## How to find coefficients of a convex combination ?...

Hi, I´m new to maple and need help for he following usecase: I have a set of vectors V={v1,v2,...,vn} and a vector v, where v can be expressed as a convex combination of the vectors from V: v = c1*v1+c2*v2+...+cn*vn where c1+c2+...+cn = 1 and all coefficients are non negative How can I find the coefficients c1,c2,...,cn ? I know how to do this for a linear combination, where the coefficients have no constraints. However, here the sum of the coefficients must be 1 and all coefficients must be non negative. hope you can help. kind regards, Andreas

## simultaneous equations...

Solve the pair of simultaneous equation. 4e + 5f = 86 2f - e = 11

## Chain Rule in Maple...

Happy New Year to all! I have a problem here where x=r*exp(a) and y=r*exp(-a). I need to find d(x,y)/d(r,a) in Maple. I used the command below: solve(`∂`(x, y)/`∂`(r, theta)) and got the following result: {r=r,theta=ln(RootOf((r _Z) ∂ ((r)/(_Z))))} I wonder if there are any other methods to check d(x,y)/d(r,a). Many thanx. Antonio.

## Issue: Advanced programming guide M11 as pdf...

Is it just me, where the search functionality of Acrobat does not work in that pdf (it does for the Intro and the User Guide)? Mist! For example searching for 'can' only returns 1 hit: Canada on page 2. For M10 there is not problem to search for s.th. like 'float[8]'.

## Domino Tabloid (Tableaux) of shape A and type B...

If any of the following has been programmed into Maple, then from a sufficient number of small examples, I might be able to "back-engineer" and figure out the solution to the following problem in general. I need help to know if I understand Ian Grant Macdonald's book "Symmetric Functions and Hall Polynomials" (1995, Clarendon Press, 2nd edition), page 109, correctly. I need to know what a domino tabloid of shape A and type B is, where A and B are both partitions of the positive integer N. I need to do this only for the case where A=(N), the partition of length 1. Essentially, I need the formula for the N-th powersum of

## LinearSolve error...

Below are the commands: (where A is the augmented matrix)

with(LinearAlgebra):

A :=

## How to I check ordinary differential equations (OD...

I have been trying to check solutions for ODE in Maple. However, there is a problem. When I go to the ODE Analyzer Assistant and enter a an ODE like: diff(y(x),x)=e^x/(y+2) and press "Solve Symbolically", I get the following message: "cannot use same name "y" to represent both a parameter and a dependent variable of the problem". I wonder if you could help. Thanx a lot! Antonio

## How do I find the Inverse of a mod?...

How do I find the inverse of a mod? eg. the inverse of 7mod27 is 4. How do I get maple to find that? Is there a simple function?

## Sum elements of a set...

Hi, I've searched for this in mapleprimes.com before registering myself in the site, and found nothing. Maybe someone can help me with this. I've generated a set of prime numbers below 1000 using: genprime := proc (n) select(isprime, {\$1 .. n)}) end proc Now I want to sum all the elements from the set genprime(1000). Is it possible? Thanks in advance, André

## Manipulating Imported Data...

Hi, I am very new to maple and have a question. I have a large number of data points in an excel file, which I am trying to overlay onto an equation to see if it fits. I can import the data fine, and the curves seem similar, however, the x values for my data points are all shifted to the left (for various reasons during the recording of the data), so the data is not on top of the curve. I would like it to be. Is there any simple way to manipulate the data in maple, say by adding a number n to all the x values, so that I don't have to go back and do it in excel? Thanks for your help. Evan

## plot vectors...

Hi I am getting a problem with plot. I am trying to plot ka (number of iterations) versus va (error norm) in this worksheet: > with(linalg):with(LinearAlgebra):with(plots):SOS:=proc(x) local n,k; n:=vecdim(x); sum(x[k]^2,k=1..n); end;NJ2Next:=proc(f,x,x0) local val,jac, xn, xn1, val1, val2; val:=eval(subs(x=x0,f)); jac:=eval(jacobian(f,x),x=x0):jac:=inverse(jac); xn:=evalm(x0-jac&*val); val1:=eval(subs(x=xn,f));xn1:=evalm(xn-jac&*val1); val2:=eval(subs(x=xn1,f)); evalm(xn1-jac&*val2); end: > NJ2:=proc(f,x,x0,N) local k, sol, valf, va, ka;sol:=array(0..N):sol[0]:=x0:va:=array(1..N):ka:=array(1..N):valf:=eval(subs(x=x0,f)): for k from 1 to N do sol[k]:=NJ2Next(f,x,sol[k-1]): valf:=eval(subs(x=sol[k-1],f)): va[k]:=evalm(log(norm(sol[k]-sol[k-1],2))):ka[k]:=eval(k):err:=evalm(norm(sol[k]-sol[k-1],2)): od: print(ka):print(va) :plot([ka,va]):end: