I have four equations,

y = 1/x, y=3, y=1, x=0

restart;

P1 := plots:-implicitplot(y=1/x, x=-1..2, y=0..4, color=black, scaling=constrained):
P2 := plots:-implicitplot(y=3,   x=-1..2, y=0..4, color=black):
P3 := plots:-implicitplot(y=1,   x=-1..2, y=0..4, color=black):

plots:-display([P1,P2,P3]);

How do I fill the area between the first three equations and the y axis (x=0)?

Is it possible to do this with plottools:-transform?

I know this has to do with name scoping issue. But I do not see how to fix it now.

Calling J,Q:=LinearAlgebra:-JordanForm(A,output=['J','Q']); works in global, but not inside a proc.

What is the correct way to use this inside a proc?

Download jordan_issue.mw

Hi

I am on my way to construct a matrix for centripetal and Coriolis forces for a robot arm. However this requeers that I use a sum where the matrix index is the sumations index.

So I started testing things out before I constructed the full expresion, this is what I did.

According to the error page, this is du to that k in M[1,k] is an bad index, however in the sum this would be k=1 och k=2 whitch are vallid.

Do anybody know a way around this problem or can tell me what I did wrong.

Many thanks

Eric Ragnarsson

plots:-contourplot(16.70196911*2^(1/2)*((x^2 + 0.1*y)/((1 - x)*(3*x^2 + 0.2*y)))^(1/2)/(4.373839156*(x^2 + 0.1*y)/((1 - x)*(3*x^2 + 0.2*y)) + 1)^(1/2), x = 0.001 .. 1, y = 0.001 .. 1, contours = 20, thickness = 0, coloring = ["blue", "yellow"], axes = "boxed", filledregions = true)

I have tried many times, such as adding legendstyle = [position=correct],legend = true command, but it always report errors.

Can anyone help me solve this problem? Thank you.

Hi,

I'm trying to make Maple reduce an extensively simple complex equation, something so simple anybody with basic knowledge of complex numbers would take about 2 mins to solve manually.

Yet, I can't seem to get Maple to do it, which is disappointing. I can only hope the issue is on my side (I would be glad to be the one in the wrong).

example.mw

I expect at the last line a reduction to s^2 + 2*z*omega__n * s + omega__n^2

I tried different combinations of simplification functions without success. Simplify doesn't work much better.

Basically looking at something like this, but on Maple (this comes from Maxima), if possible *WITHOUT* the need for assume() on any scale (just like Maxima and Mathematica) :

Thanks!

I remember seeing sometime ago an option called something like "fraction free" in LinearAlgebra. But may be I was looking at something else or different package. I can't remember now. I searched the help pages now and googled and can't find it.

In Maple, when asking for eigenvectors of matrix, I'd like the vectors to come out fraction free, like with Mathematica.

It is ofcourse easy to write code to post process this and remove the fractions.

But before I do this, I thought to ask. Here is an example

restart;
A:=Matrix([[48,-30,-14,1],[65,-41,-19,0],[17,-10,-5,3],[-35,22,10,0]]);
(e,v):=LinearAlgebra:-Eigenvectors(A);

In Mathematica:

Anyone knows if such option exists somewhere?

Maple 2020.1

Heck Example 15.5 must have worked for an old version of maple.

restart;
## plot two functions and color the region between
sine :=   plot(sin(x), x=0..4*Pi, color=black,thickness=3):
s    :=   plot(sin(x), x=0..4*Pi, color=red, filled=true):
cosine := plot(cos(x), x=0..4*Pi, color=black,thickness=3):
c      := plot(cos(x), x=0..4*Pi, color=red, filled=true):
f := x -> if cos(x)>0 and sin(x)>0 then
              min(cos(x),sin(x))
          elif cos(x)<0 and sin(x)<0 then
              max(cos(x),sin(x))
          else 0
          end if;
b := plot(f(x), x=0..4*Pi, filled=true, color=green):

display([sine, cosine, b, s, c]):

Gives the error.

Error, (in f) cannot determine if this expression is true or false: 0 < cos(x)
and 0 < sin(x)

I tried verify(cos(x),0,less_than) and verify(sin(x),0,less_than), etc., but that makes f(x) always return 0.

f := sin(x);
g := cos(x);
plottools:-transform(unapply([x,y+g],x,y))(plot(f-g,x=0 .. 4*Pi,filled=true));
Works, but, I can not remember how that works.

Is it possible to use if in maple 2020.

In this example, PDEtools:-Solve throws an error, while solve returns empty solution.

Why the different behavior? Should PDEtools:-Solve also return empty solution like solve?

I noticed this, when I changed my code from using solve to using PDEtools:-Solve

restart;
eq:=[ eta1+2*eta2 = 0, eta1+2*eta2 = a1+a3, eta2 = a2+2*a3];
PDEtools:-Solve(eq,[a1, a2, a3]);


solve(eq,[a1, a2, a3])

interface(version)
Standard Worksheet Interface, Maple 2020.1, Windows 10, July 30 

   2020 Build ID 1482634


Physics:-Version()

The "Physics Updates" version in the MapleCloud is 832 and is 

   the same as the version installed in this computer, created 

   2020, October 3, 5:34 hours Pacific Time.

Maple 2020.1 

Download DataFrames_Example.mw

Hello

Just started out with maple. 

I entered a function that looks like this, to find the volume of a sphere: V := (4*Pi(d/2)^3)/3

then I use the eval command like this: eval(V, d = 6.35*mm)

and I get this:(4*Pi(3.175000000*mm)^3)/3

Anything I tried, maple doesn't want to spit out one number! I just need what that is equal to, I don't need an expression with Pi. Spent over two hours trying to figure it out, watching videos etc but no luck! hoping that someone can help me with this!

Charging a capacitor with a DC is well known and interaction with a sinusoidal signal is known to perfection.

The mathematical solutions behind an arbitrary waveform V1(t) is hard or impossible? to find .

To simplify, the arbitrary wave can be expressed with a 2-d degree polynom. This gives a fairly simple

expression with an integral. The problem however is that V2(t) - the capacitor voltage - appears on both sides and maple seems unable to resolv this into a symbolic expression.

If this can be solved it would be great ! The solution should be of the symbolic form V2(a,b,c,V2start,t1,t2,RC) and give the answer what voltage the capacitor V2 would reach arter charging between t1 and t2  with a V1(t) that is changing during charge.

How do I plot the complex function |z+1||z-1|=1 in Maple? I know there is complexplot but don't quite understand how to use it.

Why Maple gives different looking solution when calling  

dsolve(sys);

vs.

dsolve(sys,deps);

? Both solution are actually correct. But look different.  Here is an example

restart;
sys:=[
diff(x(t),t) = 2*x(t)-z(t), 
diff(y(t),t) = 2*y(t)+z(t), 
diff(z(t),t)=2*z(t),
diff(w(t),t)=-z(t)+2*w(t)];
deps:=[x(t),y(t),z(t),w(t)];

dsolve(sys);

dsolve(sys,deps);

Notice the difference:

In first case, the x(t) and y(t) solutions have 2 constants of integrations, and in the second case, they have 3 constants of integration.

If we solve this using the matrix exponential method, the solution comes out to match the first one:

A:=Matrix([[2,0,-1,0],[0,2,1,0],[0,0,2,0],[0,0,-1,2]]):
sol:=Vector([x(t),y(t),z(t),w(t)])=LinearAlgebra:-MatrixExponential(A,t).Vector([_C1,_C2,_C3,_C4]);
simplify(sol)

Again, both solution verify to 0, using odetest, and I assume now it is correct (have no reason to think odetest is not correct).

But I'd like to understand more why when passing the unknowns to dsolve, the solution comes out different looking (3 constants of integrations, vs. two in this case). Should the solution be the same looking in both cases? 

This came out, since I thought my solution was wrong, since it did not look like Maple's. 

Maple 2020.1

In a recent question, the solution involved [...]::[list$3].

H:= proc(n, x, y)
    if n=0 then y+1
    elif n=1 and y=0 then x
    elif n=2 and y=0 then 0
    elif y=0 then 1
    elif not [n,x,y]::[nonnegint$3] then 
        'procname'(n-1, x, 'procname'(n, x, y-1))
    else
        thisproc(n-1, x, thisproc(n, x, y-1))
    fi
end proc

Where is  the  form [...]::[list$3] documented?

Hi all,

There is issue with saving big numbers to txt file on WIndows

Please look at the file:

txt_issue.mw

Function save just cutting a big number.

Thank you.