Maple Questions and Posts

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please see attachment and explain why the output of the 2nd line is not 0
 

`mod`(2*n+1, 2)

1

(1)

`mod`(2*n+1, 3)

2*n+1

(2)

`mod`(2*n, 2)

0

(3)

``


 

Download mod_maple_help.mw

Dear all,

I'm trying to plot dispersion curves in Maple but I'm having some trouble. The code is attached as a file also.

f1  is my main function and I want to plot Vx with regard to f as all the rest are known variables, but I'm not able to do so.

I hope that someone can tell me why do I have this error.

Thanks in advance!

restart;
f1 := (C33*Rp*kzp+C13*kx)*(Rm*kx+kzm)*sin(kzp*h)*cos(kzm*h)-(C33*Rm*kzm-C13*kx)*(Rp*kx+kzp)*sin(kzm*h)*cos(kzp*h)=0;
Rp := (-C11*kx^2-C55*kzp^2+omega^2*rho)/((C55+C13)*kx*kzp);
Rm := (-C11*kx^2-C55*kzm^2+omega^2*rho)/((C55+C13)*kx*kzm);
kzp := sqrt(((-M+sqrt(M^2-4*N))*(1/2))*kx^2);
kzm := sqrt(((-M-sqrt(M^2-4*N))*(1/2))*kx^2);
M := (C11*C33/rho^2-2*C55*C13/rho^2+C13^2-omega^2*(C33+C55)/(rho*kx^2))*rho^2/(C33*C55);
N := (omega^2/kx^2-C11/rho)*(omega^2/kx^2-C55/rho)*rho^2/(C33*C55);
C11 := 0.435e10;
C13 := 0.259e10;
C55 := 0.112e10;
C33 := 0.108e11;
rho := 923;
h := 0.7e-2*(1/2);
kx := omega/Vx;
omega := 2*Pi*f;
f1;
plot(f1, f = 10 .. 0.100e6);
Error, (in plot) unexpected options: [(.4633081900*(-0.1717311166e12*f^2/Vx^2-0.2210791386e11*(...

Asim_dispers.mw

With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.

Vector_space_with_projections_and_forces_UPDATED.mw

Movie #01

https://www.youtube.com/watch?v=VAukLwx_FwY

Movie #02

https://www.youtube.com/watch?v=sIxBm_GN_h0

Movie #03

https://www.youtube.com/watch?v=LOZNaPN5TG8

Lenin Araujo Castillo

Ambassador of Maple

Display only the +'ve xyz axis, and also display +'ve axis as a different color than the negative axis.

I am having trouble exporting a matrix.  Attached is my file.  When I export the matrix the values for tpeak are not numeric.  They are string values indicating the analytical expression that MAPLE is displaying.  I cannot seem to find the option to express the results as numeric.

Can anyone help?

untitled5.mw

i have 4 equation and 4 variables with DirectSearch package it will give me a solution but not in a good time
when i try fsolve it just give me a blank
these are my equations :
POL[0] := .42810/(.65429+c[-2])

 POL[1] := -8.4078*c[-1]-162.64*c[0]+84.228*c[1]-6/(.80888+c[-2])^2+9.7066/(.80888+c[-2])^3-3.9257/(.80888+c[-2])^4+(1/2*(.42786*c[-1]+.42786*c[0]+.42786*c[1]+.65429/(.80888+c[-2])))*(-49.180*c[-1]+31.921*c[0]-8.6921*c[1]+2/(.80888+c[-2])-3.2355/(.80888+c[-2])^2+1.3086/(.80888+c[-2])^3)

POL[2] := 53.965*c[-1]+43.012*c[0]-103.98*c[1]-6/(1.+c[-2])^2+12./(1.+c[-2])^3-6./(1.+c[-2])^4+(1/2*(.50000*c[-1]+.50000*c[0]+.50000*c[1]+1./(1.+c[-2])))*(22.229*c[-1]-37.815*c[0]+22.229*c[1]+2/(1.+c[-2])-4./(1.+c[-2])^2+2./(1.+c[-2])^3)

POL[3] := -30.115*c[-1]+43.264*c[0]+52.171*c[1]-6/(1.2363+c[-2])^2+14.836/(1.2363+c[-2])^3-9.1704/(1.2363+c[-2])^4+(1/2*(.52893*c[-1]+.52893*c[0]+.52893*c[1]+1.5284/(1.2363+c[-2])))*(-4.5997*c[-1]+16.892*c[0]-26.026*c[1]+2/(1.2363+c[-2])-4.9452/(1.2363+c[-2])^2+3.0568/(1.2363+c[-2])^3)

i even change digits to 100 but still no awenser

my fsolve syntax

K := fsolve({seq(POL[v], v = 0 .. 2*N+2)})

the awenser fsolve gave me

K:=

thats all it gave me

I'd like to present the following bugs in the IntTutor command.

1. Initialize

Student[Calculus1]:-IntTutor((1+cos(3*x))^(3/2), x);

then press the All Steps button. The command produces the answer (see Bug1_in_IntTutor.mw)

(4/9)*sqrt(2)*sin((3/2)*x)^3-(4/3)*sqrt(2)*sin((3/2)*x)

which is not correct in view of

plot(diff((4/9)*sqrt(2)*sin((3/2)*x)^3-(4/3)*sqrt(2)*sin((3/2)*x), x)-(1+cos(3*x))^(3/2), x = 0 .. .2);

One may compare it with the Mathematica result Step-by-step2.pdf.

2. Initialize

Student[Calculus1]:-IntTutor(cos(x)^2/(1+tan(x)), x);

In the window press the Next Step button. This crashes (The kernel connection has been lost) my comp in approximately an half of hour (see screen2.docx). One may compare it with the Mathematica result Step-by-step.pdf .

Indeed,  "We wanted the best, but it turned out like always" .


I want to use a variant of the arctangent function in odeplot but I run into various problems. Here is the variant called at
> at := proc (x::realcons, yy)

if 0 < x then arctan(yy/x) elif x < 0 then Pi+arctan(yy/x) elif x = 0 then (1/2)*Pi end if end proc;


It would be nice to know if this is really what I want so I try to plot at  values for which I know the answer
> plot(at(-cos(-t), sin(t)), t = 0 .. 3.14);


Error, invalid input: at expects its 1st argument, x, to be of type realcons, but received -cos(t)


I have seen this problem before so I use single quotes with success:
plot('at(-cos(-t), sin(t))', t = 0 .. 3.14);

I get the desired plot;

Now I want to use this procedure in a plot of a numerical solution to an ODE.
The ODE is quite complicated but returns a procedure ,nans, that i use to visualize solutions via commands such as


> odeplot(nans, [[y, f(y)]], y = 0 .. 6);
No problem with any of that,

The problem arise when I define theta below
> theta := at(f(y)-(1/2)*Pi, diff(f(y), y));
and try to use it in odeplot, for example,
> odeplot(nans, [[y, theta]], y = 0 .. 6);
or
> theta1:=y->at(f(y)-Pi/(2),diff(f(y),y));


> odeplot(nans, [[y, theta1(y) ]], y = 0 .. 6);


Maple's complains about theta and theta1 and all of my attempts to fix the problem:


Error, (in plots/odeplot) curve 1 is not fully specified in terms of the ODE solution, found additional unknowns {Theta1}
or
Error, (in Theta1) invalid input: at expects its 1st argument, xx, to be of type realcons, but received f1(y)-(1/2)*Pi  or


Error, (in Theta1) invalid input: diff received HFloat(0.001), which is not valid for its 2nd argument


I supect there is an easy fix. If I give up on at and just use arctan I get an ugly jump in my plot but otherwise everything works.


I am looking for a high accuracy plot, however, and the jump obscures important features.

Please help!

Something simple. 

Two points and there doesn't seem to be an internal command to define a vector from it. 

say for example we have p=(3,6,-1) and q=(4,-2,2)

How to write pq and have the answer of q-p as a vector returned?

I have a few "regular practices" on the interface that i want to implement into conjecturing automata, and i would really really be super appreciative if i can interface it with simon's/maplsoft's inverse symbollic calculator, the only problem really is  the HTTP aspect is going  to ( im assuming) need certain information only known to the people who brought the symbolliic calc online. So thats my  question / request for help

hi

I have an equation and I want to plot this in maple.

for example, this is my equation:

w=-4.918231636*z^3+2.486861786*z^2+.8573483099*z+2.341623514

1) I want to plot z/H (H is a number) versus w so I need to switch the axises.

2) I want to plot specific area (by using commands) for example vertical axis from -0.5..0.5 and horizontal from -2..3.

i don not want to use plot property because it should be aligned for every run and it is not permanent.

thank you very much

From clues:
a1 := subs(y=n,1/y!*x^y); # diff make it equal to the left term
a2 := subs(y=n-1,1/y!*x^y);
simplify(factor(a1 - a2));
 
To find limit of below
nterm := sum(tanh(product(sum(kk, kk=1..jj),jj=1..y))*1/y!*x^y, y=n..n);
n2term := sum(tanh(product(sum(kk, kk=1..jj),jj=1..y))*1/y!*x^y, y=(n+1)..(n+1));
simplify(factor(n2term - nterm));
simplify(limit((subs(x=x+h, n2term)-n2term)/h, h=0)) = nterm;
 
question is to find a limit make n2term equal nterm after calculation

1. There is this weird bug:

evalc(Re((Re(z)+I*Im(z))^2)) assuming z::complex;
                                2
                               z 

which looks like the assumption got lost somewhere along the way.

2. simplify and evalc can't automatically handle these:

simplify(z-Re(z)-I*Im(z));
                      z - Re(z) - I Im(z)

evalc(z-Re(z)-I*Im(z)) assuming z::complex;
                      z - Re(z) - I Im(z)

simplify(Re(z)^2+Im(z)^2-abs(z)^2);
                          2        2      2
                     Re(z)  + Im(z)  - |z| 

evalc(Re(z)^2+Im(z)^2-abs(z)^2) assuming z::complex;
                          2        2      2
                     Re(z)  + Im(z)  - |z| 

One way to make it work is to do subs(z=Re(z)+I*Im(z),...) and then pass it to evalc. But see point 1. Another way that sometimes work is convert(...,abs).

Side note on convert: convert(...,Re) allows Im as well as Re. I think that's not very useful: typically the point of convert is that I want to get rid of other functions.

3. evalc tends to leave functions of complex argument unexpanded:

evalc(conjugate(sin(z))) assuming z::complex;
                                /_\
                             sin\z/

The real and imaginary parts aren't separated. Again, one way to make it work is this:

evalc(conjugate(sin(Re(z)+I*Im(z)))) assuming z::complex;
       sin(Re(z)) cosh(Im(z)) - I cos(Re(z)) sinh(Im(z))

But see point 1. Also, using just Re(z) and Im(z) won't always give the simplest form.

In fact, even for Re(sin(z)), which is technically already the real part, I'd say it's not very useful for evalc to just give back Re(sin(z)). sin(Re(z))*cosh(Im(z)) is a more useful output, with functions applied only to real quantities.

Using x+I*y instead of z won't help with the simplify examples, but evalc seems to work fine when all variables are assumed to be real.

 

There was a post in mapleprimes I asked a long time ago about how to modify the definition file in the maple help database.  It was answered but I can not locate the question. 

I have the following time delayed equation

 

Here

I want to plot the saddle node and Hopf bifurcation diagram of this equation with the parameter G or ε. However since I am new with Maple the syntax is unknown to me. Can anyone please help me in this connection

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