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Adam Ledger

Mr. Adam Ledger

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10 years, 10 days
unemployed
hobo
Perth, Australia

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These are questions asked by Adam Ledger

Number of Partitions of a number...

Adam Ledger 360 Maple 2016
partition
January 13 2020
4 2

I couldnt find this command in the number theory package, as far as what i am thinking of doing it should be straight forward but very long winded, so if I have missed this command throughout the packages up to Maple 2016 I would appreciate someone telling me otherwise I suppose it's what i am doing for the next few hours

https://en.wikipedia.org/wiki/Partition_(number_theory)
 

Help with definate sum closed form error...

Adam Ledger 360 Maple
sum
December 19 2019
2 4

Does anyone have any ideas i can try to get arround this error?
 

> 

delta := proc (x, y) options operator, arrow; piecewise(x = y, 1, x <> y, 0) end proc

n-floor(n/eta)*eta+delta(n-floor(n/eta)*eta, 0)*eta = sum(m*(sum(cos(2*Pi*(n+eta-m)*(k-1)/eta)/eta, k = 1 .. eta)), m = 1 .. eta)

> 

diff(diff(delta(x-floor(x/y)*y, 0), x), y) = diff(diff((sum(m*(sum(cos(2*Pi*(x+y-m)*(k-1)/y)/y, k = 1 .. y)), m = 1 .. y)-x+floor(x/y)*y)/y, x), y)

Error, (in SumTools:-DefiniteSum:-ClosedForm) at offset 12 in `:-24717.m`, Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc

  
> 

``


 

Download error.mw

Bug in my Division by Zero Calculator...

Adam Ledger 360 Maple 2016
programming division-by-zero
November 10 2019
0 0

Basically it spits out the subset of values for which a division by zero error will occur for the function you specify on  range you specify for each of it's arguments, but I get an ambigous error when ever exponentiation features in the function I specify, which of course dramatically reduces the application of the calculator. Division,addition,substraction and multiplication are currently the only available arithmetic operators availble for the function window that I know the error will not occur.

If some one can help it is much appriciated

 

DIVISION_BY_ZERO_CALCULATOR.mw

Simplify command on Binomial expressions...

Adam Ledger 360 Maple 2016
simplification
November 09 2019
0 2

Is there something I should be doing whenever I use simplify to avoid things like this, or should I stop using the "is" function all together?

 

> 

interface(showassumed = 0):

 

> 

sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)

(n-k+1)*binomial(n+1, k)/(k+1) = binomial(n+1, k+1)

 (1)
> 

#And we have:
is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1))

FAIL

 (2)
> 

#And since:
is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))

true

 (3)
> 

is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)) = is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))


 

Download main.mw

numtheory package lamba wtf...

Adam Ledger 360 Maple
numtheory
November 08 2019
3 2

Why is lamba protected as something it traditionally isnt for this package?

 


 

> 

restart

lambda(n) = (-1)^Omega(n)

 

 

> 

with(numtheory)

lambda(n) = (-1)^Omega(n)

  

[GIgcd, bigomega, cfrac, cfracpol, cyclotomic, divisors, factorEQ, factorset, fermat, imagunit, index, integral_basis, invcfrac, invphi, iscyclotomic, issqrfree, ithrational, jacobi, kronecker, lambda, legendre, mcombine, mersenne, migcdex, minkowski, mipolys, mlog, mobius, mroot, msqrt, nearestp, nthconver, nthdenom, nthnumer, nthpow, order, pdexpand, phi, pi, pprimroot, primroot, quadres, rootsunity, safeprime, sigma, sq2factor, sum2sqr, tau, thue, varphi]

 (1)
> 

Omega := proc (n) options operator, arrow; bigomega(n) end proc:
> 

numtheory:-lambda(667)

308

 (2)
> 

``


 

Download main.mw

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