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These are questions asked by Aixleft math

Solve an equation with unknown expressio...

Aixleft math 120 Maple 2024
solve
August 27 2024
1 1

Hi all guys, it is simple equation, I wanna get the expression of w=()^(1/4) which consists zg & fg. I use solve command but fails, could you please help me?

NULL

> 

p := (1/24)*z*g[u]+(1/24)*f*g[z]-(1/144000)*w^4*(f*g[z]+z*g[u])

(1/24)*z*g[u]+(1/24)*f*g[z]-(1/144000)*w^4*(f*g[z]+z*g[u])

 (1)
> 

solve(p = 0, w)

2*375^(1/4), (2*I)*375^(1/4), -2*375^(1/4), -(2*I)*375^(1/4)

 (2)

NULL

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How to extract the coefficient of a comp...

Aixleft math 120 Maple
polynomial series coeff
July 26 2024
1 1

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

issues about smart plot and implicit 2d ...

Aixleft math 120 Maple
implicitplot smartplot
July 10 2024
1 2

Hi all guys, first I would express my gratitude to @mmcdara . He helped me construct the matrix polynomial properly. Then on basis of it, I explore more but meet with issues. Notation : v1 and v2 is eigenvalues which consists of complicated expression containg component v and z, now I wanna implicitplot the region: abs(v1)<=1 & abs(v2)<=1 (satisfy at the same time). But I don't know how to command the code. So I define eq1:=( abs(v1)-1)* (abs(v2)<=1) and implicit it. (I know it is false but I just wanna try first). But I command the implicitplot code, the evaluating time is so long(25mins no end still). So I recall the smartplot, I once I have triggered this command, it seems that I put the mouse on the expression result (the end of the blue font), and implicit3d appears in the work bar on the right (of course this is in another file). In the file I uploaded, I tried this but failed. So I want to understand how to ensure that smartplot is triggered 100%? (Because I feel that smartplot runs very fast) and how to draw the desired region (abs(v1)<=1 & abs(v2)<=1)?

> 

restart;
v=lambda*h;
z=mu*h;
k=lambda/mu;

v = lambda*h

  

z = mu*h

  

k = lambda/mu

 (1)
> 

with(LinearAlgebra):
> 

A := Matrix([[0, 0, 0], [-(cos(alpha*v)-1)/v^2, 0, 0], [0, -(cos(beta*v)-1)/(cos(alpha*v)*v^2), 0]]);

Matrix(3, 3, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (2, 1) = -(cos(alpha*v)-1)/v^2, (2, 2) = 0, (2, 3) = 0, (3, 1) = 0, (3, 2) = -(cos(beta*v)-1)/(cos(alpha*v)*v^2), (3, 3) = 0})

 (2)
> 

C := Matrix([0, alpha, -beta])

Vector[row](3, {(1) = 0, (2) = alpha, (3) = -beta})

 (3)
> 

e := Vector(3, 1)

Vector(3, {(1) = 1, (2) = 1, (3) = 1})

 (4)
> 

E := IdentityMatrix(3)

Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

 (5)
> 

G := Matrix([[0], [sin(alpha*v)/(alpha*v)], [((sin(beta*v)*cos(alpha*v)+sin(alpha*v)*cos(beta*v)-sin(alpha*v)))/(v*cos(alpha*v)*(beta))]])

Vector(3, {(1) = 0, (2) = sin(alpha*v)/(alpha*v), (3) = (sin(beta*v)*cos(alpha*v)+sin(alpha*v)*cos(beta*v)-sin(alpha*v))/(v*cos(alpha*v)*beta)})

 (6)
> 

b := Vector(3, [1/24, (-sin(beta*v)*v^3+12*cos(beta*v)*v^2+24*cos(beta*v)*cos(v)-24*sin(beta*v)*sin(v)+24*sin(beta*v)*v-24*cos(beta*v))/(24*v^3*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v))), -(sin(alpha*v)*v^3+12*cos(alpha*v)*v^2+24*cos(v)*cos(alpha*v)+24*sin(v)*sin(alpha*v)-24*v*sin(alpha*v)-24*cos(alpha*v))/(24*v^3*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v)))])

Vector(3, {(1) = 1/24, (2) = (1/24)*(-sin(beta*v)*v^3+12*cos(beta*v)*v^2+24*cos(beta*v)*cos(v)-24*sin(beta*v)*sin(v)+24*sin(beta*v)*v-24*cos(beta*v))/(v^3*(sin(beta*v)*cos(alpha*v)+sin(alpha*v)*cos(beta*v))), (3) = -(1/24)*(sin(alpha*v)*v^3+12*cos(alpha*v)*v^2+24*cos(v)*cos(alpha*v)+24*sin(v)*sin(alpha*v)-24*v*sin(alpha*v)-24*cos(alpha*v))/(v^3*(sin(beta*v)*cos(alpha*v)+sin(alpha*v)*cos(beta*v)))})

 (7)
> 

bp := Vector(3, [1/12, -(sin(beta*v)*v^2+12*cos(beta*v)*sin(v)-12*cos(beta*v)*v+12*cos(v)*sin(beta*v)-12*sin(beta*v))/(12*v^2*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v))), -(sin(alpha*v)*v^2+12*cos(v)*sin(alpha*v)-12*cos(alpha*v)*sin(v)+12*cos(alpha*v)*v-12*sin(alpha*v))/(12*v^2*(cos(beta*v)*sin(alpha*v)+sin(beta*v)*cos(alpha*v)))])

Vector(3, {(1) = 1/12, (2) = -(1/12)*(sin(beta*v)*v^2+12*cos(beta*v)*sin(v)-12*cos(beta*v)*v+12*cos(v)*sin(beta*v)-12*sin(beta*v))/(v^2*(sin(alpha*v)*cos(beta*v)+sin(beta*v)*cos(alpha*v))), (3) = -(1/12)*(sin(alpha*v)*v^2+12*cos(v)*sin(alpha*v)-12*cos(alpha*v)*sin(v)+12*cos(alpha*v)*v-12*sin(alpha*v))/(v^2*(sin(alpha*v)*cos(beta*v)+sin(beta*v)*cos(alpha*v)))})

 (8)
> 

L0 := E + z^2 *~ A

Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = -z^2*(cos(alpha*v)-1)/v^2, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = -z^2*(cos(beta*v)-1)/(cos(alpha*v)*v^2), (3, 3) = 1})

 (9)
> 

L1 := simplify(L0^(-1))

Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = z^2*(cos(alpha*v)-1)/v^2, (2, 2) = 1, (2, 3) = 0, (3, 1) = z^4*(cos(beta*v)-1)*(1-sec(alpha*v))/v^4, (3, 2) = z^2*(cos(beta*v)-1)*sec(alpha*v)/v^2, (3, 3) = 1})

 (10)
> 

AUX := simplify(L1 . G . C . e, size)

Vector(3, {(1) = 0, (2) = sin(alpha*v)*(alpha-beta)/(alpha*v), (3) = -((z^2*beta*sec(alpha*v)*(cos(beta*v)-1)*sin(alpha*v)+v^2*alpha*sin(beta*v))*cos(alpha*v)+sin(alpha*v)*alpha*v^2*(cos(beta*v)-1))*(-alpha+beta)/(v^3*alpha*cos(alpha*v)*beta)})

 (11)
> 

N1 := simplify((1 - z^2/2) + z^4 * (b^+ . AUX), size)

(1/24)*(z^4*(cos(beta*v)-1)*(v^3-24*v+24*sin(v))*(-alpha+beta)*(sec(alpha*v)*z^2*beta*cos(alpha*v)+v^2*alpha)*sin(alpha*v)^2-12*(-sec(alpha*v)*z^6*beta*(cos(beta*v)-1)*(v^2+2*cos(v)-2)*(-alpha+beta)*cos(alpha*v)+((2*z^4*(-alpha+beta)^2*cos(v)+(-alpha+beta)^2*(v^2-2)*z^4+v^4*z^2*beta*alpha-2*v^4*beta*alpha)*cos(beta*v)-(1/12)*(-alpha+beta)*z^4*((v^3-24*v+24*sin(v))*(beta+alpha)*sin(beta*v)-12*alpha*(v^2+2*cos(v)-2)))*v^2)*cos(alpha*v)*sin(alpha*v)-12*sin(beta*v)*(-2*(-alpha+beta)*z^4*cos(v)-(v^2-2)*(-alpha+beta)*z^4+v^4*z^2*beta-2*v^4*beta)*v^2*alpha*cos(alpha*v)^2)/(v^6*(sin(alpha*v)*cos(beta*v)+sin(beta*v)*cos(alpha*v))*alpha*cos(alpha*v)*beta)

 (12)
> 

N2 := simplify(1 - z^2 * (b^+ . L1 . e), size)

(1/24)*((12*z^4*(v-z)*(v+z)*(v^2+2*cos(v)-2)*(sec(alpha*v)-1)*cos(beta*v)-12*z^4*(v-z)*(v+z)*(v^2+2*cos(v)-2)*sec(alpha*v)-(-24*z^4*sin(v)+(-v^3+24*v)*z^4+v^5*z^2-24*v^5)*v^2*sin(beta*v)+12*z^2*(v-z)*(v+z)*(v^2+z^2)*(v^2+2*cos(v)-2))*cos(alpha*v)+(sin(alpha*v)*z^4*(v-z)*(v+z)*(v^3-24*v+24*sin(v))*sec(alpha*v)+(24*z^6*sin(v)+(v^3-24*v)*z^6-v^7*z^2+24*v^7)*sin(alpha*v)-12*v^2*z^2*(v-z)*(v+z)*(v^2+2*cos(v)-2))*cos(beta*v)+(v^3-24*v+24*sin(v))*(-sin(alpha*v)*z^2*sec(alpha*v)+(v^2+z^2)*sin(alpha*v)+sin(beta*v)*v^2)*z^2*(v+z)*(v-z))/(v^7*(sin(alpha*v)*cos(beta*v)+sin(beta*v)*cos(alpha*v)))

 (13)
> 

N3 := simplify(-z^2 + z^4 * (bp^+ . AUX), size)

-(-(1/12)*z^2*(cos(beta*v)-1)*(v^2+12*cos(v)-12)*(-alpha+beta)*(sec(alpha*v)*z^2*beta*cos(alpha*v)+v^2*alpha)*sin(alpha*v)^2+(-sec(alpha*v)*z^4*beta*(cos(beta*v)-1)*(-alpha+beta)*(v-sin(v))*cos(alpha*v)+((-z^2*(-alpha+beta)^2*sin(v)+(z^2*(-alpha+beta)^2+v^2*beta*alpha)*v)*cos(beta*v)-(1/12)*(-alpha+beta)*z^2*((v^2+12*cos(v)-12)*(beta+alpha)*sin(beta*v)-12*alpha*(v-sin(v))))*v^2)*cos(alpha*v)*sin(alpha*v)+sin(beta*v)*((-alpha+beta)*z^2*sin(v)+v*((alpha-beta)*z^2+v^2*beta))*v^2*alpha*cos(alpha*v)^2)*z^2/(v^5*(sin(alpha*v)*cos(beta*v)+sin(beta*v)*cos(alpha*v))*alpha*cos(alpha*v)*beta)

 (14)
> 

NULL
> 

N4 := simplify(1 - z^2 * (bp^+ . L1 . e), size):
alpha:= 1/2 + 1/10*sqrt(5);
beta:= -1/2 + 1/10*sqrt(5);
det := simplify(N1*N4 - N2*N3, size):
tr := simplify(N1 + N4, size):
#eq1:=algsubs(v=lambda*h,det):
#eq2:=algsubs(z=mu*h,eq1):
#eq3:=algsubs(lambda=mu*k,eq2):
#eq4:=algsubs(v=lambda*h,eq3):
#csgn(sqrt(mu^10*k^10/v^10)*h^5):=1:
#simplify(series(sqrt(eq4),h,10));
#series(simplify(algsubs(v=,simplify(series(1-sqrt(det),z,8)))),z,8);
#eq1:=(sec(sqrt(5)*z/10)*(-cos(z/2)*z + 12*sin(z/2)) - 5*z)/(24*z*k);
#simplify(eq1);

1/2+(1/10)*5^(1/2)

  

-1/2+(1/10)*5^(1/2)

 (15)
> 

> 

lambda1 := (tr-sqrt(tr^2-4*det))*(1/2); lambda2 := (tr+sqrt(tr^2-4*det))*(1/2)
> 

with(plots); with(plots, implicitplot)
> 

eq11 := lambda1*lambda2-abs(lambda1)-abs(lambda2)+1 <= 0

Download 2d_implicit_plot_[v_z].mw

get the error order of the estimated pol...

Aixleft math 120 Maple
determinant taylor
July 07 2024
2 8

Hi all guys, when i am doing error analysis but I meet with an problem. I get the trace and determinant of one matrix which consists a lot trigonometric functions. I wanna get the approximation error order of trace and determinant (Like tr=2+O(v^6),det=1+O(v^6)). But I use Taylor expansion and series, it displays can't compute the series. How to know the other ways to get the error order of it? Thanks all !phase_error_try.mw

> 

restart
> 

c[2] := 1/2+(1/10)*sqrt(5); c[3] := 1/2-(1/10)*sqrt(5)

1/2+(1/10)*5^(1/2)

  

1/2-(1/10)*5^(1/2)

 (1)
> 

with(LinearAlgebra)
> 

``
> 

A := Matrix([[0, 0, 0], [-(cos((1/10)*(5+sqrt(5))*v)-1)/v^2, 0, 0], [0, -(cos((1/10)*(-5+sqrt(5))*v)-1)/(cos((1/10)*(5+sqrt(5))*v)*v^2), 0]])
> 

C := Matrix([0, 1/2+(1/10)*sqrt(5), 1/2-(1/10)*sqrt(5)])

Matrix(%id = 36893490461606184468)

 (2)
> 

e := Matrix([[1], [1], [1]])

Matrix(%id = 36893490461606180252)

 (3)
> 

E := Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])

Matrix(%id = 36893490461606177116)

 (4)
> 

G := Matrix([[0], [10*sin((1/10)*(5+sqrt(5))*v)/((5+sqrt(5))*v)], [(10*(sin((1/10)*(-5+sqrt(5))*v)*cos((1/10)*(5+sqrt(5))*v)+sin((1/10)*(5+sqrt(5))*v)*cos((1/10)*(-5+sqrt(5))*v)-sin((1/10)*(5+sqrt(5))*v)))/(v*cos((1/10)*(5+sqrt(5))*v)*(-5+sqrt(5)))]])
> 

b := Matrix([1/24, (-sin((1/10)*v*(-5+sqrt(5)))*v^3+12*cos((1/10)*v*(-5+sqrt(5)))*v^2+24*cos((1/10)*v*(-5+sqrt(5)))*cos(v)-24*sin((1/10)*v*(-5+sqrt(5)))*sin(v)+24*sin((1/10)*v*(-5+sqrt(5)))*v-24*cos((1/10)*v*(-5+sqrt(5))))/(24*v^3*(cos((1/10)*v*(-5+sqrt(5)))*sin((1/10)*v*(5+sqrt(5)))+sin((1/10)*v*(-5+sqrt(5)))*cos((1/10)*v*(5+sqrt(5))))), -(sin((1/10)*v*(5+sqrt(5)))*v^3+12*cos((1/10)*v*(5+sqrt(5)))*v^2+24*cos(v)*cos((1/10)*v*(5+sqrt(5)))+24*sin(v)*sin((1/10)*v*(5+sqrt(5)))-24*v*sin((1/10)*v*(5+sqrt(5)))-24*cos((1/10)*v*(5+sqrt(5))))/(24*v^3*(cos((1/10)*v*(-5+sqrt(5)))*sin((1/10)*v*(5+sqrt(5)))+sin((1/10)*v*(-5+sqrt(5)))*cos((1/10)*v*(5+sqrt(5)))))])
> 

bp := Matrix([1/12, -(sin((1/10)*v*(-5+sqrt(5)))*v^2+12*cos((1/10)*v*(-5+sqrt(5)))*sin(v)-12*cos((1/10)*v*(-5+sqrt(5)))*v+12*cos(v)*sin((1/10)*v*(-5+sqrt(5)))-12*sin((1/10)*v*(-5+sqrt(5))))/(12*v^2*(cos((1/10)*v*(-5+sqrt(5)))*sin((1/10)*v*(5+sqrt(5)))+sin((1/10)*v*(-5+sqrt(5)))*cos((1/10)*v*(5+sqrt(5))))), -(sin((1/10)*v*(5+sqrt(5)))*v^2+12*cos(v)*sin((1/10)*v*(5+sqrt(5)))-12*cos((1/10)*v*(5+sqrt(5)))*sin(v)+12*cos((1/10)*v*(5+sqrt(5)))*v-12*sin((1/10)*v*(5+sqrt(5))))/(12*v^2*(cos((1/10)*v*(-5+sqrt(5)))*sin((1/10)*v*(5+sqrt(5)))+sin((1/10)*v*(-5+sqrt(5)))*cos((1/10)*v*(5+sqrt(5)))))])
> 

L1 := 1/simplify(E+v^2.A); N1 := simplify(1-(1/2)*v^2+v^4*(b.L1.G.C.e)); N11 := (Typesetting[delayDotProduct](sin((1/10)*v*(5+sqrt(5)))*((v^3-24*v+24*sin(v))*sin((1/10)*v*(5+sqrt(5)))+12*cos((1/10)*v*(5+sqrt(5)))*(v^2+2*cos(v)-2))*(-5+sqrt(5)), v^2.((cos((1/10)*v*(-5+sqrt(5)))-1)*sec((1/10)*v*(5+sqrt(5)))/v^2), true)+((cos((1/10)*v*(-5+sqrt(5)))-1)*(v^3-24*v+24*sin(v))*(5+sqrt(5))*tan((1/10)*v*(5+sqrt(5)))+(96*v^2+240*cos(v)-192)*cos((1/10)*v*(-5+sqrt(5)))+2*sqrt(5)*(v^3-24*v+24*sin(v))*sin((1/10)*v*(-5+sqrt(5)))-(12*(v^2+2*cos(v)-2))*(5+sqrt(5)))*sin((1/10)*v*(5+sqrt(5)))+12*cos((1/10)*v*(5+sqrt(5)))*sin((1/10)*v*(-5+sqrt(5)))*(-6+(v^2+2*cos(v)-2)*sqrt(5)+3*v^2+10*cos(v)))/(48*sin((1/10)*v*(-5+sqrt(5)))*cos((1/10)*v*(5+sqrt(5)))+48*sin((1/10)*v*(5+sqrt(5)))*cos((1/10)*v*(-5+sqrt(5))))

Matrix(%id = 36893490461639877084)

 (5)
> 

N2 := simplify(1-v^2*b.L1.e); N22 := (Typesetting[delayDotProduct](((12*v^2+24*cos(v)-24)*cos((1/10)*(5+sqrt(5))*v)+(v^3-24*v+24*sin(v))*sin((1/10)*(5+sqrt(5))*v))*(v^2.((cos((1/10)*(5+sqrt(5))*v)-1)/v^2)+1), v^2.((cos((1/10)*(-5+sqrt(5))*v)-1)*sec((1/10)*(5+sqrt(5))*v)/v^2), true)+Typesetting[delayDotProduct]((-12*v^2-24*cos(v)+24)*cos((1/10)*(-5+sqrt(5))*v)+sin((1/10)*(-5+sqrt(5))*v)*(v^3-24*v+24*sin(v)), v^2.((cos((1/10)*(5+sqrt(5))*v)-1)/v^2), true)+((-v^3+24*v)*sin((1/10)*(-5+sqrt(5))*v)+12*v^2+24*cos(v)-24)*cos((1/10)*(5+sqrt(5))*v)+((-v^3+24*v)*cos((1/10)*(-5+sqrt(5))*v)+v^3-24*v+24*sin(v))*sin((1/10)*(5+sqrt(5))*v)+(-12*v^2-24*cos(v)+24)*cos((1/10)*(-5+sqrt(5))*v)+sin((1/10)*(-5+sqrt(5))*v)*(v^3-24*v+24*sin(v)))/(24*v*(sin((1/10)*(-5+sqrt(5))*v)*cos((1/10)*(5+sqrt(5))*v)+sin((1/10)*(5+sqrt(5))*v)*cos((1/10)*(-5+sqrt(5))*v)))

Matrix(%id = 36893490461606200972)

 (6)
> 

N3 := simplify(-v^2+v^4*bp.L1.G.C.e); N33 := v*(Typesetting[delayDotProduct](((v^2+12*cos(v)-12)*sin((1/10)*(5+sqrt(5))*v)+12*cos((1/10)*(5+sqrt(5))*v)*(v-sin(v)))*sin((1/10)*(5+sqrt(5))*v)*(-5+sqrt(5)), v^2.((cos((1/10)*(-5+sqrt(5))*v)-1)*sec((1/10)*(5+sqrt(5))*v)/v^2), true)+((cos((1/10)*(-5+sqrt(5))*v)-1)*(v^2+12*cos(v)-12)*(5+sqrt(5))*tan((1/10)*(5+sqrt(5))*v)+(96*v-120*sin(v))*cos((1/10)*(-5+sqrt(5))*v)+2*sqrt(5)*(v^2+12*cos(v)-12)*sin((1/10)*(-5+sqrt(5))*v)-(12*(5+sqrt(5)))*(v-sin(v)))*sin((1/10)*(5+sqrt(5))*v)+12*cos((1/10)*(5+sqrt(5))*v)*sin((1/10)*(-5+sqrt(5))*v)*((v-sin(v))*sqrt(5)+3*v-5*sin(v)))/(24*cos((1/10)*(5+sqrt(5))*v)*sin((1/10)*(-5+sqrt(5))*v)+24*sin((1/10)*(5+sqrt(5))*v)*cos((1/10)*(-5+sqrt(5))*v))

Matrix(%id = 36893490461733603676)

 (7)
> 

N4 := simplify(1-v^2*bp.L1.e); N44 := (Typesetting[delayDotProduct](((v^2+12*cos(v)-12)*sin((1/10)*(5+sqrt(5))*v)+12*cos((1/10)*(5+sqrt(5))*v)*(v-sin(v)))*(v^2.((cos((1/10)*(5+sqrt(5))*v)-1)/v^2)+1), v^2.((cos((1/10)*(-5+sqrt(5))*v)-1)*sec((1/10)*(5+sqrt(5))*v)/v^2), true)+Typesetting[delayDotProduct]((v^2+12*cos(v)-12)*sin((1/10)*(-5+sqrt(5))*v)-12*cos((1/10)*(-5+sqrt(5))*v)*(v-sin(v)), v^2.((cos((1/10)*(5+sqrt(5))*v)-1)/v^2), true)+(-cos((1/10)*(-5+sqrt(5))*v)*v^2+v^2+12*cos(v)+12*cos((1/10)*(-5+sqrt(5))*v)-12)*sin((1/10)*(5+sqrt(5))*v)+(-sin((1/10)*(-5+sqrt(5))*v)*v^2+12*v-12*sin(v)+12*sin((1/10)*(-5+sqrt(5))*v))*cos((1/10)*(5+sqrt(5))*v)+(v^2+12*cos(v)-12)*sin((1/10)*(-5+sqrt(5))*v)-12*cos((1/10)*(-5+sqrt(5))*v)*(v-sin(v)))/(12*sin((1/10)*(-5+sqrt(5))*v)*cos((1/10)*(5+sqrt(5))*v)+12*sin((1/10)*(5+sqrt(5))*v)*cos((1/10)*(-5+sqrt(5))*v))

Matrix(%id = 36893490461606185188)

 (8)
> 

tr := N11+N44
> 

det := N11*N44-N22*N33
> 

expand(det, v, 10)

Warning,  computation interrupted

  

` `

 (9)

NULL

NULL


 

Download phase_error_try.mw

pansion)

How to simplify a compound expressions?...

Aixleft math 120 Maple 2024
syntax simplify
July 04 2024
2 3

Hi all guys, I don't know how to simplify this easy expression? I have tried simplify command, and expand command, no use. Welcome to answer and thank you!

 

y1(x) = 2*sin(x)-sin(2*x)+cos(2*x); y2(x) = 4*sin(x)+sin(2*x)-cos(2*x); diff(y1(x), x); diff(y1(x), x); simplify*(1/2*((diff(y1(x), x))^2+(diff(y2(x), x))^2)+1/2*(3*y1(x)^2-y1(x)*y2(x)+y2(x)^2))

simplify*((1/2)*(diff(y1(x), x))^2+(1/2)*(diff(y2(x), x))^2+(3/2)*y1(x)^2-(1/2)*y1(x)*y2(x)+(1/2)*y2(x)^2)

 (1)

 

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