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serious problem. Integrate do not work a...

nm 11738 Maple 2019
int physics
September 21 2019
2 2

I just  found what seems to be a serious problem and I am not able to figure if it is related to my own installation or not.

After I installed Physics 426 (Published on Sept 17, 2019) using the Maple GUI install button (which now works for my PC), I found I am not able to integrate basic things.

It seems to affect int when using some build in function with definite integration, but it could be others also. I need to test more. 

Could someone see if they get same problem as well?  

Could also someone please remind me of the library  commands to issue in order to remove current Physics version 426 and install earlier Physics version package, say 425, or any other version, so that  to see if this is related to version of a physics package or not?

> 

restart;
> 

version()

 User Interface: 1399874
         Kernel: 1399874
        Library: 1399874

1399874

> 

interface(version)

`Standard Worksheet Interface, Maple 2019.1, Windows 10, May 21 2019 Build ID 1399874`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 426 and is the same as the version installed in this computer, created 2019, September 20, 23:28 hours, found in the directory C:\Users\me\maple\toolbox\2019\Physics Updates\lib\`

> 

infolevel[int] := 3:
> 

int(exp(x),x=0..1)

Definite Integration:   Integrating expression on x=0..1

Definite Integration:   Using the integrators [distribution, piecewise, series, o, polynomial, ln, lookup, cook, ratpoly, elliptic, elliptictrig, meijergspecial, improper, asymptotic, ftoc, ftocms, meijerg, contour]
LookUp Integrator:   unable to find the specified integral in the table
int/elliptic: trying elliptic integration
Integration Warning:   Integration method ftoc encountered an error in IntegrationTools:-Definite:-Main:
 mismatched multiple assignment of 2 variables on the left side and 1 value on the right side

Definite Integration:   Returning integral unevaluated.

int(exp(x), x = 0 .. 1)

> 

restart;
> 

int(sin(n*x),x=0..Pi)

int(sin(n*x), x = 0 .. Pi)

> 

int(tan(x),x=0..Pi)

int(tan(x), x = 0 .. Pi)

> 

int(cos(x),x=0..1)

int(cos(x), x = 0 .. 1)

> 

int(sin(x),x=0 .. Pi)

int(sin(x), x = 0 .. Pi)

> 

int(cos(x),x)

sin(x)

> 

int(x,x=0 .. 1)

1/2

 

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Error from pdsolve using periodic BC....

nm 11738 Maple 2019
pde pdsolve differential-equations
September 20 2019
1 2

Why Maple 2019.1 gives an error when no initial conditions are given for the following heat PDE with periodic BC?

I am using Physics 426 (current version). On windows 10.

When adding ic as some arbitrary function f(x), then the error goes away. But no ic needs to be given to solve this PDE. The answer can be left using arbitrary constants in this case.

I also found that this seems to happen when the BC are periodic. When using the normal Dirichlet B.C. and omitting the initial conditions, the error went away.

Am I doing something wrong or is this a bug?

> 

restart;
> 

pde:=diff(u(x,t),t)=diff(u(x,t),x$2); #try with NO IC
bc:=u(-Pi,t)=u(Pi,t),D[1](u)(-Pi,t)=D[1](u)(Pi,t);
pdsolve([pde,bc],u(x,t))

diff(u(x, t), t) = diff(diff(u(x, t), x), x)

u(-Pi, t) = u(Pi, t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t)

Error, (in pdsolve/BC/2nd_order/Series/TwoBC) invalid boolean expression: NULL

> 

restart;
> 

pde:=diff(u(x,t),t)=diff(u(x,t),x$2)-u(x,t); #now try with IC
bc:=u(-Pi,t)=u(Pi,t),D[1](u)(-Pi,t)=D[1](u)(Pi,t);
ic:=u(x,0)=f(x);
pdsolve([pde,bc,ic],u(x,t)); #solution is correct
> 

 

diff(u(x, t), t) = diff(diff(u(x, t), x), x)-u(x, t)

u(-Pi, t) = u(Pi, t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t)

u(x, 0) = f(x)

u(x, t) = exp(-t)*_C7[0]+Sum(exp(-t*(n^2+1))*(sin(n*x)*_C1[n]+cos(n*x)*_C7[n]), n = 1 .. infinity)

> 

restart;
> 

pde:=diff(u(x,t),t)=diff(u(x,t),x$2); #now try with NO IC, but not periodic BC
bc:=u(0,t)=1,u(Pi,t)=0;
pdsolve([pde,bc],u(x,t)); #solution is correct

diff(u(x, t), t) = diff(diff(u(x, t), x), x)

u(0, t) = 1, u(Pi, t) = 0

u(x, t) = ((Sum(sin(n*x)*exp(-n^2*t)*_C1(n), n = 1 .. infinity))*Pi+Pi-x)/Pi

> 

 

 

Download problem_09_20_2019.mw

why odetest no longer verify solution af...

nm 11738 Maple 2019
simplify expand trigonometry
September 08 2019
2 0

Is this documented somewhere?  Why Maple do not return 0 from odetest after expanding the solution?

update: added additional tries to simplify it to zero as suggested but they do not give zero.

> 

ode:=2*x^(1/2)*diff(y(x),x) = (1-y(x)^2)^(1/2);
sol:=dsolve(ode);

2*x^(1/2)*(diff(y(x), x)) = (1-y(x)^2)^(1/2)

y(x) = sin(x^(1/2)+(1/2)*_C1)

> 

odetest(sol,ode);

0

> 

res:=odetest(expand(sol),ode);

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res,symbolic)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res,trig)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

combine(res)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

combine(res,trig)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

expand(res)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res))

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),symbolic)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),trig)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),size)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

 

 

Download odetest_q.mw

dsolve returns signular solution which c...

nm 11738 Maple 2019
ode singular dsolve
August 30 2019
1 0

Why Maple returns -1/x as singular solution below when this solution can be obtained from the general solution when constant of integration is zero?

> 

restart;
> 

ode:=2*y(x)+2*x*y(x)^2+(2*x+2*x^2*y(x))*diff(y(x),x) = 0;
dsolve(ode,singsol=false);

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

y(x) = (-1-_C1)/x, y(x) = (-1+_C1)/x

> 

sol:=[dsolve(ode,singsol=essential)];

[y(x) = -1/x, y(x) = (-1-_C1)/x, y(x) = (-1+_C1)/x]

> 

subs(_C1=0,sol)

[y(x) = -1/x, y(x) = -1/x, y(x) = -1/x]

> 

 


Download essential.mw

strange latex result. Why an extra 1 sho...

nm 11738 Maple 2019
latex
August 29 2019
2 3

We all know that Maple's Latex is not the best of Maple to say the least.

But this one is really strange. Maple prints a `1` for no apparant reason in the latex which makes it ugly. 

I wonder if Maplesoft still maintains its Latex conversion code at all?  So one can at least hope may be one day all of this will get fixed? Year after year, and Maple's Latex still not changed.  

If Mapesoft do not intend to make any changes in its Latex conversion software at all, it will be good if an official statement is made in this regards so that at least customers know.

> 

sol:=dsolve((x-a)*(x-b)*diff(y(x),x)+k*(y(x)-a)*(y(x)-b) = 0,y(x)):
sol:=subs(_C1=C[1],sol);

y(x) = ((x-b)^(-k)*(x-a)^k*a*exp(a*k*C[1]-b*k*C[1])-(x-b)^(-k)*(x-a)^k*b*exp(a*k*C[1]-b*k*C[1])+b*((-x+b)/(-x+a))^(-k)*exp(a*k*C[1]-b*k*C[1])-b)/(-1+((-x+b)/(-x+a))^(-k)*exp(a*k*C[1]-b*k*C[1]))

> 

latex(sol)

y \left( x \right) ={1 \left(  \left( x-b \right) ^{-k} \left( x-a
 \right) ^{k}a{{\rm e}^{akC_{{1}}-bkC_{{1}}}}- \left( x-b \right) ^{-k
} \left( x-a \right) ^{k}b{{\rm e}^{akC_{{1}}-bkC_{{1}}}}+b \left( {
\frac {-x+b}{-x+a}} \right) ^{-k}{{\rm e}^{akC_{{1}}-bkC_{{1}}}}-b

 \right)  \left( -1+ \left( {\frac {-x+b}{-x+a}} \right) ^{-k}{{\rm e}
^{akC_{{1}}-bkC_{{1}}}} \right) ^{-1}}

> 

 

 

Download why_1_in_latex.mw

 

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