Advanced Search

Maple Questions and Posts

These are Posts and Questions associated with the product, Maple
View unanswered posts
Maple Questions and Posts Feed

how to use odetest to very series solution with ex...

Asked by: nm 11398
ode dsolve series
June 29 2022
2  8

I do not remember now if this was asked before. Doing search here is hard. 

But I am trying this now on 2022.1 and this gives FAIL.

What is the correct syntax to use odetest to verify solution to ode using series method with expansion around infinity? Why do I get FAIL here?
 

> 

interface(version)

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1257 and is the same as the version installed in this computer, created 2022, June 22, 16:27 hours Pacific Time.`

> 

restart;
> 

ode:=x^3*diff(y(x),x$2)+x^2*diff(y(x),x)+y(x)=0;
sol:=dsolve(ode,y(x),'series',x=infinity);
odetest(sol,ode,'series','point'=infinity)

x^3*(diff(diff(y(x), x), x))+x^2*(diff(y(x), x))+y(x) = 0

y(x) = _C1*(1-1/x+(1/4)/x^2-(1/36)/x^3+(1/576)/x^4-(1/14400)/x^5+O(1/x^6))+_C2*(ln(1/x)*(1-1/x+(1/4)/x^2-(1/36)/x^3+(1/576)/x^4-(1/14400)/x^5+O(1/x^6))+2/x-(3/4)/x^2+(11/108)/x^3-(25/3456)/x^4+(137/432000)/x^5+O(1/x^6))

Warning, unable to compute series necessary to test the given solution

FAIL

> 

 


 

Download odetest_series.mw

Update

I've testsed methods given below on 6 random ode's using Maple odetest, VV method and Axel method. THis is the result obtained using Maple 2022.1 

odetest was able to verify the solution zero out of 6 times.
VV method was able to verify the solution 3 out of 6 times.
Axel method was able to verify the solution 5 out of 6 times.

So based on this small test, Axel method seems to do the best. Attached worksheet. I will use this method to verify my series solution to ode's instead of Maple's odetest but will use Maple's odetest for non-series method solutions.


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1257 and is the same as the version installed in this computer, created 2022, June 22, 16:27 hours Pacific Time.`

> 

restart;

Example 1  Regular singular point. Complex roots

 
> 

Order:=6;
ode:=sin(x)*diff(y(x),x$2)+cos(x)*diff(y(x),x)+1/x*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0)

6

sin(x)*(diff(diff(y(x), x), x))+cos(x)*(diff(y(x), x))+y(x)/x = 0

y(x) = _C1*x^(-I)*(series(1+(1/48-(1/16)*I)*x^2+(1/57600-(217/57600)*I)*x^4+O(x^6),x,6))+_C2*x^I*(series(1+(1/48+(1/16)*I)*x^2+(1/57600+(217/57600)*I)*x^4+O(x^6),x,6))

VV method

 
> 

odetest(sol,ode):
asympt(%,x);

Error, (in asympt) unable to compute series

odetest method

 
> 

odetest(sol,ode,'series','point'=0);

y(x) = _C1*x^(-I)*(series(1+(1/48-(1/16)*I)*x^2+(1/57600-(217/57600)*I)*x^4+O(x^6),x,6))+_C2*x^I*(series(1+(1/48+(1/16)*I)*x^2+(1/57600+(217/57600)*I)*x^4+O(x^6),x,6))

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

 
> 

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 2 Regular singular point. Difference is integer

 
> 

Order:=6;
ode:=sin(x)*diff(y(x),x$2)+cos(x)*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

sin(x)*(diff(diff(y(x), x), x))+cos(x)*y(x) = 0

VV method

 
> 

odetest(sol,ode):
asympt(%,x);
convert(%,polynom);

O(x^7)

0

odetest method

 
> 

odetest(sol,ode,'series','point'=0);

Warning, unable to compute series necessary to test the given solution

FAIL

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   
> 

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 3 Regular singular point. Repeated root

 
> 

Order:=6;
ode:=(exp(x)-1)*diff(y(x),x$2)+exp(x)*diff(y(x),x)+y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

(exp(x)-1)*(diff(diff(y(x), x), x))+exp(x)*(diff(y(x), x))+y(x) = 0

VV method

 
> 

odetest(sol,ode):
asympt(%,x):
convert(%,polynom);

0

odetest method

 
> 

odetest(sol,ode,'series','point'=0);

Warning, unable to compute series necessary to test the given solution

FAIL

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   
> 

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 4 Regular singular point. Repeated root

 
> 

Order:=6;  
ode:=(exp(x)-1)*diff(y(x),x$2)+exp(x)*diff(y(x),x)+y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

(exp(x)-1)*(diff(diff(y(x), x), x))+exp(x)*(diff(y(x), x))+y(x) = 0

VV method

 
> 

odetest(sol,ode):
asympt(%,x):
convert(%,polynom);

0

odetest method

 
> 

odetest(sol,ode,'series','point'=0);

Warning, unable to compute series necessary to test the given solution

FAIL

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   
> 

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 5 . Regular singular point. Complex roots

 
> 

Order:=6;  
ode:=x^3*diff(y(x),x$2)+sin(x^3)*diff(y(x),x)+x*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

x^3*(diff(diff(y(x), x), x))+sin(x^3)*(diff(y(x), x))+x*y(x) = 0

VV method

 
> 

odetest(sol,ode):
asympt(%,x);
#convert(%,polynom);

Error, (in asympt) unable to compute series

odetest method

 
> 

odetest(sol,ode,'series','point'=0);

Error, (in odetest/series) need to determine the sign of I*3^(1/2)

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   
> 

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
#convert(%,polynom);

Error, (in MultiSeries:-multiseries) need to determine the sign of -I*3^(1/2)

Example 6 . Regular singular point. Complex roots

 
> 

Order:=6;  
ode:=x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x+1)*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

x^2*(diff(diff(y(x), x), x))+x*(diff(y(x), x))+(x+1)*y(x) = 0

VV method

 
> 

odetest(sol,ode):
asympt(%,x);
#convert(%,polynom);

Error, (in asympt) unable to compute series

odetest method

 
> 

odetest(sol,ode,'series','point'=0);

y(x) = _C1*x^(-I)*(series(1+(-1/5-(2/5)*I)*x+(-1/40+(3/40)*I)*x^2+(3/520-(7/1560)*I)*x^3+(-1/2496+(1/12480)*I)*x^4+(9/603200+(1/361920)*I)*x^5+O(x^6),x,6))+_C2*x^I*(series(1+(-1/5+(2/5)*I)*x+(-1/40-(3/40)*I)*x^2+(3/520+(7/1560)*I)*x^3+(-1/2496-(1/12480)*I)*x^4+(9/603200-(1/361920)*I)*x^5+O(x^6),x,6))

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   
> 

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

> 

 

> 

 


 

Download test_new_odetest.mw

 

 

 

Maple's WeierstrassP vs Weierstrass' P-function...

Asked by: Axel Vogt 5936
special-function weierstrassp
June 29 2022
4  2

What is the [explict] relation between Maple's WeierstrassP and Weierstrass' P-function (e.g. https://en.wikipedia.org/wiki/Weierstrass_elliptic_function) ?

Expecting numerical value from Integrate but getti...

Asked by: shashi598 50
integration distribution numeric
June 29 2022
2  2

pdf.mw
 

> 

with(stats)
> 

"f(x):=statevalf[pdf,normald[0,2*4.47]] "

proc (x) options operator, arrow, function_assign; statevalf[pdf, normald[0, 2*4.47]] end proc

 (1)
> 

plot(f(x), -20 .. 20)

 
> 

int(x*f(x), x)

.5000000000*x^2*statevalf[pdf, normald[0, 8.94]]

 (2)
> 

NULL


 

Download pdf.mw

Want to integrate x*f(x) where x is from -20..20, I am expecting a pure float number but getting symbols like statevalf_pdf in answer.

 

Is there a way to differentiate between errors?...

Asked by: Lana 55
error try-catch
June 28 2022
4  2

I am using some custom procedures which return error messages if something doesn´t work as planned and would need to make a distinction (when using try..catch) between these errors and all the other potential error messages Maple can return. Is there a way to do this efficiently - without having to list all of the error messages from my own procedures after catch?

RK-4 for System of Nonlinear ODE'S...

Asked by: Tamour_Zubair 80
ode homework numeric
June 28 2022
1  5

Hello Everyone;

Hope you are fine. My problem is convert into nonlinear system of ODE's and further i need make the code of apply rk-4 for the formulated ODE's. Kindly guide me. The file is attached. I am waiting for your kind response.

Thanks

Question3.mw

 


 

> 

restart
> 

``
> 

var111 := [C[1, 1](t), C[1, 2](t), C[1, 3](t), C[2, 1](t), C[2, 2](t), C[2, 3](t), C[3, 1](t), C[3, 2](t), C[3, 3](t), ZETA[1](t), ZETA[2](t), ZETA[3](t)]:
> 

sysM := [diff(C[1, 1](t), t) = -(3/16)*Pi*(C[2, 1](t)+4*C[1, 1](t)), diff(C[1, 2](t), t) = -5*Pi*(C[2, 2](t)+4*C[1, 2](t)), diff(C[1, 3](t), t) = -(945/4)*Pi*(C[2, 3](t)+4*C[1, 3](t)), diff(C[2, 1](t), t) = -(1/8)*Pi*(C[3, 1](t)+6*C[2, 1](t)+6*C[1, 1](t)), diff(C[2, 2](t), t) = -10.4719755119659774615421446110*C[3, 2](t)-62.8318530717958647692528676658*C[2, 2](t)-62.8318530717958647692528676658*C[1, 2](t)-2.38361014507273884349657421134*10^15*ZETA[1](t)*C[1, 1](t), diff(C[2, 3](t), t) = -494.800842940392435057866332869*C[3, 3](t)-2968.80505764235461034719799721*C[2, 3](t)-2968.80505764235461034719799721*C[1, 3](t)-1.35954060126371030332767566128*10^16*ZETA[1](t)*C[1, 2](t)-1.35954060126371030332767566128*10^16*ZETA[2](t)*C[1, 1](t), diff(C[3, 1](t), t) = -(3/8)*Pi*(2*C[3, 1](t)+3*C[2, 1](t)), diff(C[3, 2](t), t) = -62.8318530717958647692528676658*C[3, 2](t)-94.2477796076937971538793014986*C[2, 2](t)-1.12625579354686910355213131486*10^17*ZETA[1](t)*C[2, 1](t), diff(C[3, 3](t), t) = -2968.80505764235461034719799721*C[3, 3](t)-4453.20758646353191552079699581*C[2, 3](t)-6.42382934097103118322326749959*10^17*ZETA[1](t)*C[2, 2](t)-6.42382934097103118322326749959*10^17*ZETA[2](t)*C[2, 1](t), diff(ZETA[1](t), t) = -(1/3)*C[2, 1](t), diff(ZETA[2](t), t) = -(1/3)*C[2, 2](t), diff(ZETA[3](t), t) = -(1/3)*C[2, 3](t)]:
> 

ICS := [C[1, 1] = 0.998238989835086492681507032141e-1, C[1, 2] = -0.137051161872492529218951625903e-1, C[1, 3] = -0.629146365720807620696267926206e-2, C[2, 1] = 0.923300332435106257640735267282e-1, C[2, 2] = -0.126762613568515069966837491839e-1, C[2, 3] = -0.581915808273854734025727975244e-2, C[3, 1] = -0.190143920352772604950256237747e-1, C[3, 2] = 0.261054171122321128306306984717e-2, C[3, 3] = 0.119839394846335068333097530793e-2, ZETA[1] = .464598743230343884242076682299, ZETA[2] = .429720916976380440572769663279, ZETA[3] = -0.884964696113332752036741498040e-1]:
> 

``


 

Download Question3.mw

How to have Maple solve this simple ODE?...

Asked by: Rouben Rostamian 8531
ode dsolve differential-equations
June 27 2022
5  9

The worksheet here shows a couple of failed attempts at coaxing Maple to calculate the general solution of a pretty simple second order ODE.  I have also included the expected solution which I  have calculated by hand.  Perhaps I am missing a key trick.  Any ideas?

The ODE that I am actually interested in is significantly more complex. The one in the worksheet is a much simplified "bare bones" specimen that exhibits the issue that I am facing.

Attempt to solve with Heaviside

> 

restart;
> 

de := diff(u(x),x$2) = Heaviside(x - a)*u(x);

diff(diff(u(x), x), x) = Heaviside(x-a)*u(x)

dsolve fails:

> 

dsolve(de);

u(x) = DESol({diff(diff(_Y(x), x), x)-Heaviside(x-a)*_Y(x)}, {_Y(x)})

Attempt to solve with piecewise

> 

restart;
> 

de := diff(u(x),x$2) = piecewise(x < a, 0, 1)*u(x);

de := diff(u(x), x, x) = piecewise(x < a, 0, 1)*u(x)

> 

dsolve(de);

Error, (in dsolve) give the main variable as a second argument

> 

dsolve(de, u(x));

Error, (in dsolve) give the main variable as a second argument

> 

 

> 

 

The solution is easy to calculate by hand

We just solve the (quite trivial) DE over the intervals x < a and x>a

separately, and patch the two solutions by requiring the continuity

of u(x) and diff(u(x), x) at x = a.  We get

> 

sol := piecewise(x < a,
        x*c[1] + c[2],
        ((a*c[1] + c[1] + c[2])*exp(x))/(2*exp(a)) + ((a*c[1] - c[1] + c[2])*exp(-x))/(2*exp(-a)));

sol := piecewise(x < a, x*c[1]+c[2], (a*c[1]+c[1]+c[2])*exp(x)/(2*exp(a))+(a*c[1]-c[1]+c[2])*exp(-x)/(2*exp(-a)))

Download solving-an-ode.mw

Select Values in Matrix...

Asked by: patrick22 30
matrix
June 27 2022
3  3

Hello,

I am fairly new to Maple. Suppose I have two Matrices

A := <<true, false, true> | <true, false, true> | <false, false, false>>

B := <<1, 2, 6> | <3, 4, 7> | <22, 33, 44>>

and apply select(A, B)

Why do I receive [[[(),3,22],[(),(),()],[(),7,44]]] instead of [[[1,(),6],[3,(),7],[(),(),()]]] as a result? I just want to select every element of B where A is true.

I appreciate any insight.

algebra,factoring...

Asked by: rolfjg 45
factor automatic-simplification
June 27 2022
1  1

This is a simple algebraic, but I would like to know how to officially solve the problem,

I tried factor(6*a+12*b+18*c); it simply outputs what I input.

I tried primpart(6*a+12*b+18*c) ; the output is: a+2b+3c

I tried content(6*a+12*b+18*c), the output is 6

What I'm looking for an output is, 6*(a+2*b+3*c), this is the answer my Algebra book is looking for, I also get this answer by

using my HP Graphing Calculator, but I'm unable to get the answer from Maples. Can anyone help?

How to plot this ODE equation in Numerical Method...

Asked by: Saha 80
ode syntax homework
June 27 2022
1  4
Could you Please Help me,the Maple code for Plot this equations in any Numerical Method
> 

restart
> 

with(PDETools, declare):
> 

with(LinearAlgebra):
> 

with(PolynomialIdeals):
> 

with(plots):
> 

declare(f(x));

f(x)*`will now be displayed as`*f

 (1)
> 

eq1 := diff(f(x), x, x, x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cos&omega;`+f(x)*`sin&omega;`)*(diff(f(x), x, x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`&rho;&beta;`[s]/`&rho;&beta;`[fl])*lambda[T]*theta = 0;

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cos&omega;`+f(x)*`sin&omega;`)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`&rho;&beta;`[s]/`&rho;&beta;`[fl])*lambda[T]*theta = 0

 (2)
> 

eq2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(eta*`cos&omega;`+f*`sin&omega;`)*(diff(theta(x), x)) = 0;

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(eta*`cos&omega;`+f*`sin&omega;`)*(diff(theta(x), x)) = 0

 (3)
> 

bcs := F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0;

F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0

 (4)
> 

a1 := [M = 1, alpha = 0, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `&rho;&beta;`[fl] = 20939.1, K[nf] = .6842, eta = 0];

[M = 1, alpha = 0, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `&rho;&beta;`[fl] = 20939.1, K[nf] = .6842, eta = 0]

  

[Pr = 6.2, M = 1, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, `&rho;&beta;`[fl] = 20939.1, K[nf] = .6842, K[f] = .613, eta = 0]

 (5)
> 

b1 := subs(a1, eq1);

diff(diff(diff(f(x), x), x), x)+.5325197465*f(x)*(diff(diff(f(x), x), x)) = 0

 (6)
> 

c1 := subs(a2, eq2);

1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0

 (7)
> 

d1 := dsolve({b1, bcs}, {bcs, c1}, numeric); d1(0)

Error, (in dsolve/numeric/process_input) invalid argument: {1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0, F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0}

  

d1(0)

 (8)
> 

``

Download  Numerical Method.mw

complex numbers...

Asked by: Amir_Maple 40
multiplication syntax
June 26 2022
2  2

Hi

I have a problem with calculating complex numbers in Maple.

I type forexample 8(cos(Pi/2)+I*sin(Pi/2)) and I get 8, I should get 8I

Should I re-install Maple or edit my settings?

best regards

solve equations...

Asked by: mehran rajabi 120
ode homework differential-equations
June 26 2022
1  11

Hi everybody,how can I solve these equations in Maple and plot the answers? tnx...

eq1 := diff(x(t), t) = 35*(y-x)

eq2 := diff(y(t), t) = -x*z-7*x+28*y

eq3 := diff(z(t), t) = x*y-3*z

How can I extract the coordinates from spacecurve...

Asked by: planetmknzm 35
coordinates spacecurve plotting
June 25 2022
4  24

Hi Dear All,

 

I need to extract the coordinates from spacecurve commend. For example;

 

h3:=spacecurve([-x,-y,z],omega=ws..0,color=green,thickness=5):
h4:=spacecurve([-x,y,z],omega=ws..0,color=blue,thickness=5):

Where, omega is a parameter difinening x, y, z.

Remove the ODE's from set with same variables...

Asked by: Tamour_Zubair 80
ode differential-equations
June 25 2022
0  6

Hello Everyone;

Hope you are fine. I have set of following ODE's;

Every variable has two ODE's. I need to take one ODE for each variable. Is that any way?
I am waiting for your kind response.

Thanks

Question2.mw

Bad solution display from LPSolve...

Asked by: Carl Love 28050
typesetting lpsolve prettyprint
June 25 2022
0  2

The solution from LPSolve shown in the worksheet below is displayed very weirdly:

  1. The first element is rounded to 3 significant digits.
  2. The variable indices have decimal points.
  3. Zeros are displayed as just decimal points with no digit 0.

Closer inspection (with, say, lprint) will reveal that the weirdness is only with the prettyprinting; the actual entries are as expected.
 

> 

restart:
> 

<(kernelopts,interface)(version), interface~([prettyprint, typesetting])[]>;

Vector(4, {(1) = `Maple 2022.1, X86 64 WINDOWS, May 26 2022, Build ID 1619613`, (2) = `Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`, (3) = 2, (4) = extended})

> 

(a,b,c):= (2,4,5):
> 

X:= Matrix((a,b), symbol= x):
Y:= Matrix((b,c), symbol= y):
Z:= Matrix((a,c), symbol= z):
> 

RegionC:= <5, 15, 8, 10, 15>:
> 

RegionA:= <90, 75>:
> 

RegionB:= <35, 20, 30, 15>:
> 

Cost1:= <
    2, 1, 3/2,   3;
  5/2, 2, 7/2, 3/2
>:

> 

Cost2:= <
    3/2, 4/5, 1/2, 3/2,   3;
      1, 1/2, 1/2,   1, 1/2;
      1, 3/2,   2,   2, 1/2;
    5/2, 3/2, 3/5, 3/2, 1/2
>:

> 

Cost3:= <
    11/4, 7/2, 5/2, 3,   5/2;
       3, 7/2, 7/2, 5/2, 2
>:
> 

Cost__Total:= (add@(add@`*`~)~)([Cost||(1..3)], [X,Y,Z]):
> 

CapB:= add(X[i], i= 1..a) <=~ RegionB:
> 

CapA:= add(<X|Z>[..,j], j= 1..b+c) <=~ RegionA:
> 

ReqC:= add(<Y,Z>[i], i= 1..a+b) >=~ RegionC:
> 

InEqOutB:= add(<X, -Y^%T>[i], i= 1..a+c) =~ 0:
> 

Cons:= seq~({CapA, CapB, ReqC, InEqOutB}):
> 

Sol:= Optimization:-LPSolve(Cost__Total, Cons, assume= nonnegative);

[103.800000000310, [x[1, 1] = HFloat(0.0), x[1, 2] = HFloat(20.000000000344205), x[1, 3] = HFloat(7.999999999311598), x[1, 4] = HFloat(0.0), x[2, 1] = HFloat(0.0), x[2, 2] = HFloat(0.0), x[2, 3] = HFloat(0.0), x[2, 4] = HFloat(15.000000000688408), y[1, 1] = HFloat(0.0), y[1, 2] = HFloat(0.0), y[1, 3] = HFloat(-1.7763568394002505e-15), y[1, 4] = HFloat(0.0), y[1, 5] = HFloat(0.0), y[2, 1] = HFloat(0.0), y[2, 2] = HFloat(15.0), y[2, 3] = HFloat(5.000000000344206), y[2, 4] = HFloat(0.0), y[2, 5] = HFloat(0.0), y[3, 1] = HFloat(5.000000000000002), y[3, 2] = HFloat(0.0), y[3, 3] = HFloat(0.0), y[3, 4] = HFloat(0.0), y[3, 5] = HFloat(2.9999999993115956), y[4, 1] = HFloat(0.0), y[4, 2] = HFloat(0.0), y[4, 3] = HFloat(2.9999999996557944), y[4, 4] = HFloat(0.0), y[4, 5] = HFloat(12.000000000688413), z[1, 1] = HFloat(0.0), z[1, 2] = HFloat(0.0), z[1, 3] = HFloat(0.0), z[1, 4] = HFloat(0.0), z[1, 5] = HFloat(0.0), z[2, 1] = HFloat(0.0), z[2, 2] = HFloat(0.0), z[2, 3] = HFloat(0.0), z[2, 4] = HFloat(10.0), z[2, 5] = HFloat(0.0)]]

> 

 

 

Download BadLPSolveDisp.mw

is it possible to keep GAMMA(1,x) as is and not r...

Asked by: nm 11398
June 25 2022
1  1

I am reading some expressions from file.

In the file, it is written as GAMMA(-1,x). When read into Maple using the read file command, it shows as  1/x*Ei(2,x)

I know these are the same mathematically. But I am translating these expressions to sagemath. in sagemath, Ei only accepts one argument.

Now the translator sees Ei in the input, then it keeps it as Ei as it does not know it was the GAMMA with two arguments,  which gives an error when used by sagemath since sagemath only has the one argument version of Ei.

If Maple would keep GAMMA(-1,x) as is, then the translator will just translate it to gamma(-1,x) which works in sage.

To keep things simple, I was wondering if there an option to tell Maple to keep the input as GAMMA(-1,x) and not rewrite to Ei?

Otherwise I would have to now parse each Ei to see if it is the two argument version or the one argument version, and use gamma  for the 2 argument version to keep sage happy which will complicate things for me. 

expr:=GAMMA(-1,x)

               Ei(2, x)/x

Maple 2022.1

First 299 300 301 302 303 304 305 Last Page 301 of 2219