i understand quotient group is

G/(normal subgroup)

= G composite with inverse permutation group of normal subrgoup

is this understanding correct?

If do not have subgroup or normal subgroup, how to do quotient group?

if i shift second row many times in order to find Subgroup satisfy G*Subgroup = Subgroup*G

after find Subgroup then test

inverse(g)*Subgroup*g = Subgroup

how to test whether inverse(g)*Subgroup*g belong to Subgroup?

or just use equal in inverse(g)*Subgroup*g = Subgroup?

a*b - b*a    where a , b are permutation group

how to minus this?

if a + b , then how to plus permutation group

assume the word equation is

a_i *a_j - a_j *a_i = 0

how to find which permutation group is a_i and a_j

my understanding is to try all rotations

a book use underscript i and j

can i see them as upper script for i rotations which is shift i times to left for second row

and try all combination and composite them in two for loop? 

we use Modern Computer Algebra

let f=x^15-1 belong to Z[x]. take a nontrivial factorization f≡gh mod 2 with g,h belong to Z[x] monic and of degree at least 2. computer g*,h* belong to Z[x] such that   f≡g*h* mod 16 ,deg g*=deg g, g*≡g mod 2.

show your  intermediate. can  you guess some factors of f in Z[x]?

we use Modern Computer Algebra book  

trace algorithm 15.2 on factoring f=30x^5+39x^4+35x^3+25x^2+9x+2 belong to Z[x].choose the prime p=5003 in step.

Given a 2x2 matrix I am struggling to write a function that would return a list (a,b, a1, a2) of 2 complex numbers followed by 2 vectors such that the set of the 2 vectors is a basis for CxC and also Ab1=ab1, Ab2=Bb2 if these exist

Any ideas would be greatly appreciated

Dear all,

Please someone gave an idea,

I write in maple this line but  I get an error,

> Butcher, map(x->if (x=0) then `` else x end if,Butcher);
Error, invalid arrow procedure

I'm having a weird memory leak problem when I use Compiler, and numerical NAG routines for integration - at least I think it's that combination that's causing it. To see it run this:

First define the functions to use:

F_:=Compiler:-Compile(codegen[prep2trans](codegen[optimize](codegen[makeproc](convert(sinh(x)*sin(x),float),[x]))),optimize=true);

F:=proc(k)
if not (k::numeric) then return 'procname'(args) fi;
F_(k);
end proc;

INT:=proc(X) if not X::numeric then return 'procname'(x) fi; int(F(x),x=0..X,numeric,method=_d01ajc); end proc;

Then evaluate lots of times:

for i to 10^6 do a:=rand()/1e12; INT(a);  od:

And watch your computer memory go wild. I'm using Maple 17 on a new mac with 8Gig RAM, using Mavericks. It doesn't take more than a few minutes to grind the system to a halt. A restart command does not release the memory in the mserver process. [I've noticed similar problems in the past, so it's not locallised to this OS I think.]

On a related note, there's a problem with nested NAG integrals - in the do loop try this:

int('INT'(XX),XX=0..a,numeric,method=_d01akc)-int('INT'(XX),XX=0..a,numeric,method=_d01ajc);

it never gives zero! The problem lies in using the same NAG routine twice [here _d01ajc] for a nested integral. I've never found a way around this bug!

Any help would be much appreciated!

Good afternoon sir.

I am working on problems related to functions which require dynamic geometry program or

the Geometers sketch pad. I request to you to kindly suggest me with regard to the above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Dear all;

Thanks ifor looking and help me in my work. Your remarks are welcome.Description:
 This routine uses the midpoint method to approximate the solution of
     the differential equation $y'=f(x,y)$ with the initial condition $y = y[0]$
     at $x = a$ and recursion starting value $y = y[1]$ at $x = a+h$.  The values
     are returned in $y[n]$, the value of $y$ evaluated at $x = a + nh$.       
                                                                          
Arguments:     
\begin{itemize}
\item  $f$  the integrand, a function of a two variables
                
                \item $y[]$ On input $y[0]$ is the initial value of $y$ at $x = a$, and $y[1]$
                is the value of $y$ at $x = a + h$,
                \item on output for $i \geqslant 2$
             $$ y[i] = y[i-2] + 2h f(x[i],y[i]); \quad \quad x[i] = a + i h.$$
             \end{itemize}

 
CODE USING MAPLE

 Midpoint-Method=proc(f,a,b, N)

h:=(b-a)/N;
x[0]:=a;
y[0]:=1:

 for n from 2 to N do
    x[n] := a+n*h;
    y[n+1] = y[n-1] +  2h f( x[n], y[n] );
od:
// Generate the sequence of approximations for the Improved Euler method
data_midpoint := [seq([x[n],y[n]],n=0..N)]:
//write the function;
F:=(t,y)-> value of function ;

//Generate plot which is not displayed but instead stored under the name out_fig for example
out_fig := plot(data_midpoint,style=point,color=blue)

Your remarks.

Thanks

Let a(1)=916 , a(2)=935 , a(3)=713  , a(4)=845  , a(5)=274  , a(6)=914 ,a(7)=255 . Find formula a(n)= ? ,n=1,2,3,....

I am a new user of Maple. Could anyone help me to know how to call a Maple function/procedure from a Matlab program with a simple example? And conversely, how to call a Matlab function from Maple.

Say we solve numerically and ODE using Maple. Say ode1:= { diff(Q(x),x)= Q(x)/3x , Q(1)=1 }

The solution is a procedure so now suppose we have another ODE where the solution appears.Say  ode2:= { diff(f(x),x)= Q(x)*x , f(1)=4}.

To extract the solution of the first ODE I set sol1:=dsolve(ode1,numeric) and Q:=proc(x) local s: return rhs(sol(x)[2]): end proc:

But now I got an error message when I trying sol2:=dsolve(ode2,numeric).

Is it possible to use a procedure in the definition of the ODE one wants to solve?

Rewrite the code that counts the number of primes less than using an if-then statement.  Implement    your code where j goes from 2 to 15.

j:=1;
                               1
for i from 2 to 10
while ithprime(j)<2^i do
j:=j+1
end:
print(2^i,primes=j-1):
                        2048, primes = 9

I need to edit this code to satisfy a IF then Statement. can any one help me out?

\

regards "Geordi"

In doing multiple linear regression with Statistics:-LinearFit, how do I get or compute the values commonly called R^2 and R^2[adjusted], also known as the coefficient of determination? I know that residualsumofsquares is part of it. I also need the "total sum of squares" to compute R^2. And how do I modify that to get R^2[adjusted]? These things do not seem to be among the numerous output options to LinearFit. These values (R^2 and R^2[adjusted]) are typically part of the output of other statistics software when doing multiple regression.

I'd also like the p - values for the significance of the individual parameters and the p - value for the global utility---also things that are standardly reported by statistics software.