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difference in output of solve(identity) in Maple 2...

Asked by: nm 11353
solve identity
March 11 2024
1  1

I have been trying Maple 2024 and found this strange result. 

Calling solve(identity...  on same input in Maple 2024 gives very large and complex output compare with Maple 2023.2.1.

This was causing problem, until I found that simplifying the solution now gives same output as Maple 2023.2.1

But why is this now needed in Maple 2024? i.e. why is calling simplify needed when in Maple 2023 the simpler solution was returned automatically?

I changed my code to call simplify now on result of solve(identity...  but I am just curious what happened to cause this?

Below are two worksheets, one from Maple 2024 and one from Maple 2023.2 and you see the huge difference in result.


 

56056

> 

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1693. The version installed in this computer is 1672 created 2024, February 7, 18:34 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2023\Physics Updates\lib\`

> 

restart;

238012

> 

trial_solution_constants:=[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8]];
eq:=-2*A[1]*sin(x)+2*A[2]*cos(x)-4*A[2]*x*sin(x)+2*A[3]*sin(x)+4*A[3]*x*cos(x)+2*A[4]*cos(x)-6*A[5]*sin(3*x)-8*A[5]*x*cos(3*x)+6*A[6]*cos(3*x)-8*A[6]*x*sin(3*x)-8*A[7]*cos(3*x)-8*A[8]*sin(3*x) = x*cos(x)^3;
solve(identity(eq,x),trial_solution_constants)

[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8]]

-2*A[1]*sin(x)+2*A[2]*cos(x)-4*A[2]*x*sin(x)+2*A[3]*sin(x)+4*A[3]*x*cos(x)+2*A[4]*cos(x)-6*A[5]*sin(3*x)-8*A[5]*x*cos(3*x)+6*A[6]*cos(3*x)-8*A[6]*x*sin(3*x)-8*A[7]*cos(3*x)-8*A[8]*sin(3*x) = x*cos(x)^3

[[A[1] = 3/16, A[2] = 0, A[3] = 3/16, A[4] = 0, A[5] = -1/32, A[6] = 0, A[7] = 0, A[8] = 3/128]]

> 

 


 

Download solve_identity_march_11_2024_maple_2023.mw

 


 

56056

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1693 and is the same as the version installed in this computer, created 2024, March 7, 17:27 hours Pacific Time.`

> 

restart;

56944

> 

trial_solution_constants:=[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8]];
eq:=-2*A[1]*sin(x)+2*A[2]*cos(x)-4*A[2]*x*sin(x)+2*A[3]*sin(x)+4*A[3]*x*cos(x)+2*A[4]*cos(x)-6*A[5]*sin(3*x)-8*A[5]*x*cos(3*x)+6*A[6]*cos(3*x)-8*A[6]*x*sin(3*x)-8*A[7]*cos(3*x)-8*A[8]*sin(3*x) = x*cos(x)^3;
solve(identity(eq,x),trial_solution_constants)

[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8]]

-2*A[1]*sin(x)+2*A[2]*cos(x)-4*A[2]*x*sin(x)+2*A[3]*sin(x)+4*A[3]*x*cos(x)+2*A[4]*cos(x)-6*A[5]*sin(3*x)-8*A[5]*x*cos(3*x)+6*A[6]*cos(3*x)-8*A[6]*x*sin(3*x)-8*A[7]*cos(3*x)-8*A[8]*sin(3*x) = x*cos(x)^3

[[A[1] = -(3/16)*(648*cos(3)*sin(1)^3+972*cos(3)*sin(1)^2*cos(1)+432*sin(3)*sin(1)^3+648*sin(3)*sin(1)^2*cos(1)+2268*sin(1)^4+1296*sin(1)^3*cos(1)+324*sin(3)*cos(3)-108*sin(1)*cos(3)-585*cos(3)*cos(1)-133*sin(3)^2-153*sin(3)*sin(1)-48*sin(3)*cos(1)-2025*sin(1)^2+225)/(108*sin(1)*cos(3)+99*cos(3)*cos(1)-2*sin(3)^2+153*sin(3)*sin(1)-276*sin(3)*cos(1)-162*sin(1)^2+261), A[2] = (9/32)*(-48*cos(3)*sin(1)^3-72*cos(3)*sin(1)^2*cos(1)+88*sin(3)*sin(1)^3+132*sin(3)*sin(1)^2*cos(1)+864*sin(1)^4-108*sin(1)^3*cos(1)+21*sin(3)*cos(3)+117*sin(1)*cos(3)-144*cos(3)*cos(1)+40*sin(3)^2-12*sin(3)*sin(1)-141*sin(3)*cos(1)-972*sin(1)^2+243*cos(1)*sin(1)+144)/(108*sin(1)*cos(3)+99*cos(3)*cos(1)-2*sin(3)^2+153*sin(3)*sin(1)-276*sin(3)*cos(1)-162*sin(1)^2+261), A[3] = -(3/32)*(648*cos(3)*sin(1)^3+972*cos(3)*sin(1)^2*cos(1)+432*sin(3)*sin(1)^3+648*sin(3)*sin(1)^2*cos(1)+2268*sin(1)^4+1296*sin(1)^3*cos(1)+324*sin(3)*cos(3)-216*sin(1)*cos(3)-684*cos(3)*cos(1)-131*sin(3)^2-306*sin(3)*sin(1)+228*sin(3)*cos(1)-1863*sin(1)^2-36)/(108*sin(1)*cos(3)+99*cos(3)*cos(1)-2*sin(3)^2+153*sin(3)*sin(1)-276*sin(3)*cos(1)-162*sin(1)^2+261), A[4] = 0, A[5] = (1/64)*(216*cos(3)*sin(1)^3+324*cos(3)*sin(1)^2*cos(1)+144*sin(3)*sin(1)^3+216*sin(3)*sin(1)^2*cos(1)+756*sin(1)^4+432*sin(1)^3*cos(1)+41*cos(3)^2+108*sin(3)*cos(3)-216*sin(1)*cos(3)-360*cos(3)*cos(1)-306*sin(3)*sin(1)+444*sin(3)*cos(1)-405*sin(1)^2-401)/(2*cos(3)^2+108*sin(1)*cos(3)+99*cos(3)*cos(1)+153*sin(3)*sin(1)-276*sin(3)*cos(1)-162*sin(1)^2+259), A[6] = -(3/64)*(48*cos(3)*sin(1)^3+72*cos(3)*sin(1)^2*cos(1)-88*sin(3)*sin(1)^3-132*sin(3)*sin(1)^2*cos(1)-864*sin(1)^4+108*sin(1)^3*cos(1)+40*cos(3)^2-21*sin(3)*cos(3)-117*sin(1)*cos(3)+144*cos(3)*cos(1)+12*sin(3)*sin(1)+141*sin(3)*cos(1)+972*sin(1)^2-243*cos(1)*sin(1)-184)/(2*cos(3)^2+108*sin(1)*cos(3)+99*cos(3)*cos(1)+153*sin(3)*sin(1)-276*sin(3)*cos(1)-162*sin(1)^2+259), A[7] = (27/256)*(-48*cos(3)*sin(1)^3-72*cos(3)*sin(1)^2*cos(1)+88*sin(3)*sin(1)^3+132*sin(3)*sin(1)^2*cos(1)+864*sin(1)^4-108*sin(1)^3*cos(1)+21*sin(3)*cos(3)+117*sin(1)*cos(3)-144*cos(3)*cos(1)+40*sin(3)^2-12*sin(3)*sin(1)-141*sin(3)*cos(1)-972*sin(1)^2+243*cos(1)*sin(1)+144)/(108*sin(1)*cos(3)+99*cos(3)*cos(1)-2*sin(3)^2+153*sin(3)*sin(1)-276*sin(3)*cos(1)-162*sin(1)^2+261), A[8] = -(3/256)*(744*cos(3)*sin(1)^3+1116*cos(3)*sin(1)^2*cos(1)+496*sin(3)*sin(1)^3+744*sin(3)*sin(1)^2*cos(1)+2604*sin(1)^4+1488*sin(1)^3*cos(1)+372*sin(3)*cos(3)-216*sin(1)*cos(3)-756*cos(3)*cos(1)-151*sin(3)^2-306*sin(3)*sin(1)+180*sin(3)*cos(1)-2187*sin(1)^2+36)/(108*sin(1)*cos(3)+99*cos(3)*cos(1)-2*sin(3)^2+153*sin(3)*sin(1)-276*sin(3)*cos(1)-162*sin(1)^2+261)]]

> 

simplify(%);

[[A[1] = 3/16, A[2] = 0, A[3] = 3/16, A[4] = 0, A[5] = -1/32, A[6] = 0, A[7] = 0, A[8] = 3/128]]

> 

 


 

Download solve_identity_march_11_2024.mw

 

How can I simplify multivariate rational expressio...

Asked by: ignacios 10
multivariate simplification trig
March 09 2024
2  6


 

I have the following expressions:

m^3*r*(cos(theta)^6*a^6-9*cos(theta)^4*a^4*r^2+11*cos(theta)^2*a^2*r^4-(1/3)*r^6)*(cos(theta)^2*a^2-(1/3)*r^2)/(r^2+cos(theta)^2*a^2)^9

m^3*r*(cos(theta)^6*a^6-9*cos(theta)^4*a^4*r^2+11*cos(theta)^2*a^2*r^4-(1/3)*r^6)*(cos(theta)^2*a^2-(1/3)*r^2)/(r^2+cos(theta)^2*a^2)^9

 (1)

(a^8*(r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8-80*m^3*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(1/3)*(28*(-30*sin(theta)^2*a^4*m*r^5*(1/7)+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(32*(-5*a^2*m^3-m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10))*a^6*r^2*cos(theta)^6+(14*(-260*sin(theta)^2*a^6*m*r^3*(1/7)+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4-80*a^4*m^3*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10))*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+a^2*cos(theta)^2)^9*(a^2-2*m*r+r^2)^5)

(a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+cos(theta)^2*a^2)^9*(a^2-2*m*r+r^2)^5)

 (2)

The two expressions are the same because:

simplify(m^3*r*(cos(theta)^6*a^6-9*cos(theta)^4*a^4*r^2+11*cos(theta)^2*a^2*r^4-(1/3)*r^6)*(a^2*cos(theta)^2-(1/3)*r^2)/(r^2+a^2*cos(theta)^2)^9-(a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+a^2*cos(theta)^2)^9*(a^2-2*m*r+r^2)^5))

0

 (3)

But I don't get the expression (1) from (2) with the help of simplify() command:

simplify((a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+a^2*cos(theta)^2)^9*(a^2-2*m*r+r^2)^5))

(a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+cos(theta)^2*a^2)^9*(a^2-2*m*r+r^2)^5)

 (4)

Why not? Is there any solution for this?

 

NULL


 

Download QuestionSimplifyMultivariateRationalFunction.mw

Kronecker delta not recognized...

Asked by: James Woods 45
kronecker-delta
March 09 2024
0  4

 Hello,

  Doing simple calculations I found Maple 2024 and 2023 don't recognize Kronecker delta in the expression

Full worksheet attached. Is there any way to let Maple handle this?

Remaining questions:
1. Doing calculations using Int and value left the result unevaluated eq. (6) and eq. (7) while using int gives 0. Why?
2. Is there possibility to substitute indexed (i.e.) atomic variables like p__m? For example changing by command p__m to p__k.

Thank you in advance,

delta_kron-problem.mw

serious error in Maple 2024. (in property/ConvertR...

Asked by: nm 11353
exception
March 07 2024
2  3

This code used to work OK in Maple 2023.2.1 on windows 10. Now it gives this new internal Maple error 

Error, (in property/ConvertRelation) numeric exception: division by zero

I think this is new problem in Maple 2024 as I have not seen it before. Will report it to Maplesoft. Mean while if someone has any workaround other than not using the `is` command will try it.

The following are two worksheets. One using 2023 shows it works OK (no error) and one in Maple 2024 with the new error

203072

> 

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

> 

restart;

203072

> 

r:=1/4*a*(a*x^2+6);
tmp:=-1/x^2+1/2*a+(1/x+1/2*a*x)^2;
is(tmp = r)

(1/4)*a*(a*x^2+6)

-1/x^2+(1/2)*a+(1/x+(1/2)*a*x)^2

true

 

 

Download no_numeric_exception_march_7_2024_version_2023.mw
 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

restart;
> 

r:=1/4*a*(a*x^2+6);
tmp:=-1/x^2+1/2*a+(1/x+1/2*a*x)^2;
is(tmp = r)
 

(1/4)*a*(a*x^2+6)

-1/x^2+(1/2)*a+(1/x+(1/2)*a*x)^2

Error, (in property/ConvertRelation) numeric exception: division by zero

 

 

Download numeric_exception_march_7_2024_version_2024.mw

Maple 2024 does not solve some ode's vs. 2023...

Asked by: nm 11353
ode dsolve differential-equations
March 07 2024
1  1

I was wondering if this is by design or not. Here is one example., This ode is solved by Maple 2023.2.1 on windows 10. The solution is in terms of DESol though. It takes less than one minute.

In Maple 2024 on same PC, dsolve hangs on it.

If this by design? Since DESol solution is not very useful actually. I was thinking that may be Maple is now trying to return a solution without DESol in it, and that is why it hangs or take long time. I stopped it after 5 minutes. 

Or should I report it to Maplesoft as possible bug?  

Below are 2 worksheets. One using Maple 2023 and one using 2024.

42444

> 

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1684. The version installed in this computer is 1672 created 2024, February 7, 18:34 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2023\Physics Updates\lib\`

> 

ode:=(x + 1)*diff(u(x), x, x)/((x - 1)*cosh(1/(x - 1))) - (1/((x - 1)*cosh(1/(x - 1))) - (x + 1)/((x - 1)^2*cosh(1/(x - 1))) + (x + 1)*sinh(1/(x - 1))/((x - 1)^3*cosh(1/(x - 1))^2) + (-2*x^3 - 2*x^2)*(x + 1)/((x - 1)^2*cosh(1/(x - 1))^2))*diff(u(x), x) + (x + 1)^2*(x^5 + x^4 + 2*x^2*cosh(1/(x - 1)) - 2*x*cosh(1/(x - 1)) - x - 1)*u(x)/((x - 1)^3*cosh(1/(x - 1))^3);

(x+1)*(diff(diff(u(x), x), x))/((x-1)*cosh(1/(x-1)))-(1/((x-1)*cosh(1/(x-1)))-(x+1)/((x-1)^2*cosh(1/(x-1)))+(x+1)*sinh(1/(x-1))/((x-1)^3*cosh(1/(x-1))^2)+(-2*x^3-2*x^2)*(x+1)/((x-1)^2*cosh(1/(x-1))^2))*(diff(u(x), x))+(x+1)^2*(x^5+x^4+2*x^2*cosh(1/(x-1))-2*x*cosh(1/(x-1))-x-1)*u(x)/((x-1)^3*cosh(1/(x-1))^3)

> 

DEtools:-odeadvisor(ode);

[[_2nd_order, _with_linear_symmetries]]

> 

dsolve(ode); #after about 1 minute...

u(x) = DESol({diff(diff(_Y(x), x), x)-(1/((x-1)*cosh(1/(x-1)))-(x+1)/((x-1)^2*cosh(1/(x-1)))+(x+1)*sinh(1/(x-1))/((x-1)^3*cosh(1/(x-1))^2)+(-2*x^3-2*x^2)*(x+1)/((x-1)^2*cosh(1/(x-1))^2))*(x-1)*cosh(1/(x-1))*(diff(_Y(x), x))/(x+1)+(x+1)*(x^5+x^4+2*x^2*cosh(1/(x-1))-2*x*cosh(1/(x-1))-x-1)*_Y(x)/((x-1)^2*cosh(1/(x-1))^2)}, {_Y(x)})

 

 

Download dsolve_march_7_2024_maple_2023.mw


> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

ode:=(x + 1)*diff(u(x), x, x)/((x - 1)*cosh(1/(x - 1))) - (1/((x - 1)*cosh(1/(x - 1))) - (x + 1)/((x - 1)^2*cosh(1/(x - 1))) + (x + 1)*sinh(1/(x - 1))/((x - 1)^3*cosh(1/(x - 1))^2) + (-2*x^3 - 2*x^2)*(x + 1)/((x - 1)^2*cosh(1/(x - 1))^2))*diff(u(x), x) + (x + 1)^2*(x^5 + x^4 + 2*x^2*cosh(1/(x - 1)) - 2*x*cosh(1/(x - 1)) - x - 1)*u(x)/((x - 1)^3*cosh(1/(x - 1))^3);

(x+1)*(diff(diff(u(x), x), x))/((x-1)*cosh(1/(x-1)))-(1/((x-1)*cosh(1/(x-1)))-(x+1)/((x-1)^2*cosh(1/(x-1)))+(x+1)*sinh(1/(x-1))/((x-1)^3*cosh(1/(x-1))^2)+(-2*x^3-2*x^2)*(x+1)/((x-1)^2*cosh(1/(x-1))^2))*(diff(u(x), x))+(x+1)^2*(x^5+x^4+2*x^2*cosh(1/(x-1))-2*x*cosh(1/(x-1))-x-1)*u(x)/((x-1)^3*cosh(1/(x-1))^3)

> 

DEtools:-odeadvisor(ode);

[[_2nd_order, _with_linear_symmetries]]

> 

dsolve(ode); #hangs
 

 

Download dsolve_march_7_2024_maple_2024.mw

Missing symbols in exported PDF?...

Asked by: sursumCorda 1244
export
March 07 2024
1  1

One may easily spot that the symbols “→” and “⇒” are missing here and here. 

These two PDF files were printed officially, so I think they can be considered examples of best practice for the export functionality. Does this mean that this functionality is still defective in the most recent release?

questions about NaturalLanguage package in Maple 2...

Asked by: nm 11353
chatgpt
March 06 2024
2  1

chatGPT version used by the new NaturalLanguage package seems to be using chatGPT 3?. I asked it and this what it said

NL:=NaturalLanguage;
NL:-Query("what is your name?");
"As an Artificial Intelligence, I don't have a personal name. However, If 
you're asking how to represent the question \"What is your name?\" in MathML, 
it's actually irrelevant as MathML is used for marking up mathematical notations, 
not regular text or questions. \n\nBut in English, it's as simple 
as just asking \"What is your name?

Then I asked it 

NL:-Query("what version of chatGPT are you?");

"As an AI developed by OpenAI, I don't have a specific version like software 
programs or applications. I get continuous updates and improvements over time. 
However, as of my current operation, I'm based on GPT-3 model.

some questions: It is possible to make it use chatGPT 3.5 or 4.0 with NL?

How is this free to use and without getting a key from openAI? After agreeing to terms fromn the options menu, can one continue to use it for free? I thought chatGPT requires some fee to use. But I could be wrong.  but this is nice to be able to use it this easily from Maple!

Btw, It is still not very good in math. Asked it to first this simple first order ode and got wrong answer

NL:-Query("what is the solution to the differential equation y'(x)+y(x)=sin(x)");
"Sorry, this query was too complicated. Please rephrase and/or try again."

So I tried

NL:-Query("solve the differential equation y'(x)+y(x)=sin(x)");

"The differential equation given is a first order linear 

   ordinary differential equation. 

  

  The general solution can be obtained through the following 

   steps:

  

  1. Identify the homogeneous part of the equation, which is 

   y'(x) + y(x) = 0. The solution of such a homogeneous 

   equation known as the "complementary function" is y_c = 

   e^(-x) * A. where A is an arbitrary constant which will be 

   determined by a specific condition or boundary value.

  

  2. Find a Particular Integral (solution specific to the 

   nonhomogeneous part of the differential equation) which in 

   this case is y_p = -cos(x)

  

  3. Combine the Complementary function and Particular Integral 

   to get a general solution, y(x) = e^(-x) * A - cos(x).

  

  Now let's express the solution in MathML:"


                            (-x)          
                     y x = e     A - cos x

 "Note: Here A is a to-be-determined constant. If the problem 

    was a boundary value or initial value problem, you would 

    substitute the given values into this general solution and 

    solve it for A."

The solution should be

dsolve(diff(y(x),x)+y(x)=sin(x))

                y(x) = -cos(x)/2 + sin(x)/2 + exp(-x)*c__1

 

Discover What's New in Maple 2024!

by: Karishma 810 Maple 2024
maplesoft release
March 06 2024
12  2

A blue triangle with white text Description automatically generated

 

Attention Maple enthusiasts! It gives me great pleasure to announce Maple 2024! Maple 2024 brings together a collection of new features and enhancements carefully designed to enrich your mathematical explorations. Maple 2024 is the result of a lot of hard work by a lot of people, and there is far more in it than I can cover here. But I’d like to share with you some of my favorite features in this release.

 

AI Formula Assistant

The AI Formula Assistant in Maple 2024 is undoubtedly the feature that excites me the most, especially considering how often I’m asked the question: 'When will Maple include AI features?' This assistant serves as your new mathematical companion and will change the way you look up and enter formulas and equations. Driven by advanced AI technology, it presents a range of relevant options based on your search query. Alongside suggestions, you'll also receive detailed explanations for each formula and its parameters so you can select the one you need, and then you can insert the formula into your document at a click of a button, as a proper Maple expression.

A screenshot of a computer Description automatically generated

 

 

NaturalLanguage Package

The Formula Assistant is built on top of the new NaturalLanguage package, which integrates powerful language models like GPT-4 and ChatGPT from OpenAI into Maple. With this feature, you can leverage large language models to process natural language within Maple. Ask the AI to explain concepts, provide additional details, find specific Maple commands, and more. Of course, since this is a Maple package, you can also use it as a basis to build your own AI-powered applications inside Maple. We’re really looking forward to seeing what you will do with it!

 

A close-up of a document Description automatically generated

 

 

Argument Completion
We’ve had a lot of requests from people who wanted Maple’s command completion features to do even more, and I’m happy to say that Maple 2024 delivers. The new argument completion feature in Maple 2024 is poised to significantly enhance your experience with commands. For many users, including myself, not being aware of all the options a command takes is a challenge, often leading me to refer to help pages for clarification. With argument completion, that's no longer a concern. Just enter the command with the help of the existing command completion feature, then automatic argument completion takes over to guide you through the rest. Give it a try with the 'plot' command!

A screenshot of a computer Description automatically generated

 

Check My Work

A personal favorite feature that's gotten even better in Maple 2024 is Check My Work. As someone who has tutored students, I vividly recall their stress before exams, often receiving emails and text messages from them seeking last-minute help. At the time, I found myself wishing the students had a way to check their work themselves, so we would all be less stressed! So I was super excited when we added the first Check My Work feature a couple of years ago, and am very happy that it gets better ever year. In Maple 2024, we’ve expanded its capabilities to support problems involving factoring, simplification, and limits.

A screenshot of a computer Description automatically generated

Scrollable Matrices:
This feature will definitely resonate with many of the engineers in the Maple Primes community. If you're someone who works with worksheets containing large matrices, you've likely wished that you could scroll the matrices inside your document instead of having to launch a separate matrix browser. With Maple 2024, your wish has come true.

 

A white sheet with numbers and lines Description automatically generated with medium confidence

 

Color Bars

And finally, for those of you who appreciated the addition of color bars in Maple 2023 but wanted to see them extended to more 2D and 3D plots, you'll be delighted to know that this is exactly what we’ve done. We’ve also added new customization options, providing you with greater control over appearance.

 

A close-up of a graph Description automatically generated

 

This is just a partial glimpse of what's new in Maple 2024. For a comprehensive overview, visit What’s New in Maple 2024.

Exporting Graphs to PDF Using Maple Code?...

Asked by: lcz 1039
graphtheory pdf plotting
September 20 2023
1  0
The following code effectively converts the image to the JPG format.
with(GraphTheory):
s:=DrawGraph(CompleteGraph(5),size=[250,250])
Export("D:\\s1.jpg",s)

But I would like to export it using PDF format. However, the modified code below seems to be quite unsuccessful. I am aware that Maple has export options in the front end, but I still prefer to use code for this purpose.

Export("D:\\s1.pdf",s)

Error, (in Export) invalid input: member received _ImportExport:-InfoTable["PDF"][4], which is not valid for its 2nd argument, s

There are two reasons for this.

with(GraphTheory):
Graphs:=[NonIsomorphicGraphs(6,8,output=graphs,outputform = graph)]:
num_g:=nops(Graphs):
num:=ceil((num_g)/5.):
M1:=Matrix (num,5,(i,j)->`if`((i-1)*5+j<=num_g, DrawGraph(Graphs[(i-1)*5+j],size=[250,250] ,overrideoptions ,showlabels=false,style=planar, stylesheet =  [
 vertexcolor     = orange
,vertexfontcolor = black
,vertexborder    = false
,edgethickness   = 0.6
,edgecolor       = MidnightBlue
,vertexshape     =  "circle"
,vertexfont      = [Arial, 4],
vertexthickness=5], caption = cat(H__,5*(i-1)+j),captionfont=["ROMAN",7]),plot(x = 0 .. 1, axes = none))):
DocumentTools:-Tabulate (M1[1..5,.. ],widthmode=percentage ,width=80 , exterior =all):

How to remove the mosaic of vertices?...

Asked by: lcz 1039
graphtheory pdf export
June 14 2022
1  1

I  generated some graphs via maple and would like to put them in my paper. So I am going to convert the following worksheet to pdf.

with(GraphTheory):
Graphs:=[NonIsomorphicGraphs(6,8,output=graphs,outputform = graph)]:
num_g:=nops(Graphs):
num:=ceil((num_g)/5.):
M1:=Matrix (num,5,(i,j)->`if`((i-1)*5+j<=num_g, DrawGraph(Graphs[(i-1)*5+j],size=[250,250] ,overrideoptions ,showlabels=false,style=planar, stylesheet =  [
 vertexcolor     = orange
,vertexfontcolor = black
,vertexborder    = false
,edgethickness   = 0.6
,edgecolor       = MidnightBlue
,vertexshape     =  "circle"
,vertexfont      = [Arial, 4],
vertexthickness=5], caption = cat(H__,5*(i-1)+j),captionfont=["ROMAN",7]),plot(x = 0 .. 1, axes = none))):
DocumentTools:-Tabulate (M1[1..5,.. ],widthmode=percentage ,width=80 , exterior =all) :

 

 

But there was a problem with the exported pdf. There was some mosaic stuff at the vertices of all those graphs. It was strange. (I want to reduce the size of vertices of the graphs in order not to look crowded.)

 

Only when I insert the option vertexpadding and set a large enough size  of vertex (for this example, we set vertexpadding=7),  it won't go wrong. However, in fact, we often need make vertice‘s size smaller , especially when there are more vertices.

Using a pdf viewer, it seems that after exporting, there is a box above each vertex.

 

 

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