('kV');

C__out := 2*Unit('nF');
R__blead := 520*Unit('`k&Omega;`');

I__fly := proc (t) options operator, arrow; Unit('A')*piecewise(t < 3.25*Unit('us'), (1+(-1)*t/(3.25*Unit('us')))*.2, 0) end proc;

dsolve({I__fly(t*Unit('s'))-V__C(t*Unit('s'))/R__blead = C__out*(diff(V__C(t*Unit('s')), t)), V__C(0*Unit('s')) = V__out}, V__C(t*Unit('s')));
Error, (in Units:-Standard:-+) the units `A` and `S` have incompatible dimensions

Is there a way to make Maple assume the unit of what it's trying to solve ? I need it to understands that V__C is in Unit('V') ...

Thanks