## variable programing?...

hey is there a easy way to make maple solve an equation with similar different variables,

for eksample

defining the different variables

x_0:=1       x_1:=4           x_2:=10

setting up and equation

solve x * 5

recieving answers for all defined x variables

= [5,20,50]

## back on the horse of course...

Hi, my question is concerning a "summand counting function" i require ie suppose for the following input

of [a+b+c,a+b,a+b+c+d,a] mapping this function will produce the output [3,2,4,1]

## Append number to a list...

Experts,

This may sound like a dumb question, but i'm seeking a procedure to do it better.

with(combinat, setpartition) :
P := [\$2..5] :

Tours := setpartition(P);M:=nops(Tours)

 (1)

number of elements in each 'group'

seq(nops(Tours[i]),i=1..nops(Tours))

 (2)

i need to add 1 to each 'subgroup' : These are the first two:

[[[1,op(Tours[1,1])],[1,op(Tours[1,2])]],[[1,op(Tours[2,1])],[1,op(Tours[2,2])],[1,op(Tours[2,3])]]]

 (3)

I need to add 1 to each 'subgroup' in a more automatic way.

## Vectorization of Symbolic Functions...

Maple provides efficient vectorization and automatic parallelization for many common operators. For example

`x -> 2*~x*~cos~(x*~x)`

But in my application it is common to want to create rather long vectorized operators starting from some complicated symbolic computations. Doing conversions by hand from symbolic expressions to element-wise operations is laborious and error prone.

As a very simple example consider that it is possible to obtain (almost) the same result as above by writing the following as a vectorized operation

`D(x->sin(x^2))~`

But there are at least two problems with this. First of all it is not nearly as efficient as the first operator and second, perhaps not unrelated, is that the datatype returned when applying this operator to a Vector/rtable of hardware floats (e.g. datatype=float[8]) becomes something  more general.

My question is how can I convert a complicated symbolic expression into an efficient numeric element-wise vector operation?

I have tried several different approaches but so far without success. In the case above for example it seemed natural to expect that the following derivative

`D(x->sin~(x^~2))`

would produce a vectorized result, but this is not the case. In another attempt I was unable to see how to perform substitions into an expression, e.g. like this

`unapply(subs(`*`=`*`~, cos=cos~, diff(sin(x),x)), x)`

I would be glad to receive suggestions and/or references to relevant documentation.

## Subtleties between map(...) and the tilde operator...

Hello everyone,

Is it normal that commands #1 and #2 below do not return the same thing ?

L := [`Norman.Mailer`, `Richard.Brautigan`]

#1

map(u -> convert(u, string), L);

["Norman.Mailer", "Richard.Brautigan"]

#2

`convert/string`~(L)

["`Norman.Mailer`", "`Richard.Brautigan`"]

Side question : I am not really familiar with the tilde operator and I often use map instead.
Does it exist a better practice in these matters ?

## how to use foldr to generalize two maps into one m...

let aa = map (+1.2) [1,2]
let bb = map (+1.4) [2,3]
foldr (aa . bb) [3.0,4.0]

## Apply '/' to a list of lists...

I have a long list of two element lists, for example,

A := [ [2,3], [4,5] ,[6,7]];

I want apply '/' to the elements of each sublist.

The result will be

R := [2/3, 4/5, 6/7];

I do not need the list, I could use vectors or matrices.

Is it possible to do this other than by iteration?

Tom Dean

## Kernel of a map between two polynomial rings...

Assume we have a map f from a polynomial ring R to another polynomial ring S, I know how to compute kernel (a generator for the kernel ideal) of these maps by Singular, but I want to know can I do it with Maple too? Thanks.

An example;

Consider the homomorphism f:k[x,y]-->k[u,v] sending x to v and y to v^2 then using Singular;

ring r1=0,(x,y),lp;

ring r2=0,(u,v),lp;

ideal i=v,v2;

map f=r1,i;

setring r1;

kernel(r2,f);

_[1]=x2-y

So at above I took k a field of characteristic zero. The kernel is the ideal generated by x^2-y.

## Plotting the image of a set in the plane...

Hi,

What I want is quite simple but I have not seen it implemented anywhere yet.

I have an explicit map F from the plane into itself. (not an ODE but simply a map)

Then I have a set X, (something like a line segment or a rectangle in the plane) for which I

really need to keep track of the images \$F(X), F^2(X), F^3(X)\$, and so on.

Is there a way to plot the image of a set in Maple?

Thank you very much for your interests in the question.