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Limitrule not easy to understand ...

Asked by: janhardo 700
calculus step-by-step calculus1
July 27 2024
0  9

I'm a little busy with the Rule feature in Maple 
Just started with the limits and can't get 1 limit rule working in my FSimp procedure yet
As a limit example I saw this in Maple help 

with(Student:-Calculus1);
infolevel[Student[Calculus1]] := 1;

Rule[lhopital, ln(x)](Limit(x*ln(x), x = 0, right));
Creating problem #2

                  lim   (x ln(x)) =   lim   (-x)
                x -> 0+             x -> 0+

A meaningless example of how one limit of a function is equal to another limit of a function, when I think there is no connection between the two functions. ( I don't see it ) 
You might as well calculate the limit value right away.

It gets more interesting when you analyze the function/expression : x*ln(x) and start rewriting it, to a [0/0] or [infinity/infinity] form in this case and from this it shows the need to start using lhopital rule.

The Rule feature has a Hint capability and gives as a hint, lhopital that this rule is applied 
Of course, you also have a series of standard limits, beyond the lhopital limits
The Rule feature for the limit is not yet step by step, because the need to start using a lhopital limit rule has not yet been demonstrated by the user

How could I install the update package of Differen...

Asked by: yvnog 5
July 26 2024
1  5

I'm interested in installing the package update from I M Anderson's site, the Differential Geometry Software Project. This corresponds to the 2022 update. There are many new features:
- Submanifold theory
- Differential operators and  Pseudo-Differential Operators
- Principal connections
- Integrable System Library
- Cartan normal connections
and more. 
It's unfortunate that this update isn't included in this version of Maple 2024

How to extract the coefficient of a complicated po...

Asked by: Aixleft math 120
polynomial series coeff
July 26 2024
1  2

Hi all guys, how can I extract the coefficient of order 6 of expand(SUMY-T) as below? I use the coeff but no use and I search last posts in mapleprime but no fit for my case, and substitute the parematers of a,b,c....

Thank you!

> 

A[21] = 3/20-(1/20)*sqrt(5), A[31] = 0, A[32] = 3/20+(1/20)*sqrt(5), a[21] = 1/30-(1/75)*sqrt(5), a[31] = -1288/452405, a[32] = 98209/2714430-(1/75)*sqrt(5), b[1] = 1/24, b[2] = 1/16+(1/48)*sqrt(5), b[3] = 1/16-(1/48)*sqrt(5), bp[1] = 1/12, bp[2] = 5/24+(1/24)*sqrt(5), bp[3] = 5/24-(1/24)*sqrt(5), c[2] = 1/2-(1/10)*sqrt(5), c[3] = 1/2+(1/10)*sqrt(5)
> 

T := (1/6)*h^3*G+(1/24)*h^4*((diff(y(x), x))*G[y]+F*G[z])+(1/120)*h^5*(G[yy]*(diff(y(x), x))^2+2*G[yz]*(diff(y(x), x))*F+F*G[y]+G[zz]*F^2+G*G[z])+(1/720)*h^6*(G[yyy]*(diff(y(x), x))^3+3*(diff(y(x), x))^2*G[yyz]*F+3*(diff(y(x), x))*G[yy]*F+3*(diff(y(x), x))*G[yzz]*F^2+3*G[yz]*(diff(y(x), x))*G+3*G[yz]*F^2+G[y]*G+G[zzz]*F^3+3*F*G[zz]*G+G[z]*((diff(y(x), x))*G[y]+F*G[z]))
> 

NULL
> 

SUMY := y(x)+h*(diff(y(x), x))+(1/2)*h^2*F+h^3*b[1]*G+h^3*b[2]*(G+((diff(y(x), x))*G[y]*c[2]+F*G[z]*c[2])*h+((1/2)*(diff(y(x), x))^2*G[yy]*c[2]^2+(diff(y(x), x))*F*G[yz]*c[2]^2+(1/2)*F^2*G[zz]*c[2]^2+(1/2)*F*G[y]*c[2]^2+G*G[z]*A[21])*h^2+((diff(y(x), x))*G*G[yz]*A[21]*c[2]+F*G*G[zz]*A[21]*c[2]+(1/6)*(diff(y(x), x))^3*G[yyy]*c[2]^3+(1/6)*F^3*G[zzz]*c[2]^3+(1/2)*(diff(y(x), x))*F*G[yy]*c[2]^3+G*G[y]*a[21]+(1/2)*(diff(y(x), x))^2*F*G[yyz]*c[2]^3+(1/2)*(diff(y(x), x))*F^2*G[yzz]*c[2]^3+(1/2)*F^2*G[yz]*c[2]^3)*h^3+((1/8)*F^2*G[yy]*c[2]^4+(1/2)*G^2*G[zz]*A[21]^2+(1/4)*F^3*G[yzz]*c[2]^4+(1/6)*(diff(y(x), x))^3*F*G[yyyz]*c[2]^4+(1/4)*(diff(y(x), x))^2*F^2*G[yyzz]*c[2]^4+(1/6)*(diff(y(x), x))*F^3*G[yzzz]*c[2]^4+(1/4)*(diff(y(x), x))^2*F*G[yyy]*c[2]^4+(1/2)*(diff(y(x), x))*F^2*G[yyz]*c[2]^4+(1/2)*G[yyz]*(diff(y(x), x))^2*G*A[21]*c[2]^2+(1/2)*G[zzz]*F^2*G*A[21]*c[2]^2+(1/24)*(diff(y(x), x))^4*G[yyyy]*c[2]^4+(1/24)*F^4*G[zzzz]*c[2]^4+G[yzz]*(diff(y(x), x))*F*G*A[21]*c[2]^2+(1/2)*F*G*G[yz]*A[21]*c[2]^2+(diff(y(x), x))*G*G[yy]*a[21]*c[2]+F*G*G[yz]*a[21]*c[2])*h^4+((1/120)*(diff(y(x), x))^5*G[yyyyy]*c[2]^5+(1/8)*F^3*G[yyz]*c[2]^5+(1/120)*F^5*G[zzzzz]*c[2]^5+(1/12)*F^4*G[yzzz]*c[2]^5+(1/12)*(diff(y(x), x))^2*F^3*G[yyzzz]*c[2]^5+(1/12)*(diff(y(x), x))^3*F^2*G[yyyzz]*c[2]^5+(1/24)*(diff(y(x), x))^4*F*G[yyyyz]*c[2]^5+(1/24)*(diff(y(x), x))*F^4*G[yzzzz]*c[2]^5+(1/8)*(diff(y(x), x))*F^2*G[yyy]*c[2]^5+(1/4)*(diff(y(x), x))*F^3*G[yyzz]*c[2]^5+(1/4)*(diff(y(x), x))^2*F^2*G[yyyz]*c[2]^5+(1/12)*(diff(y(x), x))^3*F*G[yyyy]*c[2]^5+G^2*G[yz]*A[21]*a[21]+(1/2)*G[yzz]*F^2*G*a[21]*c[2]^2+(1/2)*G[zzz]*F*G^2*A[21]^2*c[2]+(1/2)*F*G*G[yy]*a[21]*c[2]^2+(1/6)*G[zzzz]*F^3*G*A[21]*c[2]^3+(1/2)*G[yyy]*(diff(y(x), x))^2*G*a[21]*c[2]^2+(1/2)*G[yzz]*(diff(y(x), x))*G^2*A[21]^2*c[2]+(1/6)*G[yyyz]*(diff(y(x), x))^3*G*A[21]*c[2]^3+(1/2)*G[yzz]*F^2*G*A[21]*c[2]^3+(1/2)*G[yzzz]*(diff(y(x), x))*F^2*G*A[21]*c[2]^3+(1/2)*G[yyzz]*(diff(y(x), x))^2*F*G*A[21]*c[2]^3+(1/2)*G[yyz]*(diff(y(x), x))*F*G*A[21]*c[2]^3+G[yyz]*(diff(y(x), x))*F*G*a[21]*c[2]^2)*h^5+((1/6)*G[zzz]*G^3*A[21]^3+(1/16)*F^4*G[yyzz]*c[2]^6+(1/720)*F^6*G[zzzzzz]*c[2]^6+(1/48)*F^5*G[yzzzz]*c[2]^6+(1/2)*G^2*G[yy]*a[21]^2+(1/720)*G[yyyyyy]*(diff(y(x), x))^6*c[2]^6+(1/48)*F^3*G[yyy]*c[2]^6+(1/8)*(diff(y(x), x))*F^3*G[yyyz]*c[2]^6+(1/16)*(diff(y(x), x))^2*F^2*G[yyyy]*c[2]^6+(1/12)*(diff(y(x), x))*F^4*G[yyzzz]*c[2]^6+(1/8)*(diff(y(x), x))^2*F^3*G[yyyzz]*c[2]^6+(1/12)*(diff(y(x), x))^3*F^2*G[yyyyz]*c[2]^6+(1/48)*(diff(y(x), x))^4*F*G[yyyyy]*c[2]^6+(1/36)*F^3*G[yyyzzz]*(diff(y(x), x))^3*c[2]^6+(1/48)*F^4*G[yyzzzz]*(diff(y(x), x))^2*c[2]^6+(1/48)*F^2*G[yyyyzz]*(diff(y(x), x))^4*c[2]^6+(1/120)*F*G[yyyyyz]*(diff(y(x), x))^5*c[2]^6+(1/120)*F^5*G[yzzzzz]*(diff(y(x), x))*c[2]^6+(1/4)*G[yzzz]*F^3*G*A[21]*c[2]^4+(1/6)*G[yzzz]*F^3*G*a[21]*c[2]^3+(1/4)*G[zzzz]*F^2*G^2*A[21]^2*c[2]^2+(1/2)*G[yyz]*F^2*G*a[21]*c[2]^3+(1/4)*G[yzz]*F*G^2*A[21]^2*c[2]^2+(1/24)*G[zzzzz]*F^4*G*A[21]*c[2]^4+(1/8)*G[yyz]*F^2*G*A[21]*c[2]^4+(1/6)*G[yyyy]*(diff(y(x), x))^3*G*a[21]*c[2]^3+(1/4)*G[yyzz]*(diff(y(x), x))^2*G^2*A[21]^2*c[2]^2+(1/24)*G[yyyyz]*(diff(y(x), x))^4*G*A[21]*c[2]^4+G[yyz]*(diff(y(x), x))*G^2*A[21]*a[21]*c[2]+(1/4)*G[yyzzz]*(diff(y(x), x))^2*F^2*G*A[21]*c[2]^4+(1/6)*G[yyyzz]*(diff(y(x), x))^3*F*G*A[21]*c[2]^4+(1/2)*G[yzzz]*(diff(y(x), x))*F*G^2*A[21]^2*c[2]^2+(1/4)*G[yyyz]*(diff(y(x), x))^2*F*G*A[21]*c[2]^4+(1/2)*G[yyzz]*(diff(y(x), x))*F^2*G*A[21]*c[2]^4+G[yzz]*F*G^2*A[21]*a[21]*c[2]+(1/2)*G[yyyz]*(diff(y(x), x))^2*F*G*a[21]*c[2]^3+(1/2)*G[yyzz]*(diff(y(x), x))*F^2*G*a[21]*c[2]^3+(1/6)*G[yzzzz]*(diff(y(x), x))*F^3*G*A[21]*c[2]^4+(1/2)*G[yyy]*(diff(y(x), x))*F*G*a[21]*c[2]^3)*h^6+O(h^7))+h^3*b[3]*(G+((diff(y(x), x))*G[y]*c[3]+F*G[z]*c[3])*h+((1/2)*F*G[y]*c[3]^2+(1/2)*(diff(y(x), x))^2*G[yy]*c[3]^2+(1/2)*F^2*G[zz]*c[3]^2+G*G[z]*A[31]+G*G[z]*A[32]+(diff(y(x), x))*F*G[yz]*c[3]^2)*h^2+(G*G[y]*a[31]+(1/6)*(diff(y(x), x))^3*G[yyy]*c[3]^3+(1/6)*F^3*G[zzz]*c[3]^3+(1/2)*(diff(y(x), x))*F*G[yy]*c[3]^3+(1/2)*(diff(y(x), x))^2*F*G[yyz]*c[3]^3+(1/2)*(diff(y(x), x))*F^2*G[yzz]*c[3]^3+(1/2)*F^2*G[yz]*c[3]^3+G[y]*G[z]*(diff(y(x), x))*A[32]*c[2]+G[z]^2*F*A[32]*c[2]+G*G[y]*a[32]+F*G*G[zz]*A[32]*c[3]+(diff(y(x), x))*G*G[yz]*A[32]*c[3]+F*G*G[zz]*A[31]*c[3]+(diff(y(x), x))*G*G[yz]*A[31]*c[3])*h^3+((1/24)*(diff(y(x), x))^4*G[yyyy]*c[3]^4+(1/8)*F^2*G[yy]*c[3]^4+(1/4)*F^3*G[yzz]*c[3]^4+(1/24)*F^4*G[zzzz]*c[3]^4+(1/2)*G^2*G[zz]*A[31]^2+(1/2)*G^2*G[zz]*A[32]^2+G[yzz]*(diff(y(x), x))*F*G*A[31]*c[3]^2+G[yzz]*(diff(y(x), x))*F*G*A[32]*c[3]^2+G[y]*G[yz]*(diff(y(x), x))^2*A[32]*c[2]*c[3]+G[z]*G[yz]*F*(diff(y(x), x))*A[32]*c[2]^2+G[z]*G[zz]*F^2*A[32]*c[2]*c[3]+(1/2)*(diff(y(x), x))*F^2*G[yyz]*c[3]^4+(1/4)*(diff(y(x), x))^2*F*G[yyy]*c[3]^4+(1/2)*G[zzz]*F^2*G*A[31]*c[3]^2+(1/2)*F*G*G[yz]*A[31]*c[3]^2+F*G*G[yz]*a[31]*c[3]+(1/2)*G[yyz]*(diff(y(x), x))^2*G*A[31]*c[3]^2+(diff(y(x), x))*G*G[yy]*a[31]*c[3]+(1/2)*F*G*G[yz]*A[32]*c[3]^2+F*G*G[yz]*a[32]*c[3]+(1/2)*G[zzz]*F^2*G*A[32]*c[3]^2+(1/2)*G[z]*G[yy]*(diff(y(x), x))^2*A[32]*c[2]^2+(diff(y(x), x))*G*G[yy]*a[32]*c[3]+(1/2)*G[yyz]*(diff(y(x), x))^2*G*A[32]*c[3]^2+(1/2)*G[z]*G[zz]*F^2*A[32]*c[2]^2+(1/2)*G[y]*G[z]*F*A[32]*c[2]^2+G[y]*G[z]*F*a[32]*c[2]+(1/6)*(diff(y(x), x))^3*F*G[yyyz]*c[3]^4+(1/4)*(diff(y(x), x))^2*F^2*G[yyzz]*c[3]^4+(1/6)*(diff(y(x), x))*F^3*G[yzzz]*c[3]^4+G[y]^2*(diff(y(x), x))*a[32]*c[2]+G^2*G[zz]*A[31]*A[32]+G[z]^2*G*A[21]*A[32]+G[y]*G[zz]*F*(diff(y(x), x))*A[32]*c[2]*c[3]+G[z]*G[yz]*F*(diff(y(x), x))*A[32]*c[2]*c[3])*h^4+((1/2)*G[z]*G[yzz]*F^2*(diff(y(x), x))*A[32]*c[2]^3+(1/8)*(diff(y(x), x))*F^2*G[yyy]*c[3]^5+(1/4)*(diff(y(x), x))*F^3*G[yyzz]*c[3]^5+(1/4)*(diff(y(x), x))^2*F^2*G[yyyz]*c[3]^5+(1/12)*(diff(y(x), x))^3*F*G[yyyy]*c[3]^5+(1/24)*(diff(y(x), x))^4*F*G[yyyyz]*c[3]^5+(1/12)*(diff(y(x), x))^3*F^2*G[yyyzz]*c[3]^5+(1/12)*(diff(y(x), x))^2*F^3*G[yyzzz]*c[3]^5+(1/24)*(diff(y(x), x))*F^4*G[yzzzz]*c[3]^5+(1/2)*G[y]^2*F*a[32]*c[2]^2+(1/2)*G[z]*G[yy]*F*(diff(y(x), x))*A[32]*c[2]^3+G[y]*G*G[zz]*(diff(y(x), x))*A[32]^2*c[2]+(1/2)*G[y]*G[yyz]*(diff(y(x), x))^3*A[32]*c[2]*c[3]^2+(1/2)*G[z]*G[zzz]*F^3*A[32]*c[2]*c[3]^2+G[z]*G[yz]*F^2*a[32]*c[2]*c[3]+G[z]*G*G[zz]*F*A[32]^2*c[2]+(1/2)*G[z]*G[yz]*F^2*A[32]*c[2]*c[3]^2+(1/2)*G[y]*G[zz]*F^2*A[32]*c[2]^2*c[3]+(1/6)*G[z]*G[zzz]*F^3*A[32]*c[2]^3+G^2*G[yz]*A[32]*a[31]+G^2*G[yz]*A[31]*a[31]+G^2*G[yz]*A[31]*a[32]+(1/2)*G[yz]*G[yy]*(diff(y(x), x))^3*A[32]*c[2]^2*c[3]+G[y]*G[yz]*F*(diff(y(x), x))*a[32]*c[2]^2+(1/2)*G[y]*G[yy]*(diff(y(x), x))^2*a[32]*c[2]^2+(1/6)*(diff(y(x), x))^3*G*G[yyyz]*A[32]*c[3]^3+G[y]*G[yzz]*F*(diff(y(x), x))^2*A[32]*c[2]*c[3]^2+G[z]*G[yz]*(diff(y(x), x))*G*A[21]*A[32]*c[2]+G[y]*G[zz]*(diff(y(x), x))*G*A[31]*A[32]*c[2]+G[z]*G[yz]*(diff(y(x), x))*G*A[21]*A[32]*c[3]+G[z]*G[zz]*F*G*A[21]*A[32]*c[2]+G[z]*G[zz]*F*G*A[31]*A[32]*c[2]+G[z]*G[zz]*F*G*A[21]*A[32]*c[3]+G[y]*G[z]*G*A[32]*a[21]+(1/2)*G[yzz]*(diff(y(x), x))*G^2*A[31]^2*c[3]+(1/6)*G[yyyz]*(diff(y(x), x))^3*G*A[31]*c[3]^3+(1/2)*F*G*G[yy]*a[31]*c[3]^2+(1/6)*G[zzzz]*F^3*G*A[31]*c[3]^3+G[y]*G[z]*G*A[21]*a[32]+(1/120)*F^5*G[zzzzz]*c[3]^5+G[y]*G[yz]*F*(diff(y(x), x))*a[32]*c[2]*c[3]+(1/2)*G[z]*G[yyz]*F*(diff(y(x), x))^2*A[32]*c[2]*c[3]^2+(1/6)*F^3*G*G[zzzz]*A[32]*c[3]^3+(1/2)*F^2*G*G[yzz]*A[32]*c[3]^3+(1/2)*F^2*G*G[yzz]*a[32]*c[3]^2+(1/2)*(diff(y(x), x))^2*G*G[yyy]*a[32]*c[3]^2+(1/2)*(diff(y(x), x))*G^2*G[yzz]*A[32]^2*c[3]+G[z]*G[yzz]*F^2*(diff(y(x), x))*A[32]*c[2]*c[3]^2+(1/12)*F^4*G[yzzz]*c[3]^5+(1/8)*F^3*G[yyz]*c[3]^5+(1/120)*(diff(y(x), x))^5*G[yyyyy]*c[3]^5+(1/2)*G[z]*G[yz]*F^2*A[32]*c[2]^3+(1/2)*G[zz]^2*F^3*A[32]*c[2]^2*c[3]+G[y]*G[yy]*(diff(y(x), x))^2*a[32]*c[2]*c[3]+G[yz]^2*F*(diff(y(x), x))^2*A[32]*c[2]^2*c[3]+(diff(y(x), x))*F*G*G[yyz]*a[32]*c[3]^2+(1/2)*(diff(y(x), x))*F^2*G*G[yzzz]*A[32]*c[3]^3+(1/2)*(diff(y(x), x))*F*G*G[yyz]*A[32]*c[3]^3+(1/2)*(diff(y(x), x))^2*F*G*G[yyzz]*A[32]*c[3]^3+(1/2)*G[yyz]*(diff(y(x), x))*F*G*A[31]*c[3]^3+(1/2)*G[yyzz]*(diff(y(x), x))^2*F*G*A[31]*c[3]^3+(1/2)*G[yzzz]*(diff(y(x), x))*F^2*G*A[31]*c[3]^3+G[yyz]*(diff(y(x), x))*F*G*a[31]*c[3]^2+G[yzz]*(diff(y(x), x))*G^2*A[31]*A[32]*c[3]+G[zzz]*F*G^2*A[31]*A[32]*c[3]+3*G[yz]*G[zz]*F^2*(diff(y(x), x))*A[32]*c[2]^2*c[3]*(1/2)+(1/2)*F*G^2*G[zzz]*A[32]^2*c[3]+(1/2)*G[yyy]*(diff(y(x), x))^2*G*a[31]*c[3]^2+(1/2)*G[yzz]*F^2*G*A[31]*c[3]^3+(1/2)*G[yzz]*F^2*G*a[31]*c[3]^2+(1/2)*G[zzz]*F*G^2*A[31]^2*c[3]+(1/2)*F*G*G[yy]*a[32]*c[3]^2+(1/2)*G[z]*G[yyz]*F*(diff(y(x), x))^2*A[32]*c[2]^3+(1/6)*G[z]*G[yyy]*(diff(y(x), x))^3*A[32]*c[2]^3+(1/2)*G[y]*G[zz]*F^2*a[32]*c[2]^2+(1/2)*G[y]*G[yz]*F*(diff(y(x), x))*A[32]*c[2]^2*c[3]+G[z]*G[yy]*F*(diff(y(x), x))*a[32]*c[2]*c[3]+(1/2)*G[y]*G[zzz]*F^2*(diff(y(x), x))*A[32]*c[2]*c[3]^2+(1/2)*G[yy]*G[zz]*F*(diff(y(x), x))^2*A[32]*c[2]^2*c[3]+(1/2)*G[y]*G[yz]*F*(diff(y(x), x))*A[32]*c[2]*c[3]^2+G^2*G[yz]*A[32]*a[32])*h^5+((1/6)*G[z]*G[yzzz]*F^3*(diff(y(x), x))*A[32]*c[2]^4+(1/16)*F^4*G[yyzz]*c[3]^6+(1/2)*G[z]*G[yyz]*F^2*(diff(y(x), x))*A[32]*c[2]*c[3]^3+(1/2)*G^2*G[yy]*a[31]^2+(1/2)*G[y]*G[yzz]*F^2*(diff(y(x), x))*a[32]*c[2]^3+(1/6)*G[zz]*G[yyy]*F*(diff(y(x), x))^3*A[32]*c[2]^3*c[3]+(1/2)*(diff(y(x), x))*F*G^2*G[yzzz]*A[32]^2*c[3]^2+(1/6)*(diff(y(x), x))*F^3*G*G[yzzzz]*A[32]*c[3]^4+(1/4)*G[y]*G[yz]*F^2*A[32]*c[2]^2*c[3]^2+(1/36)*F^3*G[yyyzzz]*(diff(y(x), x))^3*c[3]^6+(1/48)*F^4*G[yyzzzz]*(diff(y(x), x))^2*c[3]^6+(1/6)*G^3*G[zzz]*A[32]^3+(diff(y(x), x))*G^2*G[yyz]*A[32]*a[32]*c[3]+(1/2)*(diff(y(x), x))*F*G*G[yyy]*a[32]*c[3]^3+(1/2)*G[y]*G[yz]*F^2*a[32]*c[2]^2*c[3]+(1/4)*G[yz]*G[yy]*F*(diff(y(x), x))^2*A[32]*c[2]^2*c[3]^2+(1/12)*(diff(y(x), x))^3*F^2*G[yyyyz]*c[3]^6+(1/8)*(diff(y(x), x))^2*F^3*G[yyyzz]*c[3]^6+(1/6)*G[zzz]*G^3*A[31]^3+(1/2)*G[zz]*G[yyz]*F^2*(diff(y(x), x))^2*A[32]*c[2]^3*c[3]+(1/4)*G[z]*G[yyzz]*F^2*(diff(y(x), x))^2*A[32]*c[2]^4+G[z]*G[zz]*G^2*A[21]*A[32]^2+3*G[yz]*G[yy]*F*(diff(y(x), x))^2*a[32]*c[2]^2*c[3]*(1/2)+(1/4)*(diff(y(x), x))^2*F*G*G[yyyz]*A[32]*c[3]^4+(1/4)*(diff(y(x), x))^2*F^2*G*G[yyzzz]*A[32]*c[3]^4+(1/2)*G[yz]*G[zz]*F^3*a[32]*c[2]^2*c[3]+G[y]*G*G[zzz]*F*(diff(y(x), x))*A[32]^2*c[2]*c[3]+(1/720)*F^6*G[zzzzzz]*c[3]^6+(1/720)*G[yyyyyy]*(diff(y(x), x))^6*c[3]^6+(1/2)*G[y]*G*G[zz]*F*A[32]^2*c[2]^2+(1/24)*G[z]*G[yyyy]*(diff(y(x), x))^4*A[32]*c[2]^4+(1/2)*(diff(y(x), x))*F^2*G*G[yyzz]*a[32]*c[3]^3+(1/4)*G[z]*G[yyy]*F*(diff(y(x), x))^2*A[32]*c[2]^4+(1/6)*G[z]*G[yyyz]*F*(diff(y(x), x))^3*A[32]*c[2]^4+(1/2)*G[y]*G[yzzz]*F^2*(diff(y(x), x))^2*A[32]*c[2]*c[3]^3+(1/6)*(diff(y(x), x))^3*G*G[yyyy]*a[32]*c[3]^3+(1/2)*G[yy]*G[yzz]*F*(diff(y(x), x))^3*A[32]*c[2]^2*c[3]^2+(1/48)*F^2*G[yyyyzz]*(diff(y(x), x))^4*c[3]^6+G[y]^2*G*a[21]*a[32]+(1/2)*G[y]*G[yyz]*F*(diff(y(x), x))^2*a[32]*c[2]^3+(1/2)*G[yz]^2*F^2*(diff(y(x), x))*A[32]*c[2]^3*c[3]+(1/4)*(diff(y(x), x))^2*G^2*G[yyzz]*A[32]^2*c[3]^2+(1/2)*G[y]*G[yy]*F*(diff(y(x), x))*a[32]*c[2]^2*c[3]+(1/2)*G[z]^2*G[zz]*F^2*A[32]^2*c[2]^2+(1/2)*G[yyzz]*(diff(y(x), x))*F^2*G*A[31]*c[3]^4+G[yyz]*(diff(y(x), x))*G^2*A[31]*a[31]*c[3]+(1/2)*G[y]*G[yzz]*F^2*(diff(y(x), x))*A[32]*c[2]*c[3]^3+(1/120)*F^5*G[yzzzzz]*(diff(y(x), x))*c[3]^6+(1/120)*F*G[yyyyyz]*(diff(y(x), x))^5*c[3]^6+(1/4)*G[yz]*G[zz]*F^3*A[32]*c[2]^2*c[3]^2+(1/2)*(diff(y(x), x))^2*F*G*G[yyyz]*a[32]*c[3]^3+G[yzz]*F*G^2*A[32]*a[31]*c[3]+(1/2)*G[zzzz]*F^2*G^2*A[31]*A[32]*c[3]^2+(1/6)*G[yzzzz]*(diff(y(x), x))*F^3*G*A[31]*c[3]^4+(1/2)*G[yyzz]*(diff(y(x), x))^2*G^2*A[31]*A[32]*c[3]^2+(1/2)*G[yyy]*(diff(y(x), x))*F*G*a[31]*c[3]^3+(1/2)*G[zz]^2*F^2*G*A[31]*A[32]*c[2]^2+G[z]*G[zz]*G^2*A[21]*A[31]*A[32]+G[yzz]*F*G^2*A[31]*a[32]*c[3]+(1/2)*G[yzz]*F*G^2*A[31]*A[32]*c[3]^2+(1/2)*G[z]*G[yzz]*F^3*A[32]*c[2]*c[3]^3+(1/2)*G[yz]*G[zzz]*F^3*(diff(y(x), x))*A[32]*c[2]^2*c[3]^2+G[z]*G[yzz]*(diff(y(x), x))*F*G*A[21]*A[32]*c[3]^2+G[z]*G[yzz]*(diff(y(x), x))*F*G*A[21]*A[32]*c[2]^2+G[z]*G[zzz]*F^2*G*A[31]*A[32]*c[2]*c[3]+G[zz]*G[yz]*(diff(y(x), x))*F*G*A[31]*A[32]*c[2]^2+G[y]*G[yzz]*(diff(y(x), x))^2*G*A[31]*A[32]*c[2]*c[3]+(1/2)*G[y]*G[yzz]*F^2*(diff(y(x), x))*A[32]*c[2]^2*c[3]^2+(1/4)*G[zzzz]*F^2*G^2*A[31]^2*c[3]^2+(1/2)*G[yyz]*F^2*G*a[31]*c[3]^3+(1/8)*G[yyz]*F^2*G*A[31]*c[3]^4+(1/4)*G[yzz]*F*G^2*A[31]^2*c[3]^2+(1/2)*G[y]^2*G[zz]*(diff(y(x), x))^2*A[32]^2*c[2]^2+(1/6)*G[y]*G[yyy]*(diff(y(x), x))^3*a[32]*c[2]^3+(1/6)*G[y]*G[yyyz]*(diff(y(x), x))^4*A[32]*c[2]*c[3]^3+G[yz]^2*F^2*(diff(y(x), x))*a[32]*c[2]^2*c[3]+(1/2)*G[yy]*G[zz]*F^2*(diff(y(x), x))*A[32]*c[2]^3*c[3]+(1/2)*G[y]*G[yy]*F*(diff(y(x), x))*a[32]*c[2]^3+(1/2)*G[yz]*G[yyz]*F*(diff(y(x), x))^3*A[32]*c[2]^2*c[3]^2+(1/4)*G[zz]*G[yyz]*F^2*(diff(y(x), x))^2*A[32]*c[2]^2*c[3]^2+(1/8)*G[z]*G[yy]*F^2*A[32]*c[2]^4+(1/2)*G[z]*G[yyy]*F*(diff(y(x), x))^2*a[32]*c[2]*c[3]^2+(1/2)*G[zzz]*G^3*A[31]*A[32]^2+G^2*G[yy]*a[31]*a[32]+(1/2)*G[y]*G[yyz]*F*(diff(y(x), x))^2*A[32]*c[2]*c[3]^3+(1/12)*(diff(y(x), x))*F^4*G[yyzzz]*c[3]^6+(1/2)*G[zzz]*G^3*A[31]^2*A[32]+(1/4)*G[yy]*G[zzz]*F^2*(diff(y(x), x))^2*A[32]*c[2]^2*c[3]^2+F*G^2*G[yzz]*A[32]*a[32]*c[3]+(1/6)*G[yz]*G[zzz]*F^3*(diff(y(x), x))*A[32]*c[2]^3*c[3]+(1/48)*(diff(y(x), x))^4*F*G[yyyyy]*c[3]^6+(1/8)*(diff(y(x), x))*F^3*G[yyyz]*c[3]^6+(1/16)*(diff(y(x), x))^2*F^2*G[yyyy]*c[3]^6+G[y]*G[z]*G[zz]*F*(diff(y(x), x))*A[32]^2*c[2]^2+G[yzz]*F*G^2*A[31]*a[31]*c[3]+(1/2)*G[yzzz]*(diff(y(x), x))*F*G^2*A[31]^2*c[3]^2+2*G[z]*G[yz]*G*F*A[32]*a[32]*c[2]+(1/2)*G[y]*G[yzz]*F^2*(diff(y(x), x))*a[32]*c[2]*c[3]^2+(1/2)*G[zz]*G[yzz]*F^3*(diff(y(x), x))*A[32]*c[2]^3*c[3]+(1/2)*G*G[yy]*G[zz]*(diff(y(x), x))^2*A[32]^2*c[2]^2+(1/2)*G[z]*G[yy]*F^2*a[32]*c[2]*c[3]^2+(1/2)*G[z]*G[yz]*F*G*A[21]*A[32]*c[2]^2+G[y]*G[yz]*(diff(y(x), x))*G*A[32]*a[21]*c[3]+(1/2)*G[z]*G[zzz]*F^2*G*A[21]*A[32]*c[2]^2+(1/4)*G[yzzz]*F^3*G*A[31]*c[3]^4+(1/24)*G[zzzzz]*F^4*G*A[31]*c[3]^4+(1/6)*G[yzzz]*F^3*G*a[31]*c[3]^3+G[yz]^2*(diff(y(x), x))^2*G*A[21]*A[32]*c[2]*c[3]+(1/24)*(diff(y(x), x))^4*G*G[yyyyz]*A[32]*c[3]^4+(1/24)*G[z]*G[zzzz]*F^4*A[32]*c[2]^4+G[yz]*G[yzz]*F^2*(diff(y(x), x))^2*A[32]*c[2]^2*c[3]^2+(1/24)*F^4*G*G[zzzzz]*A[32]*c[3]^4+(1/2)*G[yy]^2*(diff(y(x), x))^3*a[32]*c[2]^2*c[3]+(1/2)*G[y]*G[yy]*F*(diff(y(x), x))*a[32]*c[2]*c[3]^2+(1/2)*G[yz]^2*F^2*(diff(y(x), x))*A[32]*c[2]^2*c[3]^2+(1/2)*G[y]*G[yyzz]*F*(diff(y(x), x))^3*A[32]*c[2]*c[3]^3+2*G[y]*G[yz]*G*(diff(y(x), x))*A[32]*a[32]*c[2]+(1/4)*G[yy]*G[yyz]*(diff(y(x), x))^4*A[32]*c[2]^2*c[3]^2+(1/2)*G[z]*G[zz]*G^2*A[21]^2*A[32]+(1/6)*G[yyyy]*(diff(y(x), x))^3*G*a[31]*c[3]^3+(1/4)*G[yyzz]*(diff(y(x), x))^2*G^2*A[31]^2*c[3]^2+(1/24)*G[yyyyz]*(diff(y(x), x))^4*G*A[31]*c[3]^4+(1/6)*G[z]*G[zzzz]*F^4*A[32]*c[2]*c[3]^3+(1/4)*G[y]*G[yyz]*F*(diff(y(x), x))^2*A[32]*c[2]^2*c[3]^2+G[y]*G[zz]*F*G*A[32]*a[21]*c[3]+(1/2)*G[yy]*G[zz]*(diff(y(x), x))^2*G*A[31]*A[32]*c[2]^2+(1/2)*G[z]*G[zzz]*F^2*G*A[21]*A[32]*c[3]^2+G[z]*G[yz]*F*G*A[21]*a[32]*c[3]+G[zz]^2*F^2*G*A[21]*A[32]*c[2]*c[3]+(1/2)*G[yy]*G[zz]*F^2*(diff(y(x), x))*a[32]*c[2]^2*c[3]+(1/2)*G[z]*G[yzz]*F^3*a[32]*c[2]*c[3]^2+(1/4)*G[y]*G[zzz]*F^3*A[32]*c[2]^2*c[3]^2+(1/4)*G[zz]*G[zzz]*F^4*A[32]*c[2]^2*c[3]^2+(1/2)*G[y]*G[yyy]*(diff(y(x), x))^3*a[32]*c[2]*c[3]^2+(1/2)*(diff(y(x), x))*F^2*G*G[yyzz]*A[32]*c[3]^4+G[yz]*G*G[zz]*F*(diff(y(x), x))*A[32]^2*c[2]^2+(1/6)*G[z]*G[yyyz]*F*(diff(y(x), x))^3*A[32]*c[2]*c[3]^3+(1/2)*G[yz]*G[yyz]*F*(diff(y(x), x))^3*A[32]*c[2]^3*c[3]+G[y]*G[zzz]*(diff(y(x), x))*F*G*A[31]*A[32]*c[2]*c[3]+2*G[zz]*G[yz]*(diff(y(x), x))*F*G*A[21]*A[32]*c[2]*c[3]+G[z]*G[yzz]*(diff(y(x), x))*F*G*A[31]*A[32]*c[2]*c[3]+G[z]*G[yz]*F*G*A[32]*a[21]*c[2]+G[y]*G[zz]*F*G*A[21]*a[32]*c[2]+(1/2)*G[z]*G[yz]*F*G*A[21]*A[32]*c[3]^2+(1/2)*G[y]*G[zz]*F*G*A[31]*A[32]*c[2]^2+G[z]*G[yz]*F*G*A[31]*a[32]*c[2]+(1/2)*G[z]*G[yyz]*(diff(y(x), x))^2*G*A[21]*A[32]*c[2]^2+G[z]*G[yy]*(diff(y(x), x))*G*A[32]*a[21]*c[2]+G[y]*G[yz]*(diff(y(x), x))*G*A[21]*a[32]*c[2]+G[yzzz]*(diff(y(x), x))*F*G^2*A[31]*A[32]*c[3]^2+G[z]*G[yz]*F*G*A[32]*a[31]*c[2]+(1/2)*G[z]*G[yyz]*F^2*(diff(y(x), x))*A[32]*c[2]^4+(1/2)*G[zz]*G[yzz]*F^3*(diff(y(x), x))*A[32]*c[2]^2*c[3]^2+(1/2)*G[z]*G[yyzz]*F^2*(diff(y(x), x))^2*A[32]*c[2]*c[3]^3+G[y]*G*G[yzz]*(diff(y(x), x))^2*A[32]^2*c[2]*c[3]+(1/2)*G[yz]*G[yzz]*F^2*(diff(y(x), x))^2*A[32]*c[2]^3*c[3]+(1/2)*G[yz]*G[yy]*F*(diff(y(x), x))^2*A[32]*c[2]^3*c[3]+(1/2)*G[z]*G[yzzz]*F^3*(diff(y(x), x))*A[32]*c[2]*c[3]^3+(1/48)*F^3*G[yyy]*c[3]^6+(1/48)*F^5*G[yzzzz]*c[3]^6+(1/2)*G^2*G[yy]*a[32]^2+(1/4)*G[z]*G[yzz]*F^3*A[32]*c[2]^4+(1/6)*G[zz]*G[zzz]*F^4*A[32]*c[2]^3*c[3]+G[z]*G*G[zzz]*F^2*A[32]^2*c[2]*c[3]+(1/2)*F^2*G*G[yyz]*a[32]*c[3]^3+(1/6)*G[y]*G[zzzz]*F^3*(diff(y(x), x))*A[32]*c[2]*c[3]^3+(1/6)*(diff(y(x), x))^3*F*G*G[yyyzz]*A[32]*c[3]^4+(1/6)*G[yz]*G[yyy]*(diff(y(x), x))^4*A[32]*c[2]^3*c[3]+(1/2)*G[y]*G[yz]*F^2*a[32]*c[2]^3+(1/2)*G*G[zz]^2*F^2*A[32]^2*c[2]^2+(1/2)*G[yz]*G[zz]*F^3*A[32]*c[2]^3*c[3]+G[z]*G[yyz]*F^2*(diff(y(x), x))*a[32]*c[2]*c[3]^2+G[y]*G[yyz]*F*(diff(y(x), x))^2*a[32]*c[2]*c[3]^2+(1/4)*F^3*G*G[yzzz]*A[32]*c[3]^4+G[z]*G*G[yzz]*F*(diff(y(x), x))*A[32]^2*c[2]*c[3]+(1/6)*G[yyyzz]*(diff(y(x), x))^3*F*G*A[31]*c[3]^4+(1/4)*G[yyzzz]*(diff(y(x), x))^2*F^2*G*A[31]*c[3]^4+(1/2)*G[yyzz]*(diff(y(x), x))*F^2*G*a[31]*c[3]^3+(1/2)*G[yyyz]*(diff(y(x), x))^2*F*G*a[31]*c[3]^3+(1/4)*G[yyyz]*(diff(y(x), x))^2*F*G*A[31]*c[3]^4+G[yyz]*(diff(y(x), x))*G^2*A[32]*a[31]*c[3]+G[yyz]*(diff(y(x), x))*G^2*A[31]*a[32]*c[3]+G[y]*G[yz]*(diff(y(x), x))*G*A[32]*a[31]*c[2]+(1/2)*G[z]*G[yyz]*(diff(y(x), x))^2*G*A[21]*A[32]*c[3]^2+G[y]*G[yz]*(diff(y(x), x))*G*A[31]*a[32]*c[2]+G[z]*G[yy]*(diff(y(x), x))*G*A[21]*a[32]*c[3]+(1/6)*F^3*G*G[yzzz]*a[32]*c[3]^3+(1/4)*F^2*G^2*G[zzzz]*A[32]^2*c[3]^2+(1/4)*F*G^2*G[yzz]*A[32]^2*c[3]^2+(1/8)*F^2*G*G[yyz]*A[32]*c[3]^4+(1/6)*G[y]*G[zzz]*F^3*a[32]*c[2]^3)*h^6+O(h^7))
> 

coeff(SUMY, h, 6)

Error, unable to compute coeff

NULL

NULL

Download location_truncation_error_of_y.mw

Understanding the ScientificConstants package....

Asked by: zenterix 405
2dmath subscript scientificconstants
July 26 2024
0  3

I am going through the documentation on ScientificConstants and trying things out in a worksheet.

My first question about this package is about the following

with(ScientificConstants)

GetConstants()

`A[r](alpha)`, `A[r](d)`, `A[r](e)`, `A[r](h)`, `A[r](n)`, `A[r](p)`, E[h], F, G, G[0], K[J], M[Earth], M[Sun], M[u], N[A], Phi[0], R, R[Earth], R[K], R[infinity], V[m], Z[0], a[0], a[e], a[mu], alpha, b, c, c[1, L], c[1], c[2], e, epsilon[0], g, g[e], g[mu], g[n], g[p], gamma[e], gamma[n], gamma[p], gamma_prime[h], gamma_prime[p], h, hbar, k, l[P], lambda[C, mu], lambda[C, n], lambda[C, p], lambda[C, tau], lambda[C], m[P], m[alpha], m[d], m[e], `m[e]/m[mu]`, m[h], m[mu], m[n], m[p], m[tau], `m[tau]c^2`, m[u], mu[0], mu[B], mu[N], mu[d], `mu[d]/mu[e]`, mu[e], `mu[e]/mu[p]`, `mu[e]/mu_prime[p]`, mu[mu], mu[n], `mu[n]/mu_prime[p]`, mu[p], mu_prime[h], `mu_prime[h]/mu_prime[p]`, mu_prime[p], n[0], r[e], sigma, sigma[e], sigma_prime[p], t[P]

 (1)

Copy and paste from the list above.

GetConstant(g[n])

neutron_g_factor, symbol = g[n], derive = 2*mu[n]/mu[N]

 (2)

Manually try to type in g__n.

GetConstant(g__n)

Error, (in ScientificConstants:-GetConstant) `g__n` is not a known Constant

  

NULL

Why doesn't the latter work?

Download ScientificConstants.mw

Understanding how Units[TestDimensions] works....

Asked by: zenterix 405
2dmath units
July 26 2024
0  2

I have multiple questions on how Units[TestDimensions] works from reading the Maple documentation. I will use this thread to ask them.

My first question regards the difference between Unit(expr) and units inserted using shortcut (CMD+SHIFT+U) on a mac?

restart

Automatically loading the Units[Simple] subpackage
 

  

What is the difference between the following two commands?

Units:-TestDimensions(x*Unit('m')+y*Unit('s'), output = dimensions)

{x::(length^(-1+_t3[7, 1])*mass^_t3[7, 2]*time^_t3[7, 3]*electric_current^_t3[7, 4]*thermodynamic_temperature^_t3[7, 5]*amount_of_substance^_t3[7, 6]*luminous_intensity^_t3[7, 7]*currency^_t3[7, 8]*amount_of_information^_t3[7, 9]*logarithmic_gain^_t3[7, 10]), y::(length^_t3[7, 1]*mass^_t3[7, 2]*time^(-1+_t3[7, 3])*electric_current^_t3[7, 4]*thermodynamic_temperature^_t3[7, 5]*amount_of_substance^_t3[7, 6]*luminous_intensity^_t3[7, 7]*currency^_t3[7, 8]*amount_of_information^_t3[7, 9]*logarithmic_gain^_t3[7, 10]), (x*Units:-Unit(m))::(length^_t3[7, 1]*mass^_t3[7, 2]*time^_t3[7, 3]*electric_current^_t3[7, 4]*thermodynamic_temperature^_t3[7, 5]*amount_of_substance^_t3[7, 6]*luminous_intensity^_t3[7, 7]*currency^_t3[7, 8]*amount_of_information^_t3[7, 9]*logarithmic_gain^_t3[7, 10]), (y*Units:-Unit(s))::(length^_t3[7, 1]*mass^_t3[7, 2]*time^_t3[7, 3]*electric_current^_t3[7, 4]*thermodynamic_temperature^_t3[7, 5]*amount_of_substance^_t3[7, 6]*luminous_intensity^_t3[7, 7]*currency^_t3[7, 8]*amount_of_information^_t3[7, 9]*logarithmic_gain^_t3[7, 10]), (x*Units:-Unit(m)+y*Units:-Unit(s))::(length^_t3[7, 1]*mass^_t3[7, 2]*time^_t3[7, 3]*electric_current^_t3[7, 4]*thermodynamic_temperature^_t3[7, 5]*amount_of_substance^_t3[7, 6]*luminous_intensity^_t3[7, 7]*currency^_t3[7, 8]*amount_of_information^_t3[7, 9]*logarithmic_gain^_t3[7, 10])}

 (1)

Units:-TestDimensions(2*Unit(m)+y*Unit(s), output = dimensions)

{y::(length/time), (y*Units:-Unit(s))::length, (2*Units:-Unit(m)+y*Units:-Unit(s))::length}

 (2)

NULL

I think my question is what is the difference between inserting units using CMD+SHIFT+U on a mac, which generates the units as seen in the first command, versus using Unit(expr) as in the second version of the command?

Download Units_-_TestDimensions.mw

Is there a way to see the code of Units:-TestDimen...

Asked by: zenterix 405
procedure module showstat
July 26 2024
1  1

I read in the programming guide that to print the body of Maple library commands we set the Maple interface variable `verboseproc` to 2 then use the print command passing in the procedure we're interested in as argument.

Built-in kernel commands are compiled in machine code and not written in Maple language so we cannot view their definitions.

According to the guide, if we try to print such procedures we will see that the procedure has only an `option builtin` statement and no visible body.

If I try to view `Units:-TestDimensions`, as follows

```interface(verboseproc=1);
print(Units:-TestDimensions);

```

then what I see is

In this case there isn't the `option builtin` but neither is there a visible body.

Is this procedure built-in or is there a way to see the code?

calculate adomian polynomial ...

Asked by: salim-barzani 1560
polynomial homework adomian-decomposition
July 25 2024
0  11

Hi
i write my code for calculate this type of function but the result is so different from mine i  will post here i hope someone tell me where is problem

i have this

i want this

Download EX1.mw

Can i get cayley graphs of infinite groups by decl...

Asked by: trahmada 10
graphtheory group
July 25 2024
2  1

Hello!
I am wondering if there is any way i can produce a cayley graph of a fixed radius for a finitely presented infinite group? That is if i take a FinPresInfGrp such as Z² is there any way i could create the cayley graph for the first 5 steps away from e?

I have tried increasing  _EnvMaxCosetsToddCoxeter however i imagine that this is a bit pointless!

Any help would be very much appriciated :)

arcsecond versus arcsecant...

Asked by: Nicole Sharp 160
units alias arcsec
July 25 2024
1  2

Is there a way to reassign the arcsecant function "arcsec()" as "asec()" so that "arcsec" can be assigned to the arcsecond unit "Unit(arcsec)"?

Ideally, I would like all of the inverse trigonometric functions to use the shorter notation "asec()" instead of "arcsec()".  I usually do this as aliases, i.e. "alias(asin = arcsin) : alias(asec = arcsec) :" but this won't allow reusing "arcsec" for a unit instead.

Example error for Maple 2023:

alias(asec = arcsec) :
AddUnit(astronomical_unit, context = astronomy, default = true, prefix = SI, conversion = 149597870700*m) : # https://en.wikipedia.org/wiki/astronomical_unit
AddUnit(second, context = angle, spelling = arcsecond, plural = arcseconds, symbol = arcsec, prefix = SI_negative) :

AddUnit(parsec, context = astronomy, default = true, prefix = SI, conversion = AU/tan(arcsec)) ; # https://en.wikipedia.org/wiki/Parsec#Calculating_the_value_of_a_parsec

"Pi/648000" has to be used instead of "arcsec" here when defining the parsec since "arcsec" is already reserved for the arcsecant function, even with "alias(asec = arcsec) ;".

Correction: it looks like the parsec was redefined by the IAU in 2012 as exactly "648000*AU/Pi" without any tangents (or sines) in the definition (so the angle subtended by 1 AU at 1 PC is actually 0.999999999992" not 1").  Both "astronomical_unit" and "parsec" have the wrong values in Maple 2023 which need to be corrected manually.  But the conflict between arcseconds and arcsecants remains the same.

https://iau.org/static/resolutions/IAU2015_English.pdf

https://iopscience.iop.org/article/10.3847/0004-6256/152/2/41

What exactly is the difference between considering...

Asked by: zenterix 405
units
July 25 2024
1  4

I am reading the documentation on the `Units[Simple]` package.

There is a section that says

"In the Simple Units environment, in contrast to the Standard and Natural environments, unassigned variables are not automatically assumed to represent unit-free quantities. For example, 5m+x is a valid expression if x is unassigned, because x may represent a length. On the other hand (5m+x)(6s+x) is an invalid expression because the first factor implies that x represents a length and the second factor implies that x is a duration."

The way I understood this paragraph is that in Units:-Simple an unassigned variable is not assumed to represent a unit-free quantity, but in Units:-Standard it is assumed to represent a unit-free quantity.

Consider the expression 5m+x. This expression works in Units:-Simple but not in Units:-Standard.

Units:-Simple adds a quantity 5m to a quantity without units. But why can one add a quantity with units to a quantity without units?

Units:-Standard tries to add a quantity 5m to a quantity that is assumed to have units. What units are assumed?

Next, consider (5m+x)(6s+x).

This fails in both packages, as can be seen below (actually, for some reason, the embed below is not showing the expressions typed in for Units:-Standard, but can be seen if you download the worksheet I imagine).

restart

with(Units:-Simple)

5*Unit('m')+x

5*Units:-Unit(m)+x

 (1)

(5*Unit('m')+x)*(6*Unit('s')+x)

Error, (in Units:-Simple:-*) the following expressions imply incompatible dimensions: {5*Units:-Unit(m)+x, 6*Units:-Unit(s)+x}

  

restart

with(Units:-Standard)

(5*Unit('m')+x)*(6*Unit('s')+x)

Error, (in Units:-Standard:-+) the units `m` and `1` have incompatible dimensions

  

5*Unit('m')+x

Error, (in Units:-Standard:-+) the units `m` and `1` have incompatible dimensions

  

NULL

So my question is, what exactly is the difference between considering unassigned variables to be unit-free vs not unit-free?

Download Units_Simple_vs_Standard.mw

Is there a dedicated command to get the value and ...

Asked by: C_R 3412
units
July 25 2024
2  5

I am looking for commands that extract from a product the value and the unit.
For example:
How to get 1.65 and m/s^2 from

g_moon := 1.635000000*Unit(('m')/'s'^2)

I was probably looking in the wrong place in Maples unit documentation.
I am not interested in lowlevel commands like op(g_moon)[1]. Something more self-explaining like GetUnit.

Quandl on Maple...

Asked by: Nicole Sharp 160
quandl
July 24 2024
0  3

I just saw that Maple 2024 no longer supports importing Quandl data.

If this is a feature that I will like to use, it is possible to keep both Maple 2023 and Maple 2024 installed at the same time on Microsoft Windows 11 without conflicts?  Or should I just not upgrade to Maple 2024?  I currently have a perpetual license for Maple 2023 and am on the 15-day trial for Maple 2024.

How Making loop for collecting solution?...

Asked by: salim-barzani 1560
homework pde differential-equations
July 24 2024
1  4

Hi
i did calculation part by part of adomian laplace method but if we can make a loop for it is gonna be so great and take back a lot of time

> 

restart
> 

with(inttrans)
> 

pde := diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = t^2*x+x

diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = t^2*x+x

 (1)
> 

eq := laplace(pde, t, s)

s*laplace(u(x, t), t, s)-u(x, 0)+laplace(u(x, t)*(diff(u(x, t), x)), t, s) = x*(s^2+2)/s^3

 (2)
> 

eq2 := subs({u(x, 0) = 0}, eq)

s*laplace(u(x, t), t, s)+laplace(u(x, t)*(diff(u(x, t), x)), t, s) = x*(s^2+2)/s^3

 (3)
> 

NULL
> 

lap := s^alpha*laplace(u(x, t), t, s) = x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s)

s^alpha*laplace(u(x, t), t, s) = x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s)

 (4)
> 

lap1 := lap/s^alpha

laplace(u(x, t), t, s) = (x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s))/s^alpha

 (5)
> 

NULL
> 

lap2 := invlaplace(lap1, s, t)

u(x, t) = -invlaplace(s^(-alpha)*laplace(u(x, t)*(diff(u(x, t), x)), t, s), s, t)+x*(invlaplace(s^(-1-alpha), s, t)+2*invlaplace(s^(-3-alpha), s, t))

 (6)
> 

NULL
> 

lap3 := u(x, t) = t^alpha*x/GAMMA(alpha+1)+2*x*t^(alpha+2)/GAMMA(alpha+3)-invlaplace(laplace(u(x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)

u(x, t) = t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha)-invlaplace(laplace(u(x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)

 (7)
> 

NULL
> 

NULL
> 

NULL
> 

NULL

``

 (8)
> 

u[1](x, t) = -invlaplace(laplace(u[0](x, t)*(diff(u[0](x, t), x)), t, s)/s^alpha, s, t)

u[1](x, t) = -invlaplace(laplace(u[0](x, t)*(diff(u[0](x, t), x)), t, s)/s^alpha, s, t)

 (9)
> 

"u[0](x,t):=(t^alpha x)/(GAMMA(1+alpha))+(2 x t^(alpha+2))/(GAMMA(3+alpha))"

proc (x, t) options operator, arrow, function_assign; t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha) end proc

 (10)
> 

n := N

N

 (11)
> 

k := K

K

 (12)
> 

f := proc (u) options operator, arrow; u*(diff(u, x)) end proc

proc (u) options operator, arrow; u*(diff(u, x)) end proc

 (13)
> 

for j from 0 to 3 do A[j] := subs(lambda = 0, (diff(f(seq(sum(lambda^i*u[i](x, t), i = 0 .. 20), m = 1 .. 2)), [`$`(lambda, j)]))/factorial(j)) end do

(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))

  

u[1](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[1](x, t), x))

  

u[2](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+u[1](x, t)*(diff(u[1](x, t), x))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[2](x, t), x))

  

u[3](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+u[2](x, t)*(diff(u[1](x, t), x))+u[1](x, t)*(diff(u[2](x, t), x))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[3](x, t), x))

 (14)
> 

S1 := u[1](x, t) = -invlaplace((t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))/s^alpha, s, t)

u[1](x, t) = -x*(t^alpha)^2*invlaplace(s^(-alpha), s, t)*(1/GAMMA(1+alpha)^2+4*t^2/(GAMMA(3+alpha)*GAMMA(1+alpha))+4*t^4/GAMMA(3+alpha)^2)

 (15)
> 

NULL
> 

NULL
> 

u[1](x, t) = x*GAMMA(2*alpha+1)*t^(3*alpha)/(GAMMA(1+alpha)^2*GAMMA(3*alpha+1))-4*x*GAMMA(2*alpha+3)*t^(3*alpha+2)/(GAMMA(1+alpha)*GAMMA(3+alpha)*GAMMA(3*alpha+3))-4*`xΓ`(2*alpha+5)/(GAMMA(3+alpha)^2*GAMMA(3*alpha+3))

u[1](x, t) = x*GAMMA(2*alpha+1)*t^(3*alpha)/(GAMMA(1+alpha)^2*GAMMA(3*alpha+1))-4*x*GAMMA(2*alpha+3)*t^(3*alpha+2)/(GAMMA(1+alpha)*GAMMA(3+alpha)*GAMMA(3*alpha+3))-4*`xΓ`(2*alpha+5)/(GAMMA(3+alpha)^2*GAMMA(3*alpha+3))

 (16)
> 

NULL
> 

u[2](x, t) = -invlaplace(laplace(u[1](x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)
> 

NULL
> 

NULL


for get definition use this pdf for fractional derivation

[Copyrighted material removed by moderator - see https://doi.org/10.4236/am.2018.94032]

Download solving_example_1.mw

MapleCloud for Maple 2024...

Asked by: Nicole Sharp 160
maplecloud
July 24 2024
0  2

I just installed the 15-day trial for the new Maple 2024.  It looks like Maple 2024 has the same problem as Maple 2023 in that it will not maintain a connection to MapleCloud.  I can sign in to MapleCloud no problem but as soon as I close the window, it forgets my password and I have to log back in each time I want to access MapleCloud.  Is there a way for Maple 2023 or Maple 2024 to remember my Maplesoft password so I do not have to log back in every time I want to access MapleCloud?

minimize a polynomial function...

Asked by: Sotto 60
minimize
July 24 2024
0  6

Dear all,

I am trying to minimize this polynomial function G on [0,1]x[0,1]:

Maple 2022 seems unable to find the (approximate) minimum. Even adding _EnvExplicit:=true, as suggested here on a previous post, does not fix the issue.

Any suggestion?

Thanks, Nicola

> 

restart:
> 

_EnvExplicit:=true:
> 

G := (x, y) -> ((-1)*38.87*y^4 + 39.7800000000000*y^3 + (-1)*6.76000000000000*y^2 + 10.4000000000000*y - 3.90000000000000)*x^4 + (39.78*y^4 + (-1)*40.4600000000000*y^3 + 6.80000000000000*y^2 + (-1)*10.2000000000000*y + 3.40000000000000)*x^3 + ((-1)*6.76*y^4 + 6.80000000000000*y^3 + (-1)*1.12000000000000*y^2 + 1.60000000000000*y - 0.400000000000000)*x^2 + (10.4*y^4 + (-1)*10.2000000000000*y^3 + 1.60000000000000*y^2 + (-1)*2.00000000000000*y)*x + 1. + (-1)*3.9*y^4 + (-1)*0.4*y^2 + 3.4*y^3

proc (x, y) options operator, arrow; (-38.87*y^4+39.7800000000000*y^3-6.76000000000000*y^2+10.4000000000000*y-3.90000000000000)*x^4+(39.78*y^4-40.4600000000000*y^3+6.80000000000000*y^2-10.2000000000000*y+3.40000000000000)*x^3+(-6.76*y^4+6.80000000000000*y^3-1.12000000000000*y^2+1.60000000000000*y-.400000000000000)*x^2+(10.4*y^4-10.2000000000000*y^3+1.60000000000000*y^2-2.00000000000000*y)*x+1.-3.9*y^4-.4*y^2+3.4*y^3 end proc

 (1)
> 

minimize(G(x,y),x=0..1,y=0..1)
 

NULL

Download Untitled.mw

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