Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

 

"a=4 x+1/diff(f(y),y)";
b := 3*(4*x + 1)/(diff(f(y), y)*(3*x + 1));
subs((4*x + 1)/diff(f(y), y) = a, b);
 

I am trying to figure out which computational method is used in function Issimilar, (which determines similarity of matrices) in Maple 2018 and whether or not its a rational one.

how can i use curve fitting tools for get m and n in this equation  for excel data

equation

i want to get m and n?

New_Microsoft_Excel_Worksheet.xlsx

 

How would one code a real time clock (digital's the easiest - of course, or analog) within maple?

Hi,

Why extracting the features of the events doesn't return the good results when executed within a loop (see the pink test) ?

Thanks in advance.

PS: please, spare me  replies of the type "you can solve this equation formally"

 

restart;

interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

sys := { diff(x(t), t) = 1, x(0) = 0 }:
evs := [ [x(t)-0.1, none],  [x(t)-0.3, none], [x(t)-0.5, none] ]:
sol := dsolve(sys, numeric, events=evs):

plots:-odeplot(sol, [t, x(t)], t=0..0.5, gridlines=true);

 

# times that fired the events

sol(1): # initialization

sol(eventfired=[1]);
sol(eventfired=[2]);
sol(eventfired=[3]);
 

[HFloat(0.1)]

 

[HFloat(0.3)]

 

[HFloat(0.49999999999999994)]

(2)

# Same times computed  within a loop

for i from 1 to 3 do
  te := op(sol(eventfired=[i]));
end do;

HFloat(0.1)

 

HFloat(0.3)

 

HFloat(0.49999999999999994)

(3)

# Values of x(t) computed  within a loop
#
# Why are calues for events 2 and 3 wrong ?
for i from 1 to 3 do
  te := op(sol(eventfired=[i]));
# xe := sol(te);             # this doesn't return the correct result,
# xe := subs(sol(te), x(t)); # this doesn't work neither
  xe := eval(x(t), sol(te)); # this doesn't work neither
end do;

HFloat(0.1)

 

HFloat(0.1)

 

HFloat(0.0)

 

HFloat(0.0)

 

HFloat(0.0)

 

HFloat(0.0)

(4)

 


 

Download Incomprehensible.mw

 

Dear experts

I am using Maple to solve a complex equation. My idea is to separate real and imaginary parts and then solve a set of the equation when both real and imaginary parts are zero. the following are the equation and the way I made real and imaginary parts;

(K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)    +p*(-4*K^2*Q*(K^2+Q^2)        +Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)        -K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)))/(K^2*Q*cosh(Q))

eq:= (K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)+p*(-4*K^2*Q*(K^2+Q^2)+Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)-K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)))/(K^2*Q*cosh(Q)):

so the K and the Q are both complex variables and p and s are constant.

p := 0.1019367992e-3, s := 7.135575943      K:=Kr+I*Kim    Q:= sqrt(K^2-I*h^2*2*Pi/1.0e-6)

K:=Kr+I*Kim;

Q:= sqrt(K^2-I*h^2*2*Pi/1e-6);

therefore the real and imaginary parts of the equation are 

A:=evalc(Re(eq)):   B:=evalc(Im(eq)):

finally, I tried to solve it as following

sys:={eval(A,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0,eval(B,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0}:

sol2:=(fsolve(sys,{Kr=0..1,Kim=4..5}));

sys:={eval(A,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0,eval(B,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0}:

sol2:=fsolve(sys,{Kr=0..5,Kim=0..5},maxsols=5);

 

the problem is that Maple can not solve it and returns the command. I  know that there is solutions. How can I solve this equation?

 

the maple file is attached.mapleprime.mw

==============================================================

I guess Maple use Newton method to solve equation or system of equations. Is there an alternative? I mean what are the possible methods?

Hello users. I have a question on my work.

I'm trying to construct the equation and plot it. And I got 2 errors(warning).

Please help me how to solve this problem check the image below and attached file.

 

 

Question_plot_the_curvature.mw

Hello,

I am trying to pass the graphics to .txt format so that I can plot them in Origin (OriginLab).

npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
    t[i] := i*dt;
    PA[i] := x[i](t);
    printf("%e %e\n", t[i], PA[i]);
    fprintf(fd, "%e %e\n", t[i], PA[i]);
end do;
0.000000e+00 

Error, (in fprintf) number expected for floating point format
fclose(fd);
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
    t[i] := i*dt;
    PB[i] := x[i + n](t);
    printf("%e %e\n", t[i], PB[i]);
    fprintf(fd, "%e %e\n", t[i], PB[i]);
end do;
fclose(fd);
0.000000e+00 

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
    t[i] := i*dt;
    qA[i] := x[i + 2*n](t);
    printf("%e %e\n", t[i], qA[i]);
    fprintf(fd, "%e %e\n", t[i], qA[i]);
end do;
fclose(fd);
0.000000e+00 

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
    t[i] := i*dt;
    qB[i] := x[i + 3*n](t);
    printf("%e %e\n", t[i], qB[i]);
    fprintf(fd, "%e %e\n", t[i], qB[i]);
end do;
fclose(fd);
0.000000e+00 

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
    t[i] := i*dt;
    Tg[i] := x[i + 4*n](t);
    printf("%e %e\n", t[i], Tg[i]);
    fprintf(fd, "%e %e\n", t[i], Tg[i]);
end do;
fclose(fd);
0.000000e+00 

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
    t[i] := i*dt;
    Ts[i] := x[i + 5*n](t);
    printf("%e %e\n", t[i], Ts[i]);
    fprintf(fd, "%e %e\n", t[i], Ts[i]);
end do;
fclose(fd);
0.000000e+00 

Error, (in fprintf) number expected for floating point format

trabalho_final_2019.mw

Hello,

I want to write a code about numerical solving N(for example N=150) coupled differential equations (ODE ) with M boundary conditions in Maple but I do not know how to do it and I cannot find anything useful. in particular, I have trouble inserting boundary conditions which are a lot for N coupled difrential equations.

Does somebody have a code script on this matter? please let me know.

Thanks a bounch in advance.

I would like to know how to create a group with some elements (numbers) {1,2,4,...} with a defined operation on it like X_42 (modular  multiplication by 42).

Hi everyone:

I'm going to write code to give me the following matrix A?

 

 

Hello everyone, thank you in advance

I am trying to plot two functions in the same graph. I didn't realize how to copy the real functions here but:

At the same 3D plot

I need to use the function F1(x,xi,k,B) for values of x*xi <6  and other function F2(x,xi,k,B) for values of x*xi  >= 6

Thank you again and sorry for my rusty English.
 

I attached a file with these 2 functions Functions_MAPLE_PLOT_TOGETHER.mw

 

Maple can easily solve the B4 problem of the Putnam Mathematical Competition 2019  link

 

B4.  Let F be the set of functions f(x,y) that are twice continuously differentiable for x≥1, y≥1 and that satisfy the following two equations:
    x*(diff(f(x, y), x))+y*(diff(f(x, y), y)) = x*y*ln(x*y)

x^2*(diff(f(x, y), x, x))+y^2*(diff(f(x, y), y, y)) = x*y

 

For each f2F, let

 

"m(f) = min[s>=1]  (f(s+1,s+1)-f(s+1,s)-f(s,s+1)+f(s,s))"

 

Determine m(f), and show that it is independent of the choice of f.


 

# Solution

pdsolve({
x*diff(f(x,y),x)+y*diff(f(x,y),y) = x*y*ln(x*y),
x^2*diff(f(x,y),x,x)+y^2*diff(f(x,y),y,y) = x*y
});

{f(x, y) = (1/2)*(x*y+2*_C1)*ln(x*y)-(1/2)*x*y-2*_C1*ln(x)+_C2}

(1)

f:=unapply(rhs(%[]), x,y);

proc (x, y) options operator, arrow; (1/2)*(y*x+2*_C1)*ln(y*x)-(1/2)*y*x-2*_C1*ln(x)+_C2 end proc

(2)

h := f(s+1, s+1) - f(s+1, s) - f(s, s+1) + f(s, s);

(1/2)*((s+1)^2+2*_C1)*ln((s+1)^2)-(1/2)*(s+1)^2-(s*(s+1)+2*_C1)*ln(s*(s+1))+s*(s+1)+(1/2)*(s^2+2*_C1)*ln(s^2)-(1/2)*s^2

(3)

minimize(h, s=1..infinity);

(4+2*_C1)*ln(2)-1/2-(2+2*_C1)*ln(2)

(4)

answer = simplify(%);

answer = 2*ln(2)-1/2

(5)

 


Download putnam2019-b4.mw

What is the command to yield the expansion of Z^N in terms of x and y.

Z complex = x+iy,

N integer >1

e.g. Z^2 = x^2 - y^2 + 2.i.x.y

 

could you just delete the post !!!!!!!!!!!!!!!!!!!!!!!!!!!x!xxxx!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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