Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022

I was just using Maple to do a simple calculation but the units came out all complicated. 

The expression in question is work done by a van der Waals gas. The units should come out to Joules per mol. 

When I do the calculation manually (second expression below) I do get that result, albeit in more basic units than Joules.

In the first expression, in which I am using subs to sub in values with units into the expression, the final expression is very complicated. Why?

with(Units:-Simple)

simplify(subs({R = 8.314*Unit('J'/('K'*'mol')), T = 298*Unit('K'), V__1 = Unit('L'/'mol'), V__2 = 50*Unit('L'/'mol'), a = 2.283*Unit('L'^2*'bar'/'mol'^2), b = 0.4278e-1*Unit('L'/'mol')}, -R*T*ln((V__2-b)/(V__1-b))+a*(1/V__1-1/V__2)))

(-9798.522418*Units:-Unit(J/(K*mol))*Units:-Unit(K)*Units:-Unit(L/mol)+2.23734*Units:-Unit(L^2*bar/mol^2))/Units:-Unit(L/mol)

(1)

How do we simplify the units above so they become the same as the units in the same (manual) calculation below?

-(8.314*Unit('J'/('K'*'mol'))*298)*Unit('K')*ln((50*Unit('L'/'mol')-0.4278e-1*Unit('L'/'mol'))/(Unit('L'/'mol')-0.4278e-1*Unit('L'/'mol')))+2.283*Unit('L'^2*'bar'/'mol'^2)/Unit('L'/'mol')

-9570.222418*Units:-Unit(m^2*kg/(s^2*mol))

(2)

NULL

Download Units_-_Subs.mw

Dear all,

I'd like to explore graphically a polynomial surface depending on two parameters a and b.

The problem is that, as soon as I start playing with the sliders, Maple freezes and I have to 'force quit'.

Can you please tell me if you have the same problem with this example?

Thanks.

restart:

with(plots):

K := 1 - y*x - (1 - x)*(b*x^3 + a*x^2 + x + 1)*(1 - y)*(b*y^3 + a*y^2 + y + 1)

1-y*x-(1-x)*(b*x^3+a*x^2+x+1)*(1-y)*(b*y^3+a*y^2+y+1)

(1)

Explore(plot3d(K, x=0..1, y=0..1,  font= [Times, bold, 20], labels= ['x', 'y','z'],   labelfont= [Times, bold, 40],  title = "K(x,y)"), b = 0..1., a=0..1.);

 

 

Download Explore.mw

Dear all,

I have this polynomial function

G(x, y) := (-0.14*y^3 + 1.20000000000000*y^2 - 1.26000000000000*y + 0.200000000000000)*x^3 + (1.20*y^3 - 10.0800000000000*y^2 + 10.0800000000000*y - 1.20000000000000)*x^2 + (-8.82*y + 10.08*y^2 - 1.26*y^3)*x + 1. - 1.2*y^2 + 0.2*y^3

I don't understand why the command

minimize(G(x,y),x=0..1,y=0..1);

produces the error

Error, (in RootOf/RootOf:-algnum_in_range) invalid input: RootOf/RootOf:-rootof_in_range expects its 1st argument, rt, to be of type ('RootOf')(polynom(rational,_Z),identical(index) = posint), but received RootOf(7*_Z^3-93*_Z^2+327*_Z-187)

Thanks for your advices, Nicola

Dear all

I have a function like 

F[1] := (x, y) -> x*y/(1 + 10.35841093*(1 - x)*((-1)*0.9*x + 1)*(1 - y)*((-1)*0.9*y + 1))

This function is continuous on D = [0,1]x[0,1]. I'm interested in the (approximate) value of the double integral over D.

Unfortunately the entry

int(int(F[1](x,y),x=0..1.),y=0..1.)

produces Float(infinity). 

Thanks Nicola

Why Maple return 0 when I try to find coefficients of different power of lambda's.coeff.mw

i have made a full working code for differential quadrature method now i am  changing examples and it is not working although i have properly defined new parameters i am attaching my code kindly help me out
one more thing one example include summation n=0..ininity it is not even evaluating taking alot of time i am attaching both codes kindly help me out
A+B_example.mw
chelishkov_comparison.mw

I have this problem with this system of equations, when I solve the 13x13 system it does not give me any solution, neither giving seed values ​​nor placing full digits. The exercise is solved and I tried to assume close values ​​and it doesn't work for me, it leaves everything expressed with the fsolve command.

Download p1.mw

while running my code i am not able to edit it. when i close my file and re open it then it is edit able but only once after that to re edit i have to run it again.
one more query i am facing is that i have made whole code now i just want to change pde and exact solution of that pde to get different solutions of pde although my code is working for one pde but while changing pde it is giving me error why?
and some times it takes alot of time to evaluate is there any error in the code or should i change my laptop?

kindly help me with all these queries.

'odeadvisor' suggests isolating y(x) from the equation as a first step, y=G(x,y'(x)), then apply the method of 'patterns'. For the first step, y(x) = (9/4)*[(y'(x))^2]/{[int(f(x),x)]^5} is what I found but, could take it no further. Nevertheless, Maple finds an intrinsic solution of the form, (3/4)*y(x)^(4/3) +(2/3)*int(sqrt(y(x)*f(x))^(-5/3) + _C1 =0, from which an explicit solution can be obtained. If anyone can supply the steps leading to the Maple solution - that would be great.

simp.mw

please see simp.mw file

Hello everyone

I need help solving a system of equations as below. I'm looking for a way to do it, but I don't understand the general concept of how such an equation is calculated. So far I've been using a package in LabVIEW that worked similarly to Simulink and that was clear to me, whereas here I'm overwhelmed by the multitude of options and that's why I'm asking for help.

I need to solve these equations analogously to Matlab-Simulink, i.e., a time interval and integration step, and a numerical procedure in symbolic versions.

Help_me.mw

How do you substitute into a contravariant index of a tensor say

T[~mu, nu]     ?

Nothing seems to work, I tried to subs(~mu=~1,T[~mu, nu]), subs(mu=1,T[~mu, nu]), and all permutations.

Substituting values into the covariant index works fine but not contravariant.

Surely it must be possible ?

restart:with(Physics):

Setup(dimension=3,coordinates=(X=[x,y,z])):

Define(Tp3[~alpha,~beta,~gamma],B[~lambda,mu],T3[~rho,~epsilon,~sigma]):

Tp3[~alpha,~beta,~gamma]=B[~alpa,rho]B[~beta,epsilon]B[~gamma,sigma]T3[~rho,~epsilon,~sigma]

SumOverRepeatedIndices of the expression does not do anything. Why?

Thanks for the answer.

What should I do to simplify eq13 further using trig sum identities?
Thank you for your help in advance,

restart;

phi := (x,n,L) -> sqrt(2/L)*sin(n*Pi*x/L + 1/2*n*Pi);

proc (x, n, L) options operator, arrow; sqrt(2/L)*sin(n*Pi*x/L+(1/2)*n*Pi) end proc

(1)

 

eq1 := W[n,m](q,p) = simplify(1/Pi*Int(phi(q+y,n,L)*exp(-2*I*p*y)*phi(q-y,m,L),y=-L/2+abs(q)..L/2-abs(q)));

W[n, m](q, p) = 2*(Int(sin((1/2)*n*Pi*(2*q+2*y+L)/L)*exp(-(2*I)*p*y)*sin((1/2)*m*Pi*(2*q-2*y+L)/L), y = -(1/2)*L+abs(q) .. (1/2)*L-abs(q)))/(L*Pi)

(2)

eq2 := simplify(convert(eq1,int)) assuming(n,integer,m,integer);

W[n, m](q, p) = (-16*(I*((-(1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*L*p*sin(n*Pi*(abs(q)+q)/L)+(1/2)*cos(n*Pi*(abs(q)+q)/L)*(((1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*n*Pi)*exp(I*p*(L-2*abs(q)))*sin(m*Pi*(L-abs(q)+q)/L)+16*exp(-I*p*(L-2*abs(q)))*(I*L*p*((-(1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*sin(m*Pi*(abs(q)+q)/L)-(1/2)*cos(m*Pi*(abs(q)+q)/L)*m*((-(1/4)*m^2+(1/4)*n^2)*Pi^2+p^2*L^2)*Pi)*sin(n*Pi*(L-abs(q)+q)/L)+8*Pi*(-m*exp(I*p*(L-2*abs(q)))*((((1/4)*m^2-(1/4)*n^2)*Pi^2-p^2*L^2)*sin(n*Pi*(abs(q)+q)/L)+I*L*p*Pi*n*cos(n*Pi*(abs(q)+q)/L))*cos(m*Pi*(L-abs(q)+q)/L)+exp(-I*p*(L-2*abs(q)))*cos(n*Pi*(L-abs(q)+q)/L)*n*((((1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*sin(m*Pi*(abs(q)+q)/L)+I*L*p*Pi*m*cos(m*Pi*(abs(q)+q)/L))))/((m-n)^2*(m+n)^2*Pi^5-8*L^2*p^2*(m^2+n^2)*Pi^3+16*L^4*p^4*Pi)

(3)

Wigner function evaluated for q > 0 and q < 0, respectively

eq10 := simplify(eq2) assuming(q>0);
eq11 := simplify(eq2) assuming(q<0);
eq12 := simplify(eq10) assuming(m,integer,n,integer);
eq13 := simplify(eq11) assuming(m,integer,n,integer);

W[n, m](q, p) = (16*exp(-I*p*(L-2*q))*(I*p*L*((-(1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*sin(n*Pi)+(1/2)*cos(n*Pi)*Pi*n*(((1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2))*sin(2*m*Pi*q/L)-16*exp(I*p*(L-2*q))*(I*p*L*((-(1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*sin(m*Pi)-(1/2)*Pi*cos(m*Pi)*((-(1/4)*m^2+(1/4)*n^2)*Pi^2+p^2*L^2)*m)*sin(2*n*Pi*q/L)+8*Pi*(exp(-I*p*(L-2*q))*((((1/4)*m^2-(1/4)*n^2)*Pi^2-p^2*L^2)*sin(n*Pi)+I*L*n*p*Pi*cos(n*Pi))*m*cos(2*m*Pi*q/L)-((((1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*sin(m*Pi)+I*L*m*p*Pi*cos(m*Pi))*cos(2*n*Pi*q/L)*n*exp(I*p*(L-2*q))))/((m-n)^2*(m+n)^2*Pi^5-8*L^2*p^2*(m^2+n^2)*Pi^3+16*L^4*p^4*Pi)

 

W[n, m](q, p) = (-8*exp(I*p*(L+2*q))*n*(((1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*sin(m*Pi*(L+2*q)/L)+8*m*(-exp(-I*p*(L+2*q))*((-(1/4)*m^2+(1/4)*n^2)*Pi^2+p^2*L^2)*sin(n*Pi*(L+2*q)/L)+I*Pi*n*p*L*(cos(n*Pi*(L+2*q)/L)*exp(-I*p*(L+2*q))-exp(I*p*(L+2*q))*cos(m*Pi*(L+2*q)/L))))/((m-n)^2*(m+n)^2*Pi^4-8*L^2*p^2*(m^2+n^2)*Pi^2+16*L^4*p^4)

 

W[n, m](q, p) = (8*(-1)^n*(((1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*n*exp(-I*p*(L-2*q))*sin(2*m*Pi*q/L)-8*m*(-(-1)^m*exp(I*p*(L-2*q))*((-(1/4)*m^2+(1/4)*n^2)*Pi^2+p^2*L^2)*sin(2*n*Pi*q/L)+I*n*(cos(2*n*Pi*q/L)*exp(I*p*(L-2*q))*(-1)^m-exp(-I*p*(L-2*q))*(-1)^n*cos(2*m*Pi*q/L))*Pi*L*p))/((m-n)^2*(m+n)^2*Pi^4-8*L^2*p^2*(m^2+n^2)*Pi^2+16*L^4*p^4)

 

W[n, m](q, p) = (-8*exp(I*p*(L+2*q))*n*(((1/4)*m^2-(1/4)*n^2)*Pi^2+p^2*L^2)*sin(m*Pi*(L+2*q)/L)+8*m*(-exp(-I*p*(L+2*q))*((-(1/4)*m^2+(1/4)*n^2)*Pi^2+p^2*L^2)*sin(n*Pi*(L+2*q)/L)+I*Pi*n*p*L*(cos(n*Pi*(L+2*q)/L)*exp(-I*p*(L+2*q))-exp(I*p*(L+2*q))*cos(m*Pi*(L+2*q)/L))))/((m-n)^2*(m+n)^2*Pi^4-8*L^2*p^2*(m^2+n^2)*Pi^2+16*L^4*p^4)

(4)
 

 

Download test5.mw

how to determine lambda, m0, and n0? a_i, and c_i are constants and c^2 = c[1]^2 + c[2]^2. solA.mw

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