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Kitonum

21550 Reputation

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17 years, 124 days
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These are answers submitted by Kitonum

Adjustment...

Kitonum 21550
February 20 2019
0 0


 

NULL

NULL

restart

NULL

Digits := 20

20

 (1)

``

``

NULL

c := .95

.95

 (2)

NULL

theta := .9

.9

 (3)

k := 1.

1.

 (4)

p_l := 10^(-15.)

0.10000000000000000000e-14

 (5)

n := 10^10.

10000000000.

 (6)

NULL

fsolve(c = p_l^k*(1-p_l)^(n-k)*theta/(p_l^k*(1-p_l)^(n-k)*theta+p^k*(1-p)^n*(1-theta)), p = 1.09*10^(-10) .. .1)

0.14965925863591907056e-8

 (7)

NULL

NULL

NULL

``

NULL

NULL

NULL

NULL

NULL

NULL

NULL

NULL

NULL

NULL

NULL

NULL


 

Download test_(4)_new.mw

Lists vs sets...

Kitonum 21550
February 19 2019
0 0

The functions and the colors should be specified as lists not sets:

w:=x+I*y:
plots[implicitplot]([Im(w) = 2, Re(w) = 2], x = -5 .. 5, y = -5 .. 5, color = ["Blue", "Red"]) ; 


I do not use 2D math input at least because the code typing in it takes more time.

Procedure and 2 examples...

Kitonum 21550
February 19 2019
1 0 
Kollect:=proc(L::set, n::posint)
uses combinat;
`+`(seq(`+`(mul~(choose(L minus {i},n))[])*i^n, i=L));
end proc:

Examples of use:
Kollect({i1, i2, i3, i4}, 2);
Kollect({a, b, c, d, e}, 3);
 

simplify/siderels...

Kitonum 21550
February 19 2019
1 0

simplify(a, {alpha^2=0});

Inert sqrt...

Kitonum 21550
February 18 2019
0 1

You can prevent automatic fraction reduction using inert  sqrt :

%sqrt(x)/x;
value(%); 
                                        

 

Digits...

Kitonum 21550
February 18 2019
0 0

This is probably due to rounding errors. If you increase  Digits , the plots are identical:

restart;
Digits:=50:
plot(sqrt(Pi/(2*x))*BesselJ(3+1/2, x), x = 0 .. 0.5e-1);
plot(sqrt(Pi/(2*x))*BesselJ(3+.5, x), x = 0 .. 0.5e-1);

 

CurveFitting:-LeastSquares...

Kitonum 21550
February 17 2019
1 0

Perhaps this is a bug. As a workaround use  CurveFitting:-LeastSquares  instead:

CurveFitting:-LeastSquares(pts1, pts2, x, curve = 3*x+a);
                                     -61/3+3*x

Adjustment...

Kitonum 21550
February 17 2019
1 3 
restart;

Ec := (Ems+I*Eml)*(1+((Ems+I*Eml)/Ef-1)*Zeta*phi/((Ems+I*Eml)/Ef+Zeta))/(1-((Ems+I*Eml)/Ef-1)*phi/((Ems+I*Eml)/Ef+Zeta));

a:=simplify(Re(Ec)) assuming positive;
b:=simplify(Im(Ec)) assuming positive;

a  and  b  are the real and imaginary parts of  Ec .

Adjustment...

Kitonum 21550
February 16 2019
0 0


 

restart

A := binomial(n, k)

`assuming`([limit(A*(lambda/n)^k*(1-lambda/n)^(n-k), n = infinity)], [lambda > 0, lambda < n, k::posint])

lambda^k/(GAMMA(k)*k*exp(lambda))

 (1)

simplify(convert(%, factorial))

lambda^k*exp(-lambda)/factorial(k)

 (2)

`assuming`([limit(eval(A*(lambda/n)^k*(1-lambda/n)^(n-k), k = 0), n = infinity)], [lambda > 0, lambda < n])

exp(-lambda)

 (3)

``


 

Download Poisson.mw

Edit.

Simplier...

Kitonum 21550
February 16 2019
1 1


 

restart

A := binomial(n, k); assume(p >= 0, p <= 1)

binomial(n, k)

 (1)

E := sum(A*p^k*(1-p)^(n-k)*k, k = 0 .. n)

(p/(1-p)+1)^n*p*n*(1-p)^n/((1-p)*(p/(1-p)+1))

 (2)

E := simplify(E)

p*n

 (3)

simplify(sum(A*p^k*(1-p)^(n-k)*(k-E)^2, k = 0 .. n))

-p*n*(-1+p)

 (4)

subs(-1+p = -q, %)

p*n*q

 (5)

NULL


 

Download simpl_new.mw


Edit.

rsolve...

Kitonum 21550
February 14 2019
2 7

You can easily get the explicit formula for this sequence:

rsolve({y(0)=(-sqrt(5)+5)*(1/8), y(n)= 4*y(n-1)*(1-y(n-1))}, y(n));

Adjustment...

Kitonum 21550
February 13 2019
0 0


 

> 

restart;
A[0] := 0;                      
A[1] := sqrt(2*(k[1]^2-w[1]^2))/n;
A[2] := sqrt(2*(k[2]^2-w[2]^2))/n;
c[1] := 1;
c[2] := 1;
c[3] := 1;
c[4] := 1;
c[5] := 1;
c[6] := 1;
k[1] := 10.5;
k[2] := 3.5;
w[1] := 5.05;
w[2] := .5;
m := 1.9;
n := 1.75;
xi[1] := -t*w[1]+x*k[1];
xi[2] := -t*w[2]+x*k[2];
a := m/sqrt(2*(k[1]^2-w[1]^2));
b := m/sqrt(k[2]^2-w[2]^2);
g := a*(c[2]*exp(a*xi[1])+c[3]*exp(-a*xi[1]));
h := c[1]+c[2]*exp(a*xi[1])+c[3]*exp(-a*xi[1]);
G := b*(c[5]*exp(b*xi[2])+c[6]*exp(-b*xi[2]));
H := c[4]+c[5]*exp(b*xi[2])+c[6]*exp(-b*xi[2]);
u := A[0]+A[1]*g/h+A[2]*G/H;

0

  

(2*k[1]^2-2*w[1]^2)^(1/2)/n

  

(2*k[2]^2-2*w[2]^2)^(1/2)/n

  

1

  

1

  

1

  

1

  

1

  

1

  

10.5

  

3.5

  

5.05

  

.5

  

1.9

  

1.75

  

-5.05*t+10.5*x

  

-.5*t+3.5*x

  

.1459402733

  

.5484827558

  

.1459402733*exp(-.7369983802*t+1.532372870*x)+.1459402733*exp(.7369983802*t-1.532372870*x)

  

1+exp(-.7369983802*t+1.532372870*x)+exp(.7369983802*t-1.532372870*x)

  

.5484827558*exp(-.2742413779*t+1.919689645*x)+.5484827558*exp(.2742413779*t-1.919689645*x)

  

1+exp(-.2742413779*t+1.919689645*x)+exp(.2742413779*t-1.919689645*x)

  

7.439442594*(.1459402733*exp(-.7369983802*t+1.532372870*x)+.1459402733*exp(.7369983802*t-1.532372870*x))/(1+exp(-.7369983802*t+1.532372870*x)+exp(.7369983802*t-1.532372870*x))+2.799416849*(.5484827558*exp(-.2742413779*t+1.919689645*x)+.5484827558*exp(.2742413779*t-1.919689645*x))/(1+exp(-.2742413779*t+1.919689645*x)+exp(.2742413779*t-1.919689645*x))

 (1)
> 

plot3d(u, x = -20 .. .20, t = -20 .. .20);
t := 0;
plot(u, x = -15 .. 15);
 

 

0

  

 
> 

 


 

Download plots.mw

Explore...

Kitonum 21550
February 13 2019
2 1

And what if you just write a single line of code that does the same thing without any packages and plot components :

Explore(plot(sin(a*x)+cos(b*x^2), x=0..10, -3..3), a=0..1., b=0..1.);
                    

 

Adjustment...

Kitonum 21550
February 11 2019
2 0

I removed the square brackets that you use to group expressions. To do this, Maple should use only parentheses. Brackets are used to create lists. Some corrections were also made to improve the quality of the graphs:


 

> 

restart;
A[0] := 0;                           
A[1] := sqrt(2*(k[1]^2-w[1]^2))/sqrt(lambda);                             
A[2] := sqrt(2*(k[2]^2-w[2]^2))/sqrt(lambda);                             
c[1] := 1;
c[2] := 1;
c[3] := 1;
c[4] := 1;
c[5] := 1;
c[6] := 1;
k[1] := 10.5;
k[2] := 3.5;
w[1] := 5.05;
w[2] := .5;
m := 1.9;
lambda := 1.75;
xi[1] := -t*w[1]+x*k[1];
xi[2] := -t*w[2]+x*k[2];
a := m/sqrt(k[1]^2-w[1]^2);
b := m/sqrt(k[2]^2-w[2]^2);
g := a*(c[2]*cos(a*xi[1])-c[3]*sin(a*xi[1]));
h := c[1]+c[2]*sin(a*xi[1])+c[3]*cos(a*xi[1]);
G := b*(c[5]*cos(b*xi[2])-c[6]*sin(b*xi[2]));
H := c[4]+c[5]*sin(b*xi[2])+c[6]*cos(b*xi[2]);
u := A[0]+A[1]*g/h+A[2]*G/H;
  

0

  

(2*k[1]^2-2*w[1]^2)^(1/2)/lambda^(1/2)

  

(2*k[2]^2-2*w[2]^2)^(1/2)/lambda^(1/2)

  

1

  

1

  

1

  

1

  

1

  

1

  

10.5

  

3.5

  

5.05

  

.5

  

1.9

  

1.75

  

-5.05*t+10.5*x

  

-.5*t+3.5*x

  

.2063907138

  

.5484827558

  

.2063907138*cos(1.042273105*t-2.167102495*x)+.2063907138*sin(1.042273105*t-2.167102495*x)

  

1-sin(1.042273105*t-2.167102495*x)+cos(1.042273105*t-2.167102495*x)

  

.5484827558*cos(.2742413779*t-1.919689645*x)+.5484827558*sin(.2742413779*t-1.919689645*x)

  

1-sin(.2742413779*t-1.919689645*x)+cos(.2742413779*t-1.919689645*x)

  

9.841457496*(.2063907138*cos(1.042273105*t-2.167102495*x)+.2063907138*sin(1.042273105*t-2.167102495*x))/(1-sin(1.042273105*t-2.167102495*x)+cos(1.042273105*t-2.167102495*x))+3.703280398*(.5484827558*cos(.2742413779*t-1.919689645*x)+.5484827558*sin(.2742413779*t-1.919689645*x))/(1-sin(.2742413779*t-1.919689645*x)+cos(.2742413779*t-1.919689645*x))

 (1)
> 

plot3d(u, x = -10 ..0.2, t = -10 .. 0.2, view=-50..50, grid=[200,200]);
 

 
> 

plot(eval(u,t=0), x = -15 .. 15, -50..50, numpoints=5000, discont, size=[800,400]);

 
> 

 


 

Download 2plots.mw

expand, factor...

Kitonum 21550
February 10 2019
1 0

is(expand(B*exp(I*Pi/3))=expand(A));
                                                                     true

# Or

factor(expand(A/B));
polar(%);


Edit.
 

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