Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

Requesting a code to compute (and graph) the following self referencing sequence:

a(1)=1. If a(n) is a novel term (seen for the first time) then a(n+1)= d(a(n)) where d(k) is the number of divisors of k. 
if a(n) has been seen before then a(n+1) = a(n)+m where m is the least prior term which has not already been used in this way (once m is used it cannot be used again).

Sequence starts:

1,1,2,2,3,2,4,3,5,2,4,6,4,7,2,5,7,11,2...,

note that there are often multiple copies of the least unused term, which might make accounting for them tricky. 

Thanks in advance 

 

 

Can anyone please help with this?  I don't know what is the problem in this code.

 

restart; _EnvExplicit := true; with(DEtools); with(PDEtools); with(plots)

true

(1)

NULL

Check*the*constraint

eq1 := diff(X(z), z, z)+((diff(H(z), z))/H(z)-2/(1+z))*(diff(X(z), z))+exp(-sqrt(2/3)*X(z))*ZETA*(diff(Y(z), z))^2/(2*sqrt(6))-Y(z)*exp(-sqrt(2/3)*X(z))*(1-exp(-sqrt(2/3)*X(z)))/(2*H(z)^2*sqrt(6)*(1+z)^2) = 0

eq2 := diff(Y(z), z, z)+((diff(H(z), z))/H(z)-2/(1+z))*(diff(Y(z), z))-(1/3)*sqrt(6)*(diff(X(z), z))*(diff(Y(z), z))+(1-(1/2)*exp(-sqrt(2/3)*X(z)))/(2*ZETA*H(z)^2*(1+z)^2) = 0

eq3 := -2*H(z)*(1+z)*(diff(H(z), z))+3*H(z)^2+(1/2*((diff(X(z), z))^2+(1/2)*ZETA*exp(-sqrt(2/3)*X(z))*(diff(Y(z), z))^2))*H(z)^2*(1+z)^2-(1/4)*exp(-sqrt(2/3)*X(z))*Y(z)*(1-(1/2)*exp(-sqrt(2/3)*X(z))) = 0

-2*H(z)*(1+z)*(diff(H(z), z))+3*H(z)^2+((1/2)*(diff(X(z), z))^2+(1/4)*ZETA*exp(-(1/3)*6^(1/2)*X(z))*(diff(Y(z), z))^2)*H(z)^2*(1+z)^2-(1/4)*exp(-(1/3)*6^(1/2)*X(z))*Y(z)*(1-(1/2)*exp(-(1/3)*6^(1/2)*X(z))) = 0

(2)

NULL

``

NULL

NULL

diffux := solve(eq1, dif(H(z), z))

diffur := solve(eq2, dif(H(z), z))

NULL

NULL

NULL

NULL

NULL

NULL

``

Numeric*code

with(ListTools)

Seed := randomize()

with(stats[random])

sys := {subs(ZETA = 10, eq1), subs(ZETA = 10, eq2), subs(ZETA = 10, eq3)}

NULL

vv := 10^100; savf := []; L := 0; Digits := 30; MM := []; MMM := []; N := 1; kkk := []; MM; []; MMM := []

"for hh  from 1 by 1 to 1 do:L:=0: F:=0: b:=1: t:=2:while (t>b)do:"

n := 1.9; ZETA := 10; i := uniform[.60658, 1](N); ics := Y(i) = 1.8, (D(Y))(i) = 0, X(1) = .4, (D(X))(i) = 0, H(i) = .7; solution := dsolve({ics, op(subs(ZETA = 10, sys))}, {H(z), X(z), Y(z)}, type = numeric, method = bvp, output = listprocedure); m := [subs(solution, X(z))]; kk := [subs(solution, Y(z))]

"if op(kk(0))>.7 then  t:=(b)/(5): else t:=5*b :end if:end do: for T  from i by 10^(-1) to 1 do ls[T] := sqrt(0.29995*(1+ T)^(3)+5*10^(-5)*(1+ T)^(4)+0.7): sr[T] := op(kk(T)): L := L+(sr[T]-ls[T])^2 end  do:F:=sqrt(L): if F<vv  then vv:=F; sol:=solution:MM:=[op(MM),[vv,op(kk(1))]]:hhh:=vv:Pa:=[g,i]:else vv:=vv: MMM:=[op(MMM),vv]:end if:end do:"

Error, (in unknown) solution is only defined in the range .88696222680754726..1.

 

NULL

``

RH := subs(sol, Y(z)); Ry := subs(sol, X(z))

Error, invalid input: subs received sol, which is not valid for its 1st argument

 

Error, invalid input: subs received sol, which is not valid for its 1st argument

 

1-Mrad(1)+Rx(1)+Ry(1)

1-Mrad(1)+Rx(1)+Ry(1)

(3)

with(plots)

defHLCDM := sqrt(.29995*(1+z)^3+5*10^(-5)*(1+z)^4+.7)

plotqLCDM := plot((1+z)*(diff(defHLCDM, v))/defHLCDM-1, z = 0 .. 10, color = green, legend = ["q LCDM"])

plotqfR := [odeplot(sol, [z, Pa[1]*y(z)/(Pa[1]-1)+1], z = 0 .. 10, color = blue, legend = ["q R^n"])]; display(plotqLCDM, plotqfR)

plotHLCDM := plot(sqrt(.29995*(1+z)^3+5*10^(-5)*(1+z)^4+.7), z = 0 .. Pa[2], color = green, legend = ["H LCDM"], axes = boxed)

plotHfR := [odeplot(sol, [z, psi(z)], z = 0 .. Pa[2], color = blue, legend = ["H R^n"], axes = boxed)]; display(plotHLCDM, plotHfR)

 

psi*curve*fit

with(plots)

with(ListTools)

with(CurveFitting)

points1 := PolynomialInterpolation([[0, RH(0)], [1, RH(1)], [10, RH(10)], [100, RH(100)], [400, RH(400)], [800, RH(800)], [1200, RH(1200)], [1600, RH(1600)], [2000, RH(2000)], [2400, RH(2400)], [2800, RH(2800)], [3200, RH(3200)], [3600, RH(3600)], [4000, RH(4000)], [4400, RH(4400)], [4600, RH(4600)], [4800, RH(4800)], [5000, RH(5000)], [5200, RH(5200)], [5400, RH(5400)], [5600, RH(5600)], [5800, RH(5800)], [6000, RH(6000)], [6200, RH(6200)], [Pa[2], RH(Pa[2])]], v)

 

sd := plot(points1, z = 0 .. Pa[2], color = red, legend = ["curve fit"])

Error, (in plot) expecting a real constant as range endpoint but received Pa[2]

 

points11 := [[0, RH(0)], [.1, RH(.1)], [1, RH(1)], [10, RH(10)], [100, RH(100)], [400, RH(400)], [800, RH(800)], [1200, RH(1200)], [1600, RH(1600)], [2000, RH(2000)], [2400, RH(2400)], [2800, RH(2800)], [3200, RH(3200)], [3600, RH(3600)], [4000, RH(4000)], [4400, RH(4400)], [4600, RH(4600)], [4800, RH(4800)], [5000, RH(5000)], [5200, RH(5200)], [5400, RH(5400)], [5600, RH(5600)], [5800, RH(5800)], [6000, RH(6000)], [6200, RH(6200)], [Pa[2], RH(Pa[2])]]

sd := plot(points1, z = 0 .. Pa[2], color = red, legend = ["curve fit"], axes = boxed)

pntplot1 := pointplot(points11, symbol = BOX)

polycurve := PolynomialInterpolation(points11, z)

polyplot := plot(polycurve, z = 0 .. Pa[2], axes = boxed)

display([plotHLCDM, sd])

 

``

NULL

``

 

 

``

Luminosity*distnace

eq1h := diff(Hdi1(z), z)-1/points1 = 0

eq2h := diff(Hdi2(z), z)-1/defHLCDM = 0

sysh := {eq1h, eq2h}

icsh := Hdi1(0) = 0, Hdi2(0) = 0; solutionh := dsolve({icsh, op(sysh)}, {Hdi1(z), Hdi2(z)}, type = numeric, output = listprocedure)

plotLDistanceCFIT := [odeplot(solutionh, [z, (1+z)*Hdi1(z)], 0 .. Pa[2], color = blue, legend = ["Luminosity distance Curve fit"])]; plotLDistanceLCDM := [odeplot(solutionh, [z, (1+z)*Hdi2(z)], 0 .. Pa[2], color = red, legend = ["Luminosity distance LCDM"])]; display(plotLDistanceCFIT, plotLDistanceLCDM)

 

``

``

 

 

 

Download DistanceModulus.mw

 

sum2N := proc (N::integer) local summation, i, k; summation := 0; k := 0;

for i from 0 to N do if i = 1 then k := k+1

end if; summation := (i+k)^2 end do

end proc;
sum2N(10);

the result shows 121 but its not correct i think the right answer show be 2985
 

Hello MaplePrimes, 

So, I have used the discont=true option in the past and it has worked fine for me but for some reason with these functions I am using now the plots are still containing the veritcal asymptotes. Anyone spot something I am forgetting or doing incorrectly?

I have attached my maple file for easy viewing. 

Thanks. 

DiscontQuestion.mw

 

See A342180 in OEIS. Two codes have been written for this, one in Python (17 terms found), the other in Mathematica (33 terms). Could a Maple code go beyond a(33), assuming higher terms exist? 

This question may be a little dumb, but how can I calculate the resultant of two homogeneous polynomials with two variables according to these variables? Say resultant(f,g,{x,y}), where f(x,y) and g(x,y) are homogeneous polynomials with degree m and n, respectively. Any help would be greatly appreciated!

RootOfQuestion.mw

Hi Everyone, so i understand (to the best of my knowledge) the purpose of RootOf and I have worked with them before but now for some reason when i try to use allvalues to express the solution explicitly it does not express it, instead just keeps as RootOf expression. 

I have attached the maple file I am working with. 

I have also tried solve(expr, explicit) as well as convert(expr, radical) and still nothing. 

Am I missing something small? 

here is my try

for ploting points of data ( d(n(, sum(n))

new.mw

Here is my try to integrate the expression L with trapozoid or simpson 

numerical_int.mw

I am trying to solve this type of problem:

I thought I could double check my answers by creating a RandomVariable and calculating the probablity using the Probability function.

But from the RandomVariables documentation,  it seems only univariate random variables are supported.

Is there really no way to define a RandomVariable given a joint distribution?

Requesting a procedure to calculate primes p for which there exists a prime q <= p such that pi(p)=q-pi(q), where pi is the prime counting function. If possible options to select output as p, or as (p,q).

p list starts:2,13,17,29,31,43.....

q list starts: 2,11,13,17,19,23...

Thanks in advance,

David.

The input

f(x) := x^2;

n := evalf(int(f(x)^2, x = 0 .. 1));

f(x) :=  f(x)/n;

plot(f(x), x = 0 .. 1)

leads to the error

Error, (in f) too many levels of recursion
I need to reassign the function as itself divided by n that depends on the old f...

A piece of code like this is supposed to be inside a loop, so creating f_new(x):=f(x)/n doesn't solve the issue.

If it was a cpp code I'd write something like f(x)/=n for every x. How can I do it in Maple?

Thank you in advance for you answers!

I have two functions, f(x) and g(x).

Based the plot, I can see that they intersect around x equals 0, 1, around 4.5 and 10.

So I tried to find the numerical solution by solving f(x) -  g(x) for x assuming x is real.

I'm stuck here because the aswer involves RootOf and _Z and I don't know what to do next.

This is what I've tried so far:
 

``

``

"f(x):=18*log10(x)"

proc (x) options operator, arrow; 18*log10(x) end proc

(1)

"g(x):=1/(2) x^(3)-8*x^(2)+(69/(2))^()*x-27"

proc (x) options operator, arrow; (1/2)*x^3-8*x^2+(69/2)*x-27 end proc

(2)

plot([f(x), g(x)], x = -1 .. 11)

 

``

`assuming`([solve(f(x)-g(x), x)], [x::real])

exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z))

(3)

allvalues(exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z)))

exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, 1.505446443)), exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, -3.291052648)), exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, 2.302585093)), 1

(4)

``

``


 

Download intersect_curve.mw

 

I know there's an answer to this because I can get the expected answer from Wolfram Alpha (see here).

How can I accomplish this in Maple? 

Hi friends!

I have the following problem.

I'm trying to generate a matrix given a certain lenght n and a polynomial g(x) of degree r as follows:

If n=10, g(x)=x^4+3x^3+x^2+2x+1 and r=degree(g(x))=4, then the resulting matrix will be

 

 

 

 

 

i.e. a matrix with 10 columns, n-r=6 lines, and whose inputs are the coefficients of the polynomial, as follows:

Any help will be very appreciated.

Thank you!

Hi,

I have questions about linestyle in maple, how to change solid and Dash whatever  to line with cross or line with plus 

Please see a plot attached.

Look forward to hearing from you as soon as possible.

Regards,

Mathastr

plots.pdf

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