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Dkunb

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Dkunb 70 Maple 2021
assumptions assuming
March 17 2023
1 5

Why did the last line is(ysol2[1]>0) give false?

Maple does not recognize the assumption?

Thanks in advance.
 

> 

restart;
> 

 

> 

 

> 

interface(showassumed=0);

0

 (1)
> 

assume(theta>1,alpha>0,sigma1>0,beta>0,sigma2>0,delta>0,x>0,y>0,z>0);
> 

 

> 

f:=((theta*x-1)*(1-x)-y);
g:=y/(1+beta*y^2);
h:=(alpha*x-sigma1)*(1+beta*y^2);
j:=(delta*g-sigma2);
dxdt:=x*f;
dydt:=g*(h-z);
dzdt:=z*j;

(theta*x-1)*(1-x)-y

  

y/(beta*y^2+1)

  

(alpha*x-sigma1)*(beta*y^2+1)

  

delta*y/(beta*y^2+1)-sigma2

  

x*((theta*x-1)*(1-x)-y)

  

y*((alpha*x-sigma1)*(beta*y^2+1)-z)/(beta*y^2+1)

  

z*(delta*y/(beta*y^2+1)-sigma2)

 (2)

case0; x = 0, y = 0, z = 0

> 

E0:=<0,0,0>;

Vector[column](%id = 36893490685786064044)

 (3)

"case1: z=0 , h(x,y)=0, f(x,y)=0 : From y=(theta*x-1)*(1-x)=y -> 1/(theta)<x and x<1"

> 

xsol1:=solve(h=0,x) assuming x>1/theta and x<1;
ysol1:=solve(subs(x=xsol1,f)=0,y)assuming xsol1>1/theta and xsol1<1;
E1:=<xsol1,ysol1,0>;

xsol1 := sigma1/alpha

  

ysol1 := -(-sigma1*theta+alpha)*(alpha-sigma1)/alpha^2

  

Vector[column](%id = 36893490685786055012)

 (4)

case2; g(y) = 0, h(x, y) = 0

> 

ysol:=[solve(j=0,y)];
ysol2:=simplify(subs(sigma2=delta*eta,ysol)) assuming (1-4*beta*eta^2>0 and eta>0);

Warning, solve may be ignoring assumptions on the input variables.

  

[(1/2)*(delta+(-4*beta*sigma2^2+delta^2)^(1/2))/(beta*sigma2), -(1/2)*(-delta+(-4*beta*sigma2^2+delta^2)^(1/2))/(beta*sigma2)]

  

[(1/2)*(1+(-4*beta*eta^2+1)^(1/2))/(beta*eta), (1/2)*(1-(-4*beta*eta^2+1)^(1/2))/(beta*eta)]

 (5)
> 

is(ysol2[1]>0)

false

 (6)
> 

 

(1/2)*(1+(-4*beta*eta^2+1)^(1/2))/(beta*eta)

 (7)
> 

 

> 

 


 

Download Project_v1.mw

How to plot vector fields?...

Dkunb 70 Maple 2021
ode differential-equations deplot
March 08 2023
1 1
> 

restart;
> 

with(Physics):with(plots):with(DETools):
> 

sys := {diff(r(t),t)=p(t)/m,
diff(p(t),t)=l^2/(m*r(t)^3)-n*k*r(t)^(n-1),
diff(phi(t),t)=l/(m*r(t)^2)};

{diff(p(t), t) = l^2/(m*r(t)^3)-n*k*r(t)^(n-1), diff(phi(t), t) = l/(m*r(t)^2), diff(r(t), t) = p(t)/m}

 (1)
> 

sys1:=subs({n=1,k=1},sys);

{diff(p(t), t) = l^2/(m*r(t)^3)-1, diff(phi(t), t) = l/(m*r(t)^2), diff(r(t), t) = p(t)/m}

 (2)
> 

conv:=plottools:-transform((a,b)->[a*cos(b),a*sin(b)]):
> 

p1:=DEplot(sys1,[r(t),phi(t)],t=0..30,r=0..10,phi=0..2*Pi,stepsize=0.01);

Error, (in DEtools/DEplot) system must have same number of dependent variables as DE's.

  
> 

plots:-display([conv(p1)],axiscoordinates=polar);

Error, (in conv) invalid argument

  
> 

 


Could you help how to fix the code?

Download DEplot_v1.mw

DEplot for polar coordinates...

Dkunb 70 Maple 2021
differential-equations deplot plotting
March 07 2023
1 1

As2_v2.mw 

What should I fix my code in order to work?

Thanks in advance,

termination issue...

Dkunb 70 Maple 2021
performance integration numeric
December 22 2022
2 3

The loop for HFS _data_2 and SFS_data_2 and the loop for HFS _data_3 and SFS_data_3 do not seem to be terminated. I do not know what it is the issue here. Anyone who can help this?

Negativity_(v12_beta_gamma_mu).mw

Thank you in advance,

matrix index out of range...

Dkunb 70 Maple
matrix
November 23 2022
2 2
> 

restart;
> 

A:= Matrix();

A := Matrix(1, 0, {})

 (1)
> 

i_choices:= [seq(i,i=0..10,1)];

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

 (2)
> 

j_choices:= [seq(j,j=0..10,1)];

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

 (3)
> 

for i in i_choices do:
 for j in j_choices do:
   A[i,j] :=i+j;
   print(A[i,j]);
 od:
od;

Error, Matrix index out of range

  

Download test_Matrix.mw

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