Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

I will have excel sheet with minium 500 coulmns and 1000 rows say

For sample to explain my question I attach a demo excel

All my columns have headers

I am looking to find all 2 way multiplication and add them as columns to my excel sheet and return it as a new excel sheet say

The column names for the new 2 way column should be like the

header name of column you are multiply * the name of the other columsn

Now in sample file if i multiple column with name A with column with name B I get a new column with header A*B the header name should be inserted and

Below that all the elements of that A column multiplied  with that of B should come

I am looking to form columns for all possible2  way multiplication for the excel I will give.

As you can see the demo file

Excel_to_explain.xlsx

Kind help please

Hello! I've been trying to solve system of non-linear differential equations. The equations are quite messy, so I've attached the file itself dsolve.mw. I have read about the similar problems, but they all are related to some expressions having multiple branches. I'm not quite sure where this problem occurs (if it does) here and how to solve it.

HI, I attach  a document (Pade_Approximants_for_alpha.mw) extract showing the errors (Error, (in Engine:-Dispatch) badly formed input to solve: not fully algebraic
).

Can any one help us please?

Thanks. Syed Asadullah Shah

I have to maximize my non linear objective function TBCI (given in attached worksheet) with 4 inequality constraints. The decision variables are i and q.The range of i is 0 to 1 and of q is 0 to 76.

When i tru to solve it using NLP solve it is showing error-"Error, (in Optimization:-NLPSolve) constraints must be specified as a set or list of equalities and inequalities".

Please help me to solve it. please find attached the maple file

restart

with(plots); with(DEtools); with(LinearAlgebra); with(Student[VectorCalculus]); with(linalg); with(Optimization); with(student)

TC := proc (Q) options operator, arrow; O1*(1-beta)*D/Q+(1/2)*h1*Q+(1/2)*h2*(gamma-beta)*Qr/gamma+O2*beta*D/Qr+r*beta*D-q*beta*D-P*(1-i)*beta*D end proc

proc (Q) options operator, arrow; Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(O1, Student:-VectorCalculus:-`+`(1, Student:-VectorCalculus:-`-`(beta))), Student:-VectorCalculus:-D), Q^Student:-VectorCalculus:-`-`(1)), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(h1, Q), 2^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(h2, Student:-VectorCalculus:-`+`(gamma, Student:-VectorCalculus:-`-`(beta))), Qr), Student:-VectorCalculus:-`*`(2, gamma)^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(O2, beta), Student:-VectorCalculus:-D), Qr^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(r, beta), Student:-VectorCalculus:-D)), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(q, beta), Student:-VectorCalculus:-D))), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(P, Student:-VectorCalculus:-`+`(1, Student:-VectorCalculus:-`-`(i))), beta), Student:-VectorCalculus:-D))) end proc

(1)

diff(TC(Q), Q)

-O1*(1-beta)*Student:-VectorCalculus:-D/Q^2+(1/2)*h1

(2)

simplify(isolate(%, Q))

Q = RootOf(2*Student:-VectorCalculus:-D*O1*beta+_Z^2*h1-2*Student:-VectorCalculus:-D*O1)

(3)

diff(TC(Q), Qr)

(1/2)*h2*(gamma-beta)/gamma-O2*beta*Student:-VectorCalculus:-D/Qr^2

(4)

simplify(isolate(%, Qr))

Qr = RootOf((beta*h2-gamma*h2)*_Z^2+2*gamma*O2*beta*Student:-VectorCalculus:-D)

(5)

diff(TC(Q), `$`(Q, 2))

2*O1*(1-beta)*Student:-VectorCalculus:-D/Q^3

(6)

diff(TC(Q), `$`(Qr, 2))

2*O2*beta*Student:-VectorCalculus:-D/Qr^3

(7)

TC1 := proc (Q, Qr) options operator, arrow; O1*(-beta*i+1)*D/Q+(1/2)*h1*Q+(1/2)*h2*(-beta*i+gamma)*Qr/gamma+O2*i*beta*D/Qr+r*i*beta*D-q*i*beta*D-P*(1-i)*i*beta*D end proc

proc (Q, Qr) options operator, arrow; Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(O1, Student:-VectorCalculus:-`+`(1, Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(i, beta)))), Student:-VectorCalculus:-D), Q^Student:-VectorCalculus:-`-`(1)), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(h1, Q), 2^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(h2, Student:-VectorCalculus:-`+`(gamma, Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(i, beta)))), Qr), Student:-VectorCalculus:-`*`(2, gamma)^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(O2, i), beta), Student:-VectorCalculus:-D), Qr^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(r, i), beta), Student:-VectorCalculus:-D)), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(q, i), beta), Student:-VectorCalculus:-D))), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(P, Student:-VectorCalculus:-`+`(1, Student:-VectorCalculus:-`-`(i))), i), beta), Student:-VectorCalculus:-D))) end proc

(8)

diff(TC1(Q, Qr), Q)

-O1*(-beta*i+1)*Student:-VectorCalculus:-D/Q^2+(1/2)*h1

(9)

a1 := isolate(-O1*(-beta*i+1)*D/Q^2+(1/2)*h1, Q)

Q = RootOf(2*Student:-VectorCalculus:-D*O1*beta*i+_Z^2*h1-2*Student:-VectorCalculus:-D*O1)

(10)

diff(TC1(Q, Qr), Qr)

(1/2)*h2*(-beta*i+gamma)/gamma-O2*i*beta*Student:-VectorCalculus:-D/Qr^2

(11)

a2 := isolate(diff(TC1(Q, Qr), Qr), Qr)

Qr = RootOf((beta*h2*i-gamma*h2)*_Z^2+2*gamma*O2*i*beta*Student:-VectorCalculus:-D)

(12)

TC2 := proc (Q) options operator, arrow; O1*(1-gamma)*D/Q+(1/2)*h1*Q+r*gamma*D-q*gamma*D-P*(1-i)*gamma*D end proc

proc (Q) options operator, arrow; Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(O1, Student:-VectorCalculus:-`+`(1, Student:-VectorCalculus:-`-`(gamma))), Student:-VectorCalculus:-D), Q^Student:-VectorCalculus:-`-`(1)), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(h1, Q), 2^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(r, gamma), Student:-VectorCalculus:-D)), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(q, gamma), Student:-VectorCalculus:-D))), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(P, Student:-VectorCalculus:-`+`(1, Student:-VectorCalculus:-`-`(i))), gamma), Student:-VectorCalculus:-D))) end proc

(13)

b1 := isolate(diff(TC2(Q), Q), Q)

Q = RootOf(2*Student:-VectorCalculus:-D*O1*gamma+_Z^2*h1-2*Student:-VectorCalculus:-D*O1)

(14)

E1 := eval(a1, [P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, beta = 0.5e-1, gamma = 0.4e-1, q = 7.65, r = 382.5, i = .5])

Q = RootOf(76.5*_Z^2-20354080.50)

(15)

simplify(E1)

Q = 515.8162578

(16)

E2 := eval(a2, [P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, beta = 0.5e-1, gamma = 0.4e-1, q = 7.65, r = 382.5, i = .5])

Qr = RootOf(.57375*_Z^2-6958.66000)

(17)

simplify(E2)

Qr = 110.1289401

(18)

Totcost := eval(TC1(Q, Qr), [Q = 516, Qr = 110, P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, beta = 0.5e-1, gamma = 0.4e-1, q = 7.65, r = 382.5, i = .5])

-25502.577

(19)

TB1 := B1*D*P*beta*i-D*beta*i*q

B1*Student:-VectorCalculus:-D*P*beta*i-Student:-VectorCalculus:-D*beta*i*q

(20)

TBC := eval(TB1, [B1 = 3.36, P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, beta = 0.5e-1, gamma = 0.4e-1, r = 382.5])

-17396.65*q*i+44716349.16*i

(21)

Totincent := P*i^2*beta*D

P*i^2*beta*Student:-VectorCalculus:-D

(22)

TI := eval(Totincent, [B1 = 3.36, P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, beta = 0.5e-1, gamma = 0.4e-1, r = 382.5])

13308437.25*i^2

(23)

NULL

simplify(subs(P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, gamma = 0.4e-1, q = 7.65, r = 382.5, beta = 0.5e-1, Q = sqrt((2*(-beta*i+1))*O1*D/h1))); simplify(subs(P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, gamma = 0.4e-1, q = 7.65, r = 382.5, beta = 0.5e-1, Qr = sqrt(2*i*beta*gamma*O2*D/((gamma-beta)*h2))))

Q = 3230.787830*(-0.1307189542e-2*i+0.2614379084e-1)^(1/2)

 

Qr = 190.7489196*(-i)^(1/2)

(24)

TCo := eval(TC1(Q, Qr), [Q = 3230.787830*sqrt(-0.1307189542e-2*i+0.2614379084e-1), Qr = 190.7489196*sqrt(-i), P = 765, D = 347933, O1 = 30, O2 = 10, h1 = 76.5, h2 = 38.25, gamma = 0.4e-1, q = 7.65, r = 382.5, beta = 0.5e-1])

3230.787829*(-0.5e-1*i+1)/(-0.1307189542e-2*i+0.2614379084e-1)^(1/2)+123577.6345*(-0.1307189542e-2*i+0.2614379084e-1)^(1/2)+91201.82720*(-0.5e-1*i+0.4e-1)*(-i)^(1/2)+912.0182718*i/(-i)^(1/2)+6521134.252*i-13308437.25*(1-i)*i

(25)

eq1 := TCo <= 0

3230.787829*(-0.5e-1*i+1)/(-0.1307189542e-2*i+0.2614379084e-1)^(1/2)+123577.6345*(-0.1307189542e-2*i+0.2614379084e-1)^(1/2)+91201.82720*(-0.5e-1*i+0.4e-1)*(-i)^(1/2)+912.0182718*i/(-i)^(1/2)+6521134.252*i-13308437.25*(1-i)*i <= 0

(26)

eq2 := 0 <= q/P and q/P <= 1

0 <= q/P and q/P <= 1

(27)

eq3 := 0 <= i and i <= gamma/beta

0 <= i and i <= gamma/beta

(28)

eq4 := TBC >= 0

0 <= -17396.65*q*i+44716349.16*i

(29)

``

TBCI := TBC-TCo+TI

-17396.65*q*i+38195214.91*i-3230.787829*(-0.5e-1*i+1)/(-0.1307189542e-2*i+0.2614379084e-1)^(1/2)-123577.6345*(-0.1307189542e-2*i+0.2614379084e-1)^(1/2)-91201.82720*(-0.5e-1*i+0.4e-1)*(-i)^(1/2)-912.0182718*i/(-i)^(1/2)+13308437.25*(1-i)*i+13308437.25*i^2

(30)

NLPSolve(TBCI, {eq1, eq2, eq3, eq4}, assume = nonnegative)

Error, (in Optimization:-NLPSolve) constraints must be specified as a set or list of equalities and inequalities

 

``

This is Maple 2019. Suppose a directed graph D is given. 

I know that "Cycles≔CycleBasis(D)" lists down all the cycles in D and "numelems(Cycles)" gives the number of cycles in D. But if I only want to count the number of directed cycles of length k, say k=4, in D, is there a Maple function that gives us that?

Thank you all.

Dears,
I have a problem whem try to solve a optimization probolem.
The equations are "complex" (G1 equation), and this error is showed "Error, (in Optimization:-NLPSolve) could not store 0.1749271137e-1*(588.000000000000+72.0000000000000*(-3.03333333+.333333333333333*MM)*(MM-17.80)+72.0000000000000*(.333333333333333*NN-3.5666666666667)*(17.00-1.*NN)+24.50000000*(2.90+4.666666667*tan(1.000000000*arctan(.166666666666667*MM-2.96666666666667)))*(18.00+5.627472876000*sin(-1.570796327+1.000000000*arctan(.166666666666667*MM-2.96666666666667))/sin(-1.745329252+1.000000000*arctan(.166666666666667*MM-2.96666666666667)))*cos(-.5235987756000+1.000000000*arctan(.166666666666667*MM-2.96666666666667))^2*sin(.3490658504000+1.000000000*arctan(.166666666666667*MM-2.9666 ... 756000+1.000000000*arctan(.166666666666667*MM-2.96666666666667))^2)-1. in a floating-point rtable".
Someone can help me?

ATS := proc(NN::float, MM::float) 
L[7]*H[4] + L[4]*H[2] + L[1]*(H[1] - H[2]) + 1/2*(P[X1] - NN)*(H[1] - H[2]) + 1/2*(MM - P[XF])*(H[1] - H[2]); 
end proc;
bounds := 14.90 .. 16.90, 17.90 .. 19.90;
cstr8 := proc(NN::float, MM::float) 
G1 - FS; 
end proc;

NLPSolve(ATS, {cstr8}, bounds, initialpoint = [15.90, 18.90], assume = nonnegative)

Maple Input:
restart; with(RealDomain); log[2](x^2 - 6*x) = 3 + log[2](1 - x); Maple returns as solution
ln\x - 6 x/ ln(1 - x) ------------ = 3 + --------- ln(2) ln(2) "(->)" [[x = 2], [x = -4]]
Is the solution x = 2 correct?

Substituting x=2 into the original Function Maple returns correct: log[2](2^2 - 6*2);

undefined and log[2](1 - 2).; undefined. So x =2 should not be a solution of this function.

y''(x)+2(y'(x))^2+8y(x)=0   

y(0)=0 , y'(0)=1

I take the liberty to rephrase my previous question as I believe the title was not very clear and so maybe some power users did not look at it. I am making the transition from Mathcad towards Maple and get stuck solving the equation in the attached worksheet. In mathcad I would solve it like this:

How can I achieve results in Maple? I know it is a very powerful program but for me the learning curve is at this moment quite steep. Any help would be very much appreciated.

Multiple_input.mw

First of all I would like to wish all of you a happy, prosperous but especially healthy 2023! I have again a beginner question. Why is test2 not working in the attached document?

Thank you so much for your assistance!

QuestionFDS.mw

The transformed boundary conditions are

How should I draw a 2D graph for which one parameter in x axis and 3 parameters in y axis change with respect to x axis parameter in same graph. To be exact in my problem for changing β value (in x axis) what will be the optimum value for p, q and e. I had obtained the optimum p (named as ptemp in file), optimum q (named as qtemp in file), optimum e (named as etemp in file) for different values of β. But I don’t know how to plot it? Whether to give plot command inside the loop or not? Please help me. I am attaching the file with code and a sample graph. ( Find the problem in Numerical analysis - below in file)                                        new_assignment.mw

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