MaplePrimes Activity

These are questions asked by ContrapuntoBrowniano

Hi! I'm trying to find out if i can construct a sequence fn that generates all the (positive) rational numbers as n goes to infinity.

This is, the sequence shows to be an injective homomorphism fn: N -> Q+ . This sequence was constructed by cantor in his proof of rationals being countably infinite, and can really be helpful in evaluating expressions using rational numbers, but i do not knoww if it is implemented in maple, or how to construct it myself. 

Any help would be very appreciated. 

Hi! I need to simplify a polynomial over an arbitrary field F on a radical variable ν, such that for some power j, ν is in F.

the polynomial takes the form:


but, since νj is in F, this divides every element νi/j into a cotient group of order j, so this can be rewritten as a radical extension of F, in the form: 


where ki, ai are in F. I feel like this is a very straightforward technique for handwritten algebra, but i can't see a command for this on Maple 18. Nor the simplify(..., radicals) Or the combine(...,radicals) seems to help here. Maybe there's an special command for this? Must i do it myself? Please, any help is aprecciated.

Hi! This is probably simple, but
I would like to know if there's an specific algorithm to do this:

let B = {x[i], i=1..n} in such a way that:

f( B ) = Sum(a[i]*b[i], i=1..N); a_i in R; b_i in B; N>n.

so Linearcomb: f->V(R).

Linearcomb( f ) =

 (Sum(a[j],j in J))*x[1]+(Sum(a[k],k in K))*x[2] + ... +(Sum(a[z],z in Z))*x[n].

with V(R) a vector space; R the Real numbers, and B the base. Neither the "factorize", nor the "simplify" are proving useful to this. Is there something i'm missng?

Is there any command that allows me to extract the input number of any function f?


f: (x1; x2;...;xn)-> y

command (f)=n

thanks for the help!

I need to define a simple recursive algorithm (i'm not a programmer) such that:



with i=0,1,...,n; 

and with all xi's elements of a Set A

how can i achieve this?

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