Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

I'm working towards creating a way to visualise real polynomial ideals! (or at least the solutions of the polynomials in the ideals) this code creates a plot showing the solutions to all the polynomials in the ideal generated by P1 and P2 (these are specified in the code)

with(plots);
P1 := x^2+2*y^2-3;
solve(P1, y);
Plot1 := plot([%], x = -2 .. 2);

P2 := -2*x^2+2*x*y+3*y^2+x-4;
solve(%, y);
Plot2 := plot([%], x = -4 .. 2);

P2*a+P1;
solve(%, y);
seq(plot([%], x = -4 .. 2), a = 0 .. 10, .1);
display(%, Plot1, Plot2)




This is because when you multiply two polynomials their set of solution curves is just the union of the sets of curves associated with the previous polynomials.

For the next step I'd like to create a graph of the solutions associated with an ideal with three generators. To stop this from being excessively messy I'd like to do it with the RGB value of the colour of a curve is determined by  a and b where the formula for a generic polynomial that we are solving and graphing is given by:

P1+a*P2+b*P3;

where P3 is given by

P3 := x*y-3

I've tried various ways to use cury to make this work (my intuition is cury is the right function to use here)  but got no where. Any ideas how to procede?

possible to solve following equation with unknown parameter omega.

parameter constant.

I see before for one dimension ode this type equation was solved.

Now for 2d equation is possible?

can consider or I can send again.

Best

2d-2

 

maple does not work at all

it displays this error

Error, (in StringTools:-FormatMessage) unknown option MAPLE
 

How I can replace  u__0r, theta, t) with f1, 1(r, theta) in attached file.

I want in I have only f1,1] function.

Thanks 


 

````

"f[1, 1](r, theta):=`u__0`(r, theta,t)  "

proc (r, theta) options operator, arrow, function_assign; u__0(r, theta, t) end proc

(1)
``````````

"L[1, 1](r, theta):=-`A__0`*(∂)/(∂r) (F*(∂)/(∂r)`u__0`(r,theta))-1/(2)*`A__0`*(∂)/(∂r) (`K__1`*`u__0`(r,theta))+1/(2)*`A__0`*`K__1`*(∂)/(∂r)`u__0`(r,theta)-1/(2)*`A__0`*(∂)/(∂ r) (`H__1`*`u__0`(r,theta))+1/(2)*`A__0`*`H__1`*(∂)/(∂r)`u__0`(r,theta)+`K__3`*`A__0`*`u__0`(r,theta)-1/(2)*`A__0`*(∂)/(∂ r) (`K__4`*`u__0`(r,theta))+1/(2)*`A__0`*`K__4`*(∂)/(∂r)`u__0`(r,theta)+`A__0`*`K__5`*`u__0`(r,theta)-2*`A__0`*(∂)/(∂ theta) ((`H__2`)/(r)*(∂)/(∂theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((∂)^(2))/(∂ r ∂ theta)(mu*((∂)^(2))/(∂r ∂theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((∂)^(2))/(∂theta^(2))(mu*((∂)^(2))/(∂ theta^(2))`u__0`(r,theta))+rho*`A__0`*`K__16`*((∂)^(2))/(∂t^(2))`u__0`(r,theta);"

proc (r, theta) options operator, arrow, function_assign; -A__0*(diff(F*(diff(u__0(r, theta), r)), r))-(1/2)*A__0*(diff(K__1*u__0(r, theta), r))+(1/2)*A__0*K__1*(diff(u__0(r, theta), r))-(1/2)*A__0*(diff(H__1*u__0(r, theta), r))+(1/2)*A__0*H__1*(diff(u__0(r, theta), r))+K__3*A__0*u__0(r, theta)-(1/2)*A__0*(diff(K__4*u__0(r, theta), r))+(1/2)*A__0*K__4*(diff(u__0(r, theta), r))+A__0*K__5*u__0(r, theta)-2*A__0*(diff(H__2*(diff(u__0(r, theta), theta))/r, theta))+(1/4)*A__0*l^2*(diff(mu*(diff(u__0(r, theta), r, theta)), r, theta))+(1/4)*A__0*l^2*(diff(mu*(diff(u__0(r, theta), theta, theta)), theta, theta))+rho*A__0*K__16*(diff(u__0(r, theta), t, t)) end proc

(2)

``


 

Download replace

 

restart;

##########  omega and theta are variables,where J[3],F[2],H[2],etc are constants.

#### I tried with "evlf" and "evlc" command but maple was not ready to provide the solution,please help me to solve this

t1:=-1/(-16.*omega^2+exp(-4*omega)+exp(4*omega)-2.)*(-(0.5817764173e-1*I)*exp((2/9)*omega*cos(theta))*omega^5*cos(theta)*J[3]-(.6981317009*I)*exp((2/9)*omega*cos(theta))*omega^4*cos(theta)*H[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*G[3]-.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*H[2]+.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*F[2]+.9308422676*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*H[3]-.1034269187*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*G[2]-0.7757018900e-1*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^2*G[2]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*J[3]-0.9696273622e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*J[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*J[3]-.2714956613*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*H[3]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*G[3]+0.8726646261e-1*exp((2/9)*omega*cos(theta))*omega^3*J[3])*cos((2/9)*omega*sin(theta));

t2:=int(int(t1,omega=0..infinity),theta=0..2*Pi);

 

 

How I can simplify result? For factor or using rule.

Thanks

 

How can plot two  and bipolar figures as attached and extract their data.

Thank You.

Hello,

How I can write a code for the determination of Laplacian in a new form that is introduced in the maple code (First line).

Thank you.

FOR

Maple Worksheet - Error

Failed to load the worksheet //convert/FOR
 

Download FOR

 

 

Hello, i am experiencing some problems when trying to open the maple 2018 software*
I have tried unistalling and download it again.
I have tried to search for sollution but there is very ittle intel
When i open Maple 2018 it just lingeres on the start up (pic below) and just disappears after 10 seconds

Can someone please help i have a very important examination upcoming

Give the following functions find Domain, Range, Possible Asymptotes, Intercepts, Critical Points, Intervals of Increase, Decrease, Relative and Absolute Extrema, and Concavity.

A) f(x)=x(x^2-6x+8)

B) f(x) =x^3/4 -3x

Sorry,

I have been away from Maple for a year.
Then, when I used op command, I am puzzed to notice the results were different from those I know.

>op((x+5)^2*(x+y));
      _EXPSEQ((x+5)^2, x+y)

Result I know is 

        (x+5)^2, x+y

Has a modifire such as _EXPSEQ   automatically come to be attatched?
Or, can I have maple express it  in the form I know:  (x+5)^2, x+y?

Thank you in advance.

taro

 

 

 

 

 


 

 

how I can write a program code for newmark method.

in this method time has 3 order derivation

 We know the following facts: 

The SequenceGraph command returns a graph with the specified degree sequence given as input, if such a graph exists. It raises an exception otherwise. 
 But  If I  want to get more graphs  that satisfy this condition of degree sequence ? (If graphs are not many ,I want get all graphs better)
what should I do.?
For example: DrawGraph(SequenceGraph([3, 2, 2, 1, 1, 1]));  It returns the first graph below, but it is obvious that the second graph also fits the condition.

squenceGraph.mw

I can  this equation.

CV.mw
 

restart; c__v := 1.2; `τ__q` := 8.5*10^(-12); `τ__T` := 90.0*10^(-12); rho := 1000; k := 10

1.2

 

0.8500000000e-11

 

0.9000000000e-10

(1)

k*(diff(T(x, t), x, x))+k*`τ__T`*(diff(T(x, t), t, x, x)) = rho*c__v*(diff(T(x, t), t))+(diff(T(x, t), t, t))*c__v*rho*`τ__q`+(1/2)*c__v*rho*`τ__q`^2*(diff(T(x, t), t, t, t))

10*(diff(diff(T(x, t), x), x))+0.9000000000e-9*(diff(diff(diff(T(x, t), t), x), x)) = 1200.0*(diff(T(x, t), t))+0.1020000000e-7*(diff(diff(T(x, t), t), t))+0.4335000000e-19*(diff(diff(diff(T(x, t), t), t), t))

(2)

Boundary condition:

T(0, t) = 300; T(10, t) = 300

#####################################

INITIAL CONDITIONS:

 

T(x, 0) = 300; (D[1](T))(x, 0) = 0, (D[2](T))(x, 0) = 0

(D[1](T))(x, 0) = 0, (D[2](T))(x, 0) = 0

(3)

``


 

Download CV.mw

 

 

How I can take Laplace Transform from equation.

Thanks

LAPLACE

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