DJJerome1976

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These are questions asked by DJJerome1976

I'm doing some work with undirected and directed graphs, and I'm needing to find examples of longest paths and longest cycles.  How may this be done in Maple?

Hi,

I am using A:=LinearAlgebra:-RandomMatrix(10,10,generator=-10..10) to generate a random matrix. How may I specify that every row of A has at least three non-zero entries? 

Thanks!

I am playing around with certain "simple" integrals, and came across this strange behavior in Maple. Maple is able to integrate sin(x)^(1/2)*cos(x)^3, but not sin(x)^(1/3)*cos(x)^3. Any idea why?

trig_integral.mw
 

int(sin(x)^(1/2)*cos(x)^3, x)

-(2/7)*sin(x)^(7/2)+(2/3)*sin(x)^(3/2)

(1)

int(sin(x)^(1/3)*cos(x)^3, x)

int(sin(x)^(1/3)*cos(x)^3, x)

(2)

 

Why does the iscont( ) function declare that the square root function is continous over Riscont_error.mw
 

iscont(sqrt(x), x = -infinity .. infinity)

true

(1)

``


 

Download iscont_error.mw

 

I am able to generate random polynomials with non-zero coefficents, and define sets of all the positive divisors of the leading coefficient and the constant terms. My question is this, how may I apply the rational zeros theorem to generate the set of all possible rational zeros of the polynomial. I basically need to form all the possible quotients (positive and negative) with numerator in one set and denominator in the other set, ignoring duplicates. The attached worksheet has what I've done so far.rational_zeros.mw
 

attempt := 1; while attempt > 0 do q := randpoly(x, coeffs = rand(-9 .. 9), degree = 3, dense); if nops(q) = 4 then attempt := -2 end if; attempt := attempt+1 end do; q

5*x^3+3*x^2-4*x-8

(1)

NumberTheory[Divisors](coeff(q, x, 3))

{1, 5}

(2)

NumberTheory[Divisors](coeff(q, x, 0))

{1, 2, 4, 8}

(3)

``


 

Download rational_zeros.mw

 

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