## Intersection of plot with axes...

Hello

I have a simple list:

xlist := [150, 250, 500, 800, 1300, 2500, 5000]:

ylist := [.3, .5, .8, 1.0, 1.2, 1.4, 1.6]:

where after i said x:=plot(xlist,ylist);

What I want to do is ask maple" At what x value does the graph intersect with 1.5 on the y axis" or "at what y value does the graph intersect with 3000 on the x axis".

The data points are just that, I've been looking for commands to ask these questions but have been without luck. You don't need to give me the answer if you can point me to somewhere where this information is written, that would be very helpful!

Thank you.

## Error in dsolve,numeric...

first_order_error.mw

hi.please see attached file and explain how i remove error

thanks alot

## Where was that visualization used?...

Where was this graphic of a mountain crater used in Maple?  The top left graphic from here http://www.maplesoft.com/products/maple/features/Visualization.aspx#

I haven't seen it used in any webinars nor have I seen it in the application center.  5 points to anyone who can find it :)

## Singularity in dsolve/numeric/bvp...

mid_point.mw

thanks alot

dsys3 := {(diff(w(x), x, x, x, x))/x^2 = .4/(x^3*(1-w(x))^3)+40*(1+.65*(1-w(x)))/(x*(1-w(x))^2), w(0) = 0, w(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0}

dsol5 := dsolve(dsys3, numeric, output = array([.5]))

Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

## Phase angle calculation...

Hi,

I am a Maple über noob.

I am strugeling to figure out how to do simple phase calculations

For example

Phase_angle.mw

It is mainly for 3-phase angle calculation

## Slow and not accurate...

restart: with(plots):
H := a -> piecewise(a>=0,1):
f1 := y->(H(y-1*Pi)-H(y-2*Pi))*sin(y)^2:

g1:=(f1(y)/sqrt(4*Pi*t))*(sin((x-y)^2/4/t+Pi/4)-sin((x+y)^2/4/t+Pi/4)):
g2:= int(g1, y= 0..100):

g3:= diff(g2,t):
g4:= diff(g2,x\$2):
g5:= (g3^2+g4^2)/2:
E2:= unapply(Int(g5, x= 0..100, epsilon= 1e-4, digits= 7), t):
CodeTools:-Usage( plot(E2, 0..20, numpoints= 50, labels= [t, E]));

The above mentioned code should give constant figure, but it takes a lot of time and not accurate.

If you can help me to improve these codes, I would be pleased.

Thanks!

## plot y[a],y[b],y[c] vs x....

dear all

(1-pi*x/2)y[b]-1/3=int(t^4/sqrt((t^2-y[b])^2+y[a]^2),t);

x^2*y[c](1-pi*x/2)-1/3=int(t^4/sqrt((t^2-x^2*y[c])^2+y[a]^2),t);

i want to plot y[a],y[b],y[c] vs x.

plz help me.

thank you

## How to change Matrix output?...

dear all

how Matrix(2, 2, [a,b,c,d]) change to:

a b

c d

without [] !

## hypergeometric solution?...

Dear guys

I have an integral. I want to solve it by maple, but I can't. I think it's result is a hypergeometric function. Could you please guide me?

Int((2*(1-f)*t^(-f)/(3*A*f*(1-a/(A*f*t^(f-1)))))^(1/2));

I want to solve this for "t".

Thanks

## listdensityplot small bug...

a:=Matrix(10,10,0):
b:=Matrix(10,10,0):

a[1,5]:=1:

b[10,5]:=1:

animate(listdensityplot,[a*k+b*(1-k),smooth=true],k=0..1)

compared with the range option in animate

animate(listdensityplot,[a*k+b*(1-k),smooth=true,range=0..1],k=0..1)

My guess is there something happening with the default animation that causes the anomaly.

## Generating pairs in a sequence...

I wish to generate a sequence like
a[1], b[1], a[2], b[2], a[3], b[3]

The following does not work for the obvious reason:

seq(a[i], b[i], i=1..3);

What is the right way?

## Natural parametrization of curve...

Let a piecewise-linear curve be defined by a listlist. For example,

LL := [[1.1, 2.04], [1.97, 4.04], [2.96, 2.97], [4.5, 6.4], [5.08, 7.21], [1.1, 4.04], [1.1, 2.04]]:
plot(LL);

How to find its natural parametrization in Maple? A procedure is desired. See Wiki for info.

## Error in pdsolve...

Hi everyone.

I have been experiencing a problem trying to solve a coupled system of 3 differencial equations

My problem is that a got a message back as I try to solve the system:

"Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector"

by apply this point that ''all dependent variables must be functions of the same independent variables''

i again accost with another error ''

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[1, 1](w))(x, -3/400000000)

''

## Why does (-8)^(1/3) become 1+Complex(1)* (3)^(1/2)...

Hello people in mapleprimes,

I have a question about why what is shown by maple by simplify(-8)^(1/3) is 1+ Complex(1)* (3)^(1/2)?

Solutions of x^3=-8 are -2, 1+Complex(1)*(3)^(1/2) and 1- Complex(1)*(3)^(1/2). And, as for the last one, 1- Complex(1)*(3)^(1/2), it is

the conjugate of the second, so it might not need to be written, because of it being easily seen so.

Is it the same reason why just -2 is not shown as the result of simplify((-8)^(1/3))?

PS. I know the instruction to use surd in such a case.

the reason I asked this question is this:

I am reading Essential Maple, where

ln(z) = ln(rho*exp(Complex(1)*theta));

ln(rho*exp(Complex(1)*theta))=ln(rho)+Complex(1)*theta;

ln(rho)+Complex(1)*theta;=ln(rho)+Complex(1)*arctan(y,x);

and

z^a=exp(a*ln(z));

and

"Because of

exp(w*Pi*Complex(1)*k)=cos(2*Pi*k) + Complex(1)*sin(2*Pi*k);

and

cos(2*Pi*k) + Complex(1)*sin(2*Pi*k)=1;

we could equally well have chosen

ln_k z = ln(z) + 2*Pi*Complex(1)*k"

are written.

Supposing these, there is a sentence that

"we choose k=0, and thus -Pi<=theta<=Pi to be the one (that for our canonical logarithm).

Every computer algebra language and numerical language follows this standard and takes the

complex logarithm to have its imaginary part in this range.

With this definition, (-8)^(1/3)=1 + Complex(1)*sqrt(3), and not -2. (the end of quotation)"

And, I can't understand the last sentence"With this definition", so I asked the above question.

I hope someone give an answer to the above question.