Maple 2018 Questions and Posts

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

I want to solve the equation (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0 in RealDomain. I tried

RealDomain:-solve({(-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, {x});

I got four solutions

If I work around

 RealDomain:-solve({-x^2+4*x > 0, (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, x);

I only got two solutions

With Mathematica, I got three solutions 

That is mean, Maple lost the solution x = 5*Pi/4. I check this thing

f:= x-> (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(4*x-x^2) ;

and got the result 0. 

Are these bugs?

I'm currently working my thesis and can someone help me to write a code to solve this IVP

u_t + 2×u²×u_x−(u_x)²−½×u_{xx}×u=0

with initial condition



The equation sin(9*x-(1/3)*Pi) = sin(7*x-(1/3)*Pi) can be solved easy by hand with solutions k*Pi and -Pi/48 + K*Pi/8. With Maple, I tried 
solve({sin(9*x-(1/3)*Pi) = sin(7*x-(1/3)*Pi)}, x, explicit, allsolutions)

I don't get the above solutions. How can I get these solutions?

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)

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);

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:


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.




In worksheet mode when me is writing my code, running code, evaluating is and can not work well with maple?

How can inactive  action? Because have to wait many times and is very boring for me.


How to study this ellipse with LinearAlgebra without "geometry" eq := -185173378616457/6178315520000*x+86813215770519/24713262080000*(y^2)+126906272070543/24713262080000*(x^2)+256107247454961/6178315520000+(2514994832007/950510080000*x)*y-9123740375967/6178315520000*y = 0 Axis ? foci ? ...Thank you

Based on the equation at here

I tried solve the equation (x-1)*sqrt(x^2 - 4)=0 in Real domain. My code
RealDomain:-solve((x-1)*sqrt(x^2-4) = 0, x);

I got there solutions are 1, 2, -2.  I think, If we solve the given in RealDomain, we only get two solutions -2 and 2.

My question is: How many solutions are there in the equation (x-1)*sqrt(x^2 - 4)=0 by RealDomain:-solve?

Two pictures by using Mathematica.

How I can calculate integral?



"restart;    f[1,1](r,theta,phi):=r^4 sin(6 theta) sin(3 phi):    L(r, theta,phi):=(2.784615385 10^10 ((∂)^2)/(∂r^2) `f__11`(r,theta,phi)+(2.784615385 10^10 (2+2 r cos(theta)) ((∂)/(∂r) `f__11`(r,theta,phi)))/(r (2+r cos(theta)))-(0.1175000000 (((∂)^4)/(∂theta^4) `f__11`(r,theta,phi)))/(r^4)-(0.1175000000 (((∂)^4)/(∂phi^4) `f__11`(r,theta,phi)))/((2+r cos(theta))^4)-(0.1175000000 (((∂)^4)/(∂phi^2∂r^2) `f__11`(r,theta,phi)))/((2+r cos(theta))^2)-(0.1175000000 (((∂)^4)/(∂r^2∂theta^2) `f__11`(r,theta,phi)))/(r^2)-(0.2350000000 (((∂)^4)/(∂phi^2∂theta^2) `f__11`(r,theta,phi)))/(r^2 (2+r cos(theta))^2)+(0.1175000000 ((cos(theta))^2 r^2+4 (cos(theta))^2 r^4+16 cos(theta) r^3-4+17 r^2) (((∂)^2)/(∂theta^2) `f__11`(r,theta,phi)))/((2+r cos(theta))^2 r^4)+(0.1175000000 (2 (cos(theta))^2 r^2+4 (cos(theta))^2 r^4+16 cos(theta) r^3+4+12 r^2) (((∂)^2)/(∂phi^2) `f__11`(r,theta,phi)))/(r^2 (2+r cos(theta))^4)-(2.784615385 10^10 (2 (cos(theta))^2 r^2+4 r cos(theta)+4) `f__11`(r,theta,phi))/(r^2 (2+r cos(theta))^2)+(0.2350000000 (((∂)^3)/(∂r∂theta^2) `f__11`(r,theta,phi)))/(r^3 (2+r cos(theta)))-(0.2350000000 (((∂)^3)/(∂phi^2∂r) `f__11`(r,theta,phi)))/(r (2+r cos(theta))^3)+(0.2350000000 sin(theta) (((∂)^3)/(∂theta^3) `f__11`(r,theta,phi)))/(r^3 (2+r cos(theta)))-(0.2350000000 sin(theta) (((∂)^3)/(∂phi^2∂theta) `f__11`(r,theta,phi)))/(r (2+r cos(theta))^3)+(0.1175000000 sin(theta) (((∂)^3)/(∂r^2∂theta) `f__11`(r,theta,phi)))/(r (2+r cos(theta)))-(0.1175000000 (2 r cos(theta)+3) sin(theta) (2 r cos(theta)+5) ((∂)/(∂theta) `f__11`(r,theta,phi)))/(r (2+r cos(theta))^3)) r^4 sin(6 theta) sin(3 phi):"

with(Student[Calculus1]); K[rr, s] := evalf(ApproximateInt(L(r, theta, phi), r = .2 .. 1, method = simpson)); KK[rr, s] := evalf(ApproximateInt(K[rr, s], theta = 0 .. 2*Pi, method = simpson)); k2 := evalf(ApproximateInt(KK[rr, s], phi = 0 .. 2*Pi, method = simpson))




X := [0, -3]; Y := [3, 1]; Z := [5, -2]; PP := proc (M::list, N::list, K::list) local A, B, P, distPH, H, lambda, mdist; A := M; B := N; P := K; H := simplify(expand((1-lambda)*A+lambda*B)); distPH := sqrt((H[1]-P[1])^2+(H[2]-P[2])^2); mdist := diff(distPH, lambda); lambda := solve(mdist, lambda); simplify(distPH); H end proc; debug(PP); PP(X, Y, Z);#the calculation isn't finished


How I can separate three functions (u__ru__theta and u__phi) in the equation attached below.

Please also see attached figure. I want to calculate L11L22L33.




B := simplify((r*(R+r*cos(theta))^2*(mu+lambda)*(diff(`u__θ`(r, theta, phi), r, theta))+2*r^2*(R+r*cos(theta))^2*(mu+(1/2)*lambda)*(diff(u__r(r, theta, phi), r, r))+r^2*(mu+lambda)*(R+r*cos(theta))*(diff(`u__φ`(r, theta, phi), phi, r))+mu*(R+r*cos(theta))^2*(diff(u__r(r, theta, phi), theta, theta))+(diff(u__r(r, theta, phi), phi, phi))*mu*r^2-3*(R+r*cos(theta))^2*(mu+(1/3)*lambda)*(diff(`u__θ`(r, theta, phi), theta))+(2*(R+2*r*cos(theta)))*r*(R+r*cos(theta))*(mu+(1/2)*lambda)*(diff(u__r(r, theta, phi), r))-r^2*sin(theta)*(mu+lambda)*(R+r*cos(theta))*(diff(`u__θ`(r, theta, phi), r))-3*r^2*(mu+(1/3)*lambda)*cos(theta)*(diff(`u__φ`(r, theta, phi), phi))-r*mu*sin(theta)*(R+r*cos(theta))*(diff(u__r(r, theta, phi), theta))-(2*(2*cos(theta)^2*r^2+2*cos(theta)*R*r+R^2))*(mu+(1/2)*lambda)*u__r(r, theta, phi)+r*`u__θ`(r, theta, phi)*sin(theta)*(3*r*(mu+(1/3)*lambda)*cos(theta)+R*mu))/(r^2*(R+r*cos(theta))^2))







Hello, I bring here a problem with maple that in result the  "".

I can remove '' in final results?




  X= (R+r*costheta)*sinphi):
  = (R+r*costheta)*cosphi):
  Z= (r*sintheta)):

  r, theta, phi,
    X, Y, Z


        < u__rrtheta, phi),
            u__thetartheta, phi),
            u__phirtheta, phi)
          rtheta, phi

Vector(3, {(1) = (1/2)*csgn(r)*csgn(R+r*cos(theta))*(csgn(1, R+r*cos(theta))*(R+r*cos(theta))*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi)+((R+r*cos(theta))*(diff(`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi), theta))-r*sin(theta)*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi))*csgn(R+r*cos(theta))-csgn(r)*r*(diff(`#msub(mi("u"),mi("&theta;",fontstyle = "normal"))`(r, theta, phi), phi)))/(r*(R+r*cos(theta))), (2) = -(csgn(1, R+r*cos(theta))*(R+r*cos(theta))*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi)+((R+r*cos(theta))*(diff(`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi), r))+cos(theta)*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi))*csgn(R+r*cos(theta))-(diff(`#msub(mi("u"),mi("r"))`(r, theta, phi), phi)))*csgn(R+r*cos(theta))/(2*r*cos(theta)+2*R), (3) = (1/2)*(-(diff(`#msub(mi("u"),mi("r"))`(r, theta, phi), theta))+csgn(r)*r*(diff(`#msub(mi("u"),mi("&theta;",fontstyle = "normal"))`(r, theta, phi), r))+`#msub(mi("u"),mi("&theta;",fontstyle = "normal"))`(r, theta, phi)*(r*csgn(1, r)+csgn(r)))*csgn(r)/r})






maple does not work at all

it displays this error

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

car_2som_opp := proc (U::list, V::list)  #construction d'un carré connaissant 2 sommets opposés 
local dist, eqCerU, eqCerV, r, sol, X, Y; 
dist := proc (M, N) sqrt(add((M[i]-N[i])^2, i = 1 .. 2)) end proc;
r := dist(U, V)/sqrt(2); 
eqCerU := (x-U[1])^2+(y-U[2])^2 = r^2; 
eqCerV := (x-V[1])^2+(y-V[2])^2 = r^2;
sol := solve([eqCerU, eqCerV], [x, y],allsolutions,explicit);  
X := [subs(op(sol[1]), x), subs(op(sol[1]), y)]; 
Y := [subs(op(sol[2]), x), subs(op(sol[2]), y)]; 
display(plot([U, X, V, Y, U],scaling = constrained, axes = none)) 
end proc:


Need help solving this problem with a maple proc using the Crank–Nicolson method for the differential part and any other quadrature  for the integral part and thank you so much in advance any ideas or thoughts would be helpful

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