How to plot Complex vales in 2D? 

Z be complex.

rho := 1/4; mu := 1/4; E := sum(Z^k/GAMMA(k*rho+mu), k = 0 .. 5)

I am trying to run this code but this error message is coming up "Error, (in fprintf) number expected for floating point format
". What have I done wrong and how do I correct it.

Thank you and best regards.

restart;
Digits:=30:

f:=proc(n)
	-((sin(x[n]))/(2-sin(x[n])))*(2+sin(x[n]-Pi)):
end proc:

e1:=y[n+1]=h*delta[n]-(1/2)*h^2*(-u^2*sin((1/2)*u)+2*cos((1/2)*u)*u-2*cos(u)*u-4*sin((1/2)*u)+2*sin(u))*f(n)/(u^2*(2*sin((1/2)*u)-sin(u)))+(1/2)*h^2*(u^2*sin((1/2)*u)+2*cos((1/2)*u)*u-4*sin((1/2)*u)+2*sin(u)-2*u)*f(n+1)/(u^2*(2*sin((1/2)*u)-sin(u)))-(1/2)*h^2*(u*sin(u)+2*cos(u)-2)*f(n+1/2)/(u*(2*sin((1/2)*u)-sin(u)))+y[n]:
e2:=h*delta[n+1]=h*delta[n]+h^2*(u*sin((1/2)*u)+cos(u)-1)*f(n)/(u*(2*sin((1/2)*u)-sin(u)))+h^2*(u*sin((1/2)*u)+cos(u)-1)*f(n+1)/(u*(2*sin((1/2)*u)-sin(u)))-h^2*(u*sin(u)+2*cos(u)-2)*f(n+1/2)/(u*(2*sin((1/2)*u)-sin(u))):
e3:=y[n+1/2]=(1/2)*h*delta[n]-(1/8)*h^2*(-u^2*sin((1/2)*u)+4*cos((1/2)*u)*u-4*cos(u)*u-16*sin((1/2)*u)+8*sin(u))*f(n)/(u^2*(2*sin((1/2)*u)-sin(u)))+(1/8)*h^2*(u*sin((1/2)*u)+4*cos((1/2)*u)-4)*f(n+1)/(u*(2*sin((1/2)*u)-sin(u)))-(1/8)*h^2*(u^2*sin(u)+4*cos(u)*u+16*sin((1/2)*u)-8*sin(u)-4*u)*f(n+1/2)/(u^2*(2*sin((1/2)*u)-sin(u)))+y[n]:
e4:=h*delta[n+1/2]=h*delta[n]-(1/2)*h^2*(-u*sin((1/2)*u)+4*cos((1/2)*u)-2*cos(u)-2)*f(n)/(u*(2*sin((1/2)*u)-sin(u)))+(1/2)*h^2*(u*sin((1/2)*u)+4*cos((1/2)*u)-4)*f(n+1)/(u*(2*sin((1/2)*u)-sin(u)))-(1/2)*h^2*(u*sin(u)+2*cos(u)-2)*f(n+1/2)/(u*(2*sin((1/2)*u)-sin(u))):


inx:=0:
ind:=1:
iny:=2:
h:=Pi/4:
n:=0:
omega:=1:
u:=omega*h:
N:=solve(h*p = 8*Pi, p):

c:=1:
for j from 0 to 1 by 1/2 do
	t[j]:=inx+j*h:
end do:

vars:=y[n+1/2],y[n+1],delta[n+1/2],delta[n+1]:

step := [seq](eval(x, x=c*h), c=1..N):
printf("%6s%15s%15s%16s%15s%15s%15s\n", 
	"h","Num.y","Num.z","Ex.y","Ex.z","Error y","Error z");
#eval(<vars>, solve({e||(1..4)},{vars}));


st := time():
for k from 1 to N do

	par1:=x[0]=t[0],x[1/2]=t[1/2],x[1]=t[1]:
	par2:=y[n]=iny,delta[n]=ind:
	res:=eval(<vars>, fsolve(eval({e||(1..4)},[par1,par2]), {vars}));

	for i from 1 to 2 do
		exy:=eval(2+sin(c*h/2)):
		exz:=eval(-sin(c*h/2)+10*epsilon*cos(10*c*h)):
		printf("%6.5f%17.9f%15.9f%15.9f%15.9f %13.5g%15.5g\n", 
		h*c,res[i],res[i+2],exy,exz,abs(res[i]-exy),
		abs(res[i+2]-exz)):
		
		c:=c+1:

	end do:
	iny:=res[2]:
	ind:=res[4]:
	inx:=t[1]:
	for j from 0 to 1 by 1/2 do
		t[j]:=inx + j*h:
	end do:
end do:

Hi 

How to add a legend to Statistics:-Histogram?

This could be particularly useful to compare histograms, for instance in

S := Statistics:-Sample(Normal(0, 1), 1000):
T := Statistics:-Sample(Normal(1, 1), 1000):

plots:-display(
  Statistics:-Histogram(S, color=gold, transparency=0.3, legend="N(0,1)"),
  Statistics:-Histogram(T, transparency=0.3, legend="N(1,1)")
);

But doing this generates the error Error, (in Statistics:-Histogram) display does not accept the legend option

And yes indeed, even this command

h := Statistics:-Histogram(S, legend="N(0,1)")

already produces the same error.

After having examined the structure of h and using a way Carl Love gave here How to change the colour inn Statistics:-Sunflower?  I finally obtained the expected plot.
 

HS := Statistics:-Histogram(S, color=gold, transparency=0.3):
HT := Statistics:-Histogram(T, transparency=0.3):

hs := evalindets([op(HS)], specfunc(COLOUR), c-> (c, LEGEND("N(0,1)")) ):
ht := evalindets([op(HT)], specfunc(COLOUR), c-> (c, LEGEND("N(1,1)")) ):

PLOT(op(hs), op(ht))

But this rather long a way to proceed (Note: it seems that the overrideoption  that acer suggested in this prevous thread doesn't "work" here?)
Do you have any idea if there is a simpler solution?

TIA

AoA....

sir how we solve partial differential equation by Adomian Decomposition method in maple? plz send me maple code..

Dear all
I have a problem when running the follwoing code using the input proposed. 

integ_R.mw

problem : print_table , used as input in  proc 

Thank you for your help 

Dear all

I tried to compute an integral using trapezoidal rule using two differents methods but I get two different results
trap.mw

Thank you for your help 

How to solve and plot the integral equation?
b.mw
 

I am trying to input X-data, Y-data from spreadsheet-section of Numbers (Apple App) to do reression analysis in Maple. I do not understand the export or import tools very well just yet, asis obvious from numerous wrong results.

Since I want to do regression of the X-Y data trends, what format would you recommend using for the data once imported into Maple; two sequences, two-vectors, multi-row column matrix ???

If someone has worked with Numbers-Apple-App (Not Excel) into Maple to do this and can provide simple example with steps/tools used. It would be appreciated. Thanks

Dear all

I would like to sketch the solution of first ode, but by hand we can not get the solution. I used maple, to  solve the ode but unfortunattely there is no solution obtained so I can sketech the behavior of the solution. 

Is there any way to sketch the solution behavior .

sketch_solution.mw

thank you 

Hi. I have solved numerical an ODE and want to use the solution in the integrand of a subsequent integral. I'm being frustrated by my lack of knowledge and the internet isn't helping! I hope someone can put me right.....here's the relevant part of code.

dsysA := {diff(r(s), s) = sqrt((g*r(s) + h)^2 - 1 + 1/r(s)), r(0) = rinit};
dsnA := dsolve(dsysA, numeric, abserr = 10^(-6));

dsnA(0.1);
               [s = 0.1, r(s) = 1.51303353884965]

rA := s -> rhs(dsnA(s)[2]):

rA(0.2);
                        1.53235325247661

tA := s -> tinit + int((g*rA(p) + h)/(1 - 1/rA(p)), p = 0 .. s):

tA(0.01);
Error, (in rA) invalid input: rhs received dsnA(p)[2], which is not valid for its 1st argument, expr
 

Hi, I want to minimize a*x + log2(3+4.2^(-x)+2^(-2x)) , x>0 & 0<=a<=1 where a is some constant. Is there any command in maple which help me to minimize this. For command minimize, I am unable to minimize the function symbolically. I need to minimize it in terms of a.

Hi I am trying to compute the series approximation for the difference between these two divergent integrals

M := int(cosh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x));

N := int((1 + x)*sinh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x))

where x,p are positive and x is approaching zero. I would like to get a series expansion of M-N, but I am not quite if this is possible.

Dear Users!
Hope everyone fine here. I have a vector V and want a new vector after transformation like

V := Vector(5, {(1) = 2, (2) = 3, (3) = -1, (4) = 9, (5) = 7});

after square transformation of V I got a new vector W like bellow

W := Vector(5, {(1) = 4, (2) = 9, (3) = 1, (4) = 81, (5) = 49});

and similarly sin transformation of V give the following matrix as

U := Vector(5, {(1) = sin(2), (2) = sin(3), (3) = sin(-1), (4) = sin(9), (5) = sin(7)});
Please help me to get vectors W and U.

Dear all
Using cubic spline interpolation to interpolate a given function I get  
the follwoing error
Warning, solving for expressions other than names or functions is not recommended.
Error, (in solve) list of unknowns contains repeated elements: [1, 0]

and  why the  spline funciton obtained by this code is different to the one given by Maple's built in package.

inter.mw

Thank you for any help 

I want to remove the term XY
f:=(x,y)->2*x²+xy+y²+4x-y-2=0;
eq := simplify(subs(x = X-9/7, y = Y+8/7, f(x, y)));
theta:=Pi/8;
ex := simplify(subs(X = cos(theta)*X-sin(theta)*Y, Y = sin(theta)*X+cos(theta)*Y, eq)); evalf(%);
How to obtain (3+sqrt(2))/2*X²+(3-sqrt(2))/2=36 ? Thank you.