Adam Ledger

Mr. Adam Ledger

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4 years, 161 days
unemployed
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Perth, Australia

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These are questions asked by Adam Ledger

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)
 

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

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')))


 

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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)

``


 

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