Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022

To Maple support:

I was investigating this pde from a different forum.

I noticed that when using an expanded version of the pde, Maple hangs. Without expanding the PDE, Maple gives an answer in 2 seconds. 

Why does expanding the PDE makes a difference? I do not have an earlier version of Maple on my new PC to check if this is a new issue or not.
 

interface(version);

`Standard Worksheet Interface, Maple 2022.0, Windows 10, March 8 2022 Build ID 1599809`

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1230 and is the same as the version installed in this computer, created 2022, April 21, 9:8 hours Pacific Time.`

restart;
pde1:=VectorCalculus:-Laplacian(u(r,theta),'polar'[r,theta]);
pde1_expanded:=expand(pde1);
bc  := u(1,theta)=sin(theta)^4,u(3,theta)=1;
pdsolve([pde1=0,bc],u(r,theta))
 

(diff(u(r, theta), r)+r*(diff(diff(u(r, theta), r), r))+(diff(diff(u(r, theta), theta), theta))/r)/r

(diff(u(r, theta), r))/r+diff(diff(u(r, theta), r), r)+(diff(diff(u(r, theta), theta), theta))/r^2

u(1, theta) = sin(theta)^4, u(3, theta) = 1

u(r, theta) = (1/52480)*((328*r^6-26568*r^2)*ln(3)*cos(2*theta)+(-r^8+6561)*ln(3)*cos(4*theta)+19680*(ln(3)+(5/3)*ln(r))*r^4)/(ln(3)*r^4)

pdsolve([pde1_expanded=0,bc],u(r,theta)); #HANGS, Waited more than 40 minutes.

 


 

Download hangs_pde.mw

Here is a Maple 2020 worksheet that ran fine on Maple 2020, but runs slower on Maple 2022, especially when plots[display] is used it seems to take much longer?

with(NumberTheory);
with(plots);
NULL;
NULL;
theta := [14.134725, 21.022039, 25.010858, 30.424876, 32.935062, 37.586178, 40.918719, 43.327073, 48.00515, 49.773832, 52.970321, 56.446248, 59.347044, 60.831779, 65.112544, 67.079811, 69.546402, 72.067158, 75.704691, 77.144840, 79.337375, 82.91038, 84.735493, 87.425273, 88.809111, 92.491899, 94.651344, 95.870634, 98.831194];
theta := [14.134725, 21.022039, 25.010858, 30.424876, 32.935062, 

  37.586178, 40.918719, 43.327073, 48.00515, 49.773832, 

  52.970321, 56.446248, 59.347044, 60.831779, 65.112544, 

  67.079811, 69.546402, 72.067158, 75.704691, 77.144840, 

  79.337375, 82.91038, 84.735493, 87.425273, 88.809111, 

  92.491899, 94.651344, 95.870634, 98.831194]

y[1] := x -> -2*sqrt(x)*cos(theta[1]*ln(x) - argument(0.5 + theta[1]*I))/(abs(0.5 + theta[1]*I)*ln(x));
y[1] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[1\

  ]*ln(x)-argument(.5+I*theta[1]))/(abs(.5+I*theta[1])*ln(x)) 

   end proc

plot(y[1](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 14.134725*i');

y[2] := x -> -2*sqrt(x)*cos(theta[2]*ln(x) - argument(0.5 + theta[2]*I))/(abs(0.5 + theta[2]*I)*ln(x));
y[2] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[2\

  ]*ln(x)-argument(.5+I*theta[2]))/(abs(.5+I*theta[2])*ln(x)) 

   end proc

plot(y[2](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 21.022040*i');

y[3] := x -> -2*sqrt(x)*cos(theta[3]*ln(x) - argument(0.5 + theta[3]*I))/(abs(0.5 + theta[3]*I)*ln(x));
y[3] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[3\

  ]*ln(x)-argument(.5+I*theta[3]))/(abs(.5+I*theta[3])*ln(x)) 

   end proc

plot(y[3](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 25.00858*i');

y[4] := x -> -2*sqrt(x)*cos(theta[4]*ln(x) - argument(0.5 + theta[4]*I))/(abs(0.5 + theta[4]*I)*ln(x));
y[4] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[4\

  ]*ln(x)-argument(.5+I*theta[4]))/(abs(.5+I*theta[4])*ln(x)) 

   end proc

plot(y[4](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 30.424876*i');

y[5] := x -> -2*sqrt(x)*cos(theta[5]*ln(x) - argument(0.5 + theta[5]*I))/(abs(0.5 + theta[5]*I)*ln(x));
y[5] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[5\

  ]*ln(x)-argument(.5+I*theta[5]))/(abs(.5+I*theta[5])*ln(x)) 

   end proc

plot(y[5](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 32.93502*i');

T[1] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[1]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[1] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[1])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[1](x), x = 20 .. 100, title = 'T[1]');

T[2] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[2]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[2] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[2])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[2](x), x = 20 .. 100, title = 'T[2]');

T[3] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[3]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[3] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[3])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[3](x), x = 20 .. 100, title = 'T[3]');

T[4] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[3]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[4] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[3])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[4](x), x = 20 .. 100, title = 'T[4]');

T[5] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[5]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[5] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[5])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[5](x), x = 20 .. 100, title = 'T[5]');

f10 := x -> Li(x) - 2*sum(Re(Ei((1/2 + theta[n]*I)*ln(x))), n = 1 .. 10) - ln(2) + int(1/(t*(t^2 - 1)*ln(t)), t = x .. infinity);
f10 := proc (x) options operator, arrow; Li(x)-2*(sum(Re(Ei((1/2\

  +I*theta[n])*ln(x))), n = 1 .. 10))-ln(2)+int(1/(t*(t^2-1)*ln(\

  t)), t = x .. infinity) end proc

R10 := x -> sum(Moebius(l)*f10(x^(1/l))/l, l = 1 .. 8);
R10 := proc (x) options operator, arrow; sum(NumberTheory:-Moebi\

  us(l)*f10(x^(1/l))/l, l = 1 .. 8) end proc

plot1 := plot(R10(x), x = 2 .. 100);

plot2 := plot(pi(x), x = 2 .. 100);

display([plot1, plot2]);

f29 := x -> Li(x) - 2*sum(Re(Ei((1/2 + theta[n]*I)*ln(x))), n = 1 .. 29) - ln(2) + int(1/(t*(t^2 - 1)*ln(t)), t = x .. infinity);
f29 := proc (x) options operator, arrow; Li(x)-2*(sum(Re(Ei((1/2\

  +I*theta[n])*ln(x))), n = 1 .. 29))-ln(2)+int(1/(t*(t^2-1)*ln(\

  t)), t = x .. infinity) end proc

R29 := x -> sum(Moebius(l)*f29(x^(1/l))/l, l = 1 .. 8);
R29 := proc (x) options operator, arrow; sum(NumberTheory:-Moebi\

  us(l)*f29(x^(1/l))/l, l = 1 .. 8) end proc

plot3 := plot(R29(x), x = 2 .. 100);

NULL;
display([plot1, plot2, plot3]);

R29(100);
R10(100);
pi(100);
                          25.25165721

                          25.28503922

                               25

RR10 := x -> sum(Moebius(l)*f10(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2)) + 1);
RR10 := proc (x) options operator, arrow; sum(NumberTheory:-Moeb\

  ius(l)*f10(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2))+1) end 

   proc

RR10(1000);
pi(1000);
                          168.1328341

                              168

RR29 := x -> sum(Moebius(l)*f29(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2)) + 1);
RR29 := proc (x) options operator, arrow; sum(NumberTheory:-Moeb\

  ius(l)*f29(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2))+1) end 

   proc

RR29(1000);
                          167.6113955

P1 := plot(RR29(x), x = 880 .. 930);

P2 := plot(pi(x), x = 880 .. 930);

display([P1, P2]);

f0 := x -> Li(x) - ln(2) + int(1/(t*(t^2 + 1)*ln(t)), t = x .. infinity);
f0 := proc (x) options operator, arrow; Li(x)-ln(2)+int(1/(t*(t^\

  2+1)*ln(t)), t = x .. infinity) end proc

RR0 := x -> sum(Moebius(l)*f0(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2)) + 1);
RR0 := proc (x) options operator, arrow; sum(NumberTheory:-Moebi\

  us(l)*f0(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2))+1) end proc

P3 := plot(RR0(x), x = 880 .. 930);

NULL;
display([P1, P2, P3]);

P4 := plot(RR10(x), x = 880 .. 930);

display([P1, P2, P3, P4], color = [green, blue, purple, yellow]);

evalf(Li(2)), evalf(ln(2));
                   1.045163780, 0.6931471806

evalf(li(2));
                             li(2)

evalf(Ei(2));
                          4.954234356

evalf(Int(1/ln(t), t = 0 .. 2));
                        Float(undefined)

evalf(Ei(ln(2)));
                          1.045163780

Li(1000.);
                          177.6096580

isprime, [$ (1 .. 100)];
isprime, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 

  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 

  33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 

  49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 

  65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 

  81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 

  97, 98, 99, 100]

nops(select(isprime, [$ (1 .. 100)]));
                               25

theta[1];
                           14.134725

evalf(Ei((1/2 + theta[1]*I)*ln(x)));
             Ei((0.5000000000 + 14.134725 I) ln(x))

evalf(Ei(ln(1/2 + theta[1]*I)));
                  4.386989035 + 6.632175089 I

plot(Li(x), x = 0 .. 5);

To Maple support:

I see 2 problems here. Maple solves the ode using series method.

First problem: Using odetest shows the syntax according to help does not work. Which is

           odetest(sol, ODE, series, point = 0);

The above gives internal error.

When changing to the following syntax

         odetest(sol,ODE,type='series',point=0); 

No internal error.

So help page should be corrected.

The second problem is that Maple odetest does not return 0 on its own solution. I verified manually that the solution is correct actually. So I do not know why maple does not return zero here. Simplfication does not help. 
 

interface(version);

`Standard Worksheet Interface, Maple 2022.0, Windows 10, March 8 2022 Build ID 1599809`

restart;

Order:=6;
ode:=x^2*diff(diff(y(x),x),x)+x^2*diff(y(x),x)+y(x) = 0;
maple_sol:=dsolve(ode,y(x),type='series',x=0):
odetest(maple_sol,ode,series,point=0);
odetest(maple_sol,ode,'series',point=0);

6

x^2*(diff(diff(y(x), x), x))+x^2*(diff(y(x), x))+y(x) = 0

Error, (in odetest/series) complex argument to max/min: 13/2-1/2*I*3^(1/2)

Error, (in odetest/series) complex argument to max/min: 13/2-1/2*I*3^(1/2)

odetest(maple_sol,ode,type='series',point=0); #This should return zero, but it does not.

-I*3^(1/2)*x^(3/2-((1/2)*I)*3^(1/2))*(series(-1/2-(I*3^(1/2)/((I*3^(1/2)-1)*(I*3^(1/2)-2)))*x-((1/4)*((5*I)*3^(1/2)+3)/((I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^2-((1/6)*((8*I)*3^(1/2)+9)/((I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^3-((7/16)*((3*I)*3^(1/2)+5)/((I*3^(1/2)-5)*(I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^4+O(x^5),x,5))*_C1+((1/2)*I)*3^(1/2)*x^(3/2+((1/2)*I)*3^(1/2))*(series(1-(1/2)*x+(((1/2)*I)*3^(1/2)/((1+I*3^(1/2))*(I*3^(1/2)+2)))*x^2-((1/12)*((5*I)*3^(1/2)-3)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)))*x^3+((1/24)*(-9+(8*I)*3^(1/2))/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)))*x^4-((7/80)*((3*I)*3^(1/2)-5)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)*(I*3^(1/2)+5)))*x^5+O(x^6),x,6))*_C2+_C1*x^(5/2-((1/2)*I)*3^(1/2))*(series(-I*3^(1/2)/((I*3^(1/2)-1)*(I*3^(1/2)-2))-((1/2)*((5*I)*3^(1/2)+3)/((I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x-((1/2)*((8*I)*3^(1/2)+9)/((I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^2-((7/4)*((3*I)*3^(1/2)+5)/((I*3^(1/2)-5)*(I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^3+O(x^4),x,4))+_C2*x^(5/2+((1/2)*I)*3^(1/2))*(series(I*3^(1/2)/((1+I*3^(1/2))*(I*3^(1/2)+2))-((1/2)*((5*I)*3^(1/2)-3)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)))*x+((1/2)*(-9+(8*I)*3^(1/2))/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)))*x^2-((7/4)*((3*I)*3^(1/2)-5)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)*(I*3^(1/2)+5)))*x^3+O(x^4),x,4))+_C1*x^(3/2-((1/2)*I)*3^(1/2))*(series(-1/2-(I*3^(1/2)/((I*3^(1/2)-1)*(I*3^(1/2)-2)))*x-((1/4)*((5*I)*3^(1/2)+3)/((I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^2-((1/6)*((8*I)*3^(1/2)+9)/((I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^3-((7/16)*((3*I)*3^(1/2)+5)/((I*3^(1/2)-5)*(I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^4+O(x^5),x,5))+_C2*x^(3/2+((1/2)*I)*3^(1/2))*(series(-1/2+(I*3^(1/2)/((1+I*3^(1/2))*(I*3^(1/2)+2)))*x-((1/4)*((5*I)*3^(1/2)-3)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)))*x^2+((1/6)*(-9+(8*I)*3^(1/2))/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)))*x^3-((7/16)*((3*I)*3^(1/2)-5)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)*(I*3^(1/2)+5)))*x^4+O(x^5),x,5))-((1/2)*I)*3^(1/2)*x^(3/2-((1/2)*I)*3^(1/2))*(series(1-(1/2)*x-(((1/2)*I)*3^(1/2)/((I*3^(1/2)-1)*(I*3^(1/2)-2)))*x^2-((1/12)*((5*I)*3^(1/2)+3)/((I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^3-((1/24)*((8*I)*3^(1/2)+9)/((I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^4-((7/80)*((3*I)*3^(1/2)+5)/((I*3^(1/2)-5)*(I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^5+O(x^6),x,6))*_C1+I*3^(1/2)*x^(3/2+((1/2)*I)*3^(1/2))*(series(-1/2+(I*3^(1/2)/((1+I*3^(1/2))*(I*3^(1/2)+2)))*x-((1/4)*((5*I)*3^(1/2)-3)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)))*x^2+((1/6)*(-9+(8*I)*3^(1/2))/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)))*x^3-((7/16)*((3*I)*3^(1/2)-5)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)*(I*3^(1/2)+5)))*x^4+O(x^5),x,5))*_C2+x^(5/2-((1/2)*I)*3^(1/2))*(series(-1/2-(I*3^(1/2)/((I*3^(1/2)-1)*(I*3^(1/2)-2)))*x-((1/4)*((5*I)*3^(1/2)+3)/((I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^2-((1/6)*((8*I)*3^(1/2)+9)/((I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^3-((7/16)*((3*I)*3^(1/2)+5)/((I*3^(1/2)-5)*(I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^4+O(x^5),x,5))*_C1+x^(5/2+((1/2)*I)*3^(1/2))*(series(-1/2+(I*3^(1/2)/((1+I*3^(1/2))*(I*3^(1/2)+2)))*x-((1/4)*((5*I)*3^(1/2)-3)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)))*x^2+((1/6)*(-9+(8*I)*3^(1/2))/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)))*x^3-((7/16)*((3*I)*3^(1/2)-5)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)*(I*3^(1/2)+5)))*x^4+O(x^5),x,5))*_C2+(1/2)*x^(3/2-((1/2)*I)*3^(1/2))*(series(1-(1/2)*x-(((1/2)*I)*3^(1/2)/((I*3^(1/2)-1)*(I*3^(1/2)-2)))*x^2-((1/12)*((5*I)*3^(1/2)+3)/((I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^3-((1/24)*((8*I)*3^(1/2)+9)/((I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^4-((7/80)*((3*I)*3^(1/2)+5)/((I*3^(1/2)-5)*(I*3^(1/2)-4)*(I*3^(1/2)-3)*(I*3^(1/2)-2)*(I*3^(1/2)-1)))*x^5+O(x^6),x,6))*_C1+(1/2)*x^(3/2+((1/2)*I)*3^(1/2))*(series(1-(1/2)*x+(((1/2)*I)*3^(1/2)/((1+I*3^(1/2))*(I*3^(1/2)+2)))*x^2-((1/12)*((5*I)*3^(1/2)-3)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)))*x^3+((1/24)*(-9+(8*I)*3^(1/2))/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)))*x^4-((7/80)*((3*I)*3^(1/2)-5)/((1+I*3^(1/2))*(I*3^(1/2)+2)*(I*3^(1/2)+3)*(I*3^(1/2)+4)*(I*3^(1/2)+5)))*x^5+O(x^6),x,6))*_C2

 


 

Download problems_with_series_solution.mw

 

How can I found the area of the region bounded by 

y=e^xcos(x), y=o, x=−π/2, x= π/2 ?

I have an example where I try to calculate an infinite sum (G&R1.641.1)  in Maple 2022 (or 2021).  I get a different numerical result when I evaluate the sum if I express the coefficients c(m) in the sum using Maple's doublefactorial function for m!! (c1(m)) or the equivalent expression involving the factorial function (c2(m)).  Only the latter gives the correct value for the sum.  This happens even though Maple gives the same numerical value for the coefficients c1(m) and c2(m).  What's going on?? Please see the attached spreadsheet.

Download doublefactorial_test.mw

I recently upgraded to Maple 2022 just to use the new latex command. It seems I still can't export DataFrame types, I'm very disappointed. What am I doing wrong?

restart:
test:= DataFrame( [[1]], columns = [1] );
latex(test);

returns:

Error, (in DataFrame:-type) invalid input: subtype expects its 2nd argument, _t, to be of type type, but received And(symbol,satisfies(u -> substring(u,1 .. 9) = ('`\\mapleref`')))

Using File > Export As > LaTeX also doesn't work.
Printing the function call using printlevel := 100000: returns the following:

I've attached the worksheet for reference. Demo.mw
Does anyone know a workaround?

-Thanks for the Help

Irrespective of what help says, both series and taylor return series(...) rather that big-O expression

From help:

> series(x/(1-x-x^2), x=0);
series(1*x+1*x^2+2*x^3+3*x^4+5*x^5+O(x^6),x,6)
> taylor(sin(x),x=Pi);
series(-1*(x-Pi)+1/6*(x-Pi)^3-1/120*(x-Pi)^5+O((x-Pi)^7),x=-(-Pi),7)
 

I am using the method of alias(seq(c[k] = _C||k, k = 1..10)); for better latex of constants generated from solving an ode as recommended. See this for example. 

This works well 99.99% of the time. But now I noticed this in Maple 2022. Is this a display issue? When the constant is inside an inert Int it does not display the same as the other constant outside. Also the Latex is not the same. Even though lprint shows they are both correct.

This is the worksheet itself


 

restart;

interface(version);

`Standard Worksheet Interface, Maple 2022.0, Windows 10, March 8 2022 Build ID 1599809`

alias(seq(c[k] = _C||k, k = 1..10));
ode:=x*diff(y(x),x$2)-cos(x)*diff(y(x),x)+sin(x)*y(x)=2;
sol:=dsolve(ode);
lprint(sol)

c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8], c[9], c[10]

x*(diff(diff(y(x), x), x))-cos(x)*(diff(y(x), x))+sin(x)*y(x) = 2

y(x) = (c[2]+Int((c[1]+2*x)/(exp(Ci(x))*x^2), x))*exp(Ci(x))*x

y(x) = (c[2]+Int((c[1]+2*x)/exp(Ci(x))/x^2,x))*exp(Ci(x))*x

latex(sol)

y \! \left(x \right) =
\left(c_{2}+\textcolor{gray}{\int}\frac{\mathit{c[1]} +2 x}{{\mathrm e}^{\mathrm{Ci}\left(x \right)} x^{2}}\textcolor{gray}{d}x \right) {\mathrm e}^{\mathrm{Ci}\left(x \right)} x

restart;

ode:=x*diff(y(x),x$2)-cos(x)*diff(y(x),x)+sin(x)*y(x)=2;
sol:=dsolve(ode);
lprint(sol)

x*(diff(diff(y(x), x), x))-cos(x)*(diff(y(x), x))+sin(x)*y(x) = 2

y(x) = (_C2+Int((_C1+2*x)/(exp(Ci(x))*x^2), x))*exp(Ci(x))*x

y(x) = (_C2+Int((_C1+2*x)/exp(Ci(x))/x^2,x))*exp(Ci(x))*x

 


 

Download april_25_2022.mw

 

 

Hi everyone! I'd really appreciate if I could get pointed in the right direction as I am a brand new maple user.

So im trying to solve this constrainted optimization problem (See picture) using Maple symbollically. I believe I should have a closed form solution given I can substitute the one constraint into the objective function. Specifically closed form solutions for the three phi variables.

Can someone point me in the right direction as to how I should go about this? I've already taken first order conditions and tried to using the solve() function to no avail, realizing my sytem of equations weren't linear );. 

I have problems with tasks.

If you have some usefull commands, you select them all, right-click and select 'create task'. You now get a button in the 'task'-pane in Maple you can use whenever you need to insert these commands- - - brilliant!!

But now I want to modify these tasks and delete the ones I don't use anymore or the ones I made by mistake.

Right-click on the task does nothing.

Selecting 'tools' from the menu and then 'tasks' allows me to see the tasks I have made, but not to modify them or delete them

How do I modify or delete a task??

 

/Rasmus Post

Maple apparently has managed to destroy the last working piece of code in the Units package in the 2022 release.

This code is working in Maple 2021, but not in 2022 anymore.

with(Units[Simple])

[`*`, `+`, `-`, `/`, `<`, `<=`, `<>`, `=`, Im, Re, `^`, abs, add, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, cos, cosh, cot, coth, csc, csch, csgn, diff, eval, evalc, evalr, exp, expand, factor, floor, frac, frem, ln, log, log10, log2, max, min, mul, normal, piecewise, polar, root, round, sec, sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan, tanh, trunc, type, verify]

(1)

alpha := 45*Unit('degree')

45*Units:-Unit(arcdeg)

(2)

NULL

if alpha = 0 then

Error, cannot determine if this expression is true or false: 0 < 1/4*Pi

evalf(sin(alpha))

.7071067810

(3)

NULL

Download UnitsSimple_alpha.mw

Very often it happens that using solve alone, gives huge expressions that can't be used. The simplest thing to do is to wrap it inside an evalf. But then sometimes, even your system only has real solutions, you may get some complex numbers. When this evalf(solve()) being used inside an algorithm, then disastrous consequences may arise! If the system consists of a single equation of a single variable, then you may have some more tools. But if you have a system of several equations in several variables, you have less options. I am mostly interested in polynomials, I know several approaches to use and code to solve and get only the real solutions, but my codes might be not very optimized. In Maple 2022, one predefined command which is nice is RootFinding:-Isolate but it has one issue and it is that this command only likes numeric coefficients which means integers, fraction of integers and float numbers, so no square root or other real numbers of this shape in the coefficients. I thought it might be a good idea to have a list of all solving commands in Maple that only return the real solutions or have the options to restrict to only real solutions. fsolve is not very ideal, because it only returns one solution.

Hi there.

There is some floating bug in Thread-Seq.

Maple is crashing sometimes (not always, 50/50) after running the script below:

thread-seq_error.mw

What's going on?

Hi,

I am a newbie in Maple. I have the following code

with(LinearAlgebra):
w := (2*Pi)/14
v := Vector([1, sin(w*t), cos(w*t)])
simplify(sum(v . (Transpose(v)), t = k .. k + 13))

Even with some less advanced CAS I get that the result is a diagonal matrix with constant elements. However, I failed to properly tune the simplify command to get such a result. What I am doing wrong?

Hi, 

I installed syrup within Maple 2022 according to the procedure described in syrup's README file. The installation seems to run normally. After that I restarted Maple. When I now enter

with(Syrup);

it shows

[Draw, Library, Print, Solve, ToModelica, ToSpice, Version]

instead of 

[deindex, makecheckttable, printdeck, reindex, syrup]

as described in the application center: https://www.maplesoft.com/applications/Preview.aspx?id=4680

Also the example which is decribed there doesn't work:

syrup(divider, dc, 'curr');

delivers no result.

I'm working on Windows 10 64 bit.

Could it be that syrup is not yet prepared for Maple 2022, as it seems not to be updated for a long time? Or is the description in the application center not up to date?

Many thanks for your help!

Best regards,

Michael

 

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