I suppose you would have to programme this, because I couldn't find anything relating to vector spaces in my Maplesoft Linear Algebra tutor or package.

My question really is, you have a problem like, the set of all pairs of real numbers of the form (1,x) with the operations (1,y)+(1,y')=(1,y+y') and k(1,y)=(1,ky) 

( ^ taken straight out of my homework haha)

and you run through the 10 vecctor space axioms to determine whether it fails and it not a vector space, or it passes all and it is a vector space.

Is there a way to do this in Maplesoft?

which method i input a series of random number it output a periodic waveform

Hello dear all,

I use maple 16, x64. When I run this code:

Student[Calculus1][ApproximateInt](cos(y/(-1+y)), y = 0 .. 1, method = lower, iterations = 1)

it results in "0.0667344650", exactly equal with the result of executing

Student[Calculus1][ApproximateInt](cos(y/(-1+y)), y = 0 .. 1, method = lower, iterations = 10000000000)

Any idea?

Best regards

How to do composition for finite group?

is the composition like permutation group ?

if express finite group like permutation group,

if so, can elements in first row duplicate? can the second row duplicate?

however, do not know how to map when there are more than or equal two choices

my guess is that

if finite group can be expressed into permutation group

for example 3*3 matrx, each column is a permutation group

then there will be 3 permutation groups, when do composition , first column's permutation group composite with first column's permutation group , second composite with second etc

is it right?

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,....