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pik1432

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Re: Substituting an expression...

pik1432 240 Maple 2023
substitution
June 02 2023
3 5

Hello there, 

Is there any chance to ask for your expertise in this issue of substitution?

I tried to make the expression 'eq_m1' to 'eq_m1_desired' by substituting 'L__ads*L__fd/(L__fd + L__ads)' as 'L__ads_p', but did not succeeded, after a series of different attempts. Would you show me how to achive the desired expression?

> 

restart;
> 

with(LinearAlgebra):
> 

with(DynamicSystems):
> 

interface(imaginaryunit=j):
> 

eq_m1 := m1 = (X__Tq*E__B*sin(delta) - R__T*E__B*cos(delta))/(R__E^2 + 2*R__a*R__E + R__a^2 + X__E^2 + X__E*L__ads*L__fd/(L__fd + L__ads) + 2*X__E*L__l + L__aqs*X__E + L__aqs*L__ads*L__fd/(L__fd + L__ads) + L__aqs*L__l + L__l*L__ads*L__fd/(L__fd + L__ads) + L__l^2);

m1 = (X__Tq*E__B*sin(delta)-R__T*E__B*cos(delta))/(R__E^2+2*R__a*R__E+R__a^2+X__E^2+X__E*L__ads*L__fd/(L__fd+L__ads)+2*X__E*L__l+L__aqs*X__E+L__aqs*L__ads*L__fd/(L__fd+L__ads)+L__aqs*L__l+L__l*L__ads*L__fd/(L__fd+L__ads)+L__l^2)

 (1)
> 

eq_m1_desired := m1 = (X__Tq*E__B*sin(delta) - R__T*E__B*cos(delta))/(R__E^2 + 2*R__a*R__E + R__a^2 + X__E^2 + X__E*L__ads_p + 2*X__E*L__l + L__aqs*X__E + L__aqs*L__ads_p + L__aqs*L__l + L__l*L__ads_p + L__l^2);

m1 = (X__Tq*E__B*sin(delta)-R__T*E__B*cos(delta))/(L__aqs*L__l+L__aqs*X__E+L__aqs*L__ads_p+L__l^2+2*L__l*X__E+L__l*L__ads_p+R__E^2+2*R__E*R__a+R__a^2+X__E^2+X__E*L__ads_p)

 (2)
> 

######
> 

#eq_m1a := subs({L__ads*L__fd/(L__fd + L__ads) = L__ads_p}, eq_m1);
> 

#eq_m1a := subs({L__ads_p = L__ads*L__fd/(L__fd + L__ads)}, eq_m1);
> 

#eq_m1a := applyrule(L__ads*L__fd/(L__fd + L__ads) = L__ads_p, eq_m1);
> 

#eq_m1a := algsubs(L__ads_p = (L__ads*L__fd)/(L__fd + L__ads), eq_m1);
> 

#eq_m1a := algsubs((L__ads*L__fd)/(L__fd + L__ads) = L__ads_p, eq_m1);
> 

#eq_m1a := eval(eq_m1, L__ads_p = (L__ads*L__fd)/(L__fd + L__ads));
> 

 

Download Q20230602.mw

RE: LieDerivative...

pik1432 240 Maple 2022
liederivative differentialgeometry
March 07 2023
0 0

Hello there, 

Is there any chance to ask this one question?

The attached (following) worksheet shows the result of LieDerivative operation, which is not correct. 

The correct answer is given in the image in the middle of the worksheet. Is there any particular reason regarding Maple's way of conducting the operation in that way?

> 

restart;
> 

with(LinearAlgebra):
> 

with(DifferentialGeometry):
> 

with(LieAlgebras):
> 

DGsetup([x1, x2], M, verbose);

`The following coordinates have been protected:`

  

[x1, x2]

  

`The following vector fields have been defined and protected:`

  

[_DG([["vector", M, []], [[[1], 1]]]), _DG([["vector", M, []], [[[2], 1]]])]

  

`The following differential 1-forms have been defined and protected:`

  

[_DG([["form", M, 1], [[[1], 1]]]), _DG([["form", M, 1], [[[2], 1]]])]

  

`frame name: M`

 (1)
> 

 

M > 

f := evalDG((x2)*D_x1 + (c1 * (1 - x1^2) * x2 - c2 * x1)*D_x2);

_DG([["vector", M, []], [[[1], x2], [[2], -c1*x1^2*x2+c1*x2-c2*x1]]])

 (2)
M > 

h := evalDG((x1)*D_x1 + (0)*D_x2);

_DG([["vector", M, []], [[[1], x1]]])

 (3)
M > 

###### answer
M > 

M > 

LieDerivative(f, h);

_DG([["vector", M, []], [[[1], x2], [[2], x1*(2*c1*x1*x2+c2)]]])

 (4)
M > 

 

Download Q20230307.mw

RE: simplifying a numerical representati...

pik1432 240 Maple 2022
radical eigenvalues simplification
January 10 2023
2 2

Hello there, 

Is there any chance to ask if there is a way to simplify the numeric outcome from an operation?

Here is what I've been trying:

> 

restart;
> 

with(LinearAlgebra):
> 

interface(imaginaryunit=j):
> 

Amat := Matrix(2, 2, [[-0.1428571428*K__D, -0.1081971238], [376.9911185, 0]]);

Matrix(2, 2, {(1, 1) = -.1428571428*`#msub(mi("K"),mi("D",fontstyle = "normal"))`, (1, 2) = -.1081971238, (2, 1) = 376.9911185, (2, 2) = 0})

 (1)
> 

Eigenvalues(Amat);

Vector(2, {(1) = -0.7142857140e-1*`#msub(mi("K"),mi("D",fontstyle = "normal"))`+0.2000000000e-9*sqrt(0.1275510203e18*`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-0.1019733868e22), (2) = -0.7142857140e-1*`#msub(mi("K"),mi("D",fontstyle = "normal"))`-0.2000000000e-9*sqrt(0.1275510203e18*`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-0.1019733868e22)})

 (2)
> 

Desired := sqrt((2.000000000*10^(-10))^2 * (1.275510203*10^17*K__D^2 - 1.019733868*10^21));

(0.5102040812e-2*K__D^2-40.78935472)^(1/2)

 (3)
> 

 


I tried to simplify the Eigen values, to make them in the formality of the 'Desired' numerical expression, but no success yet. 

Thank you, 

Download Q20230110_m1.mw

RE: How to collect an expression by a te...

pik1432 240 Maple
syntax expand
August 12 2022
2 1

Hello there, 

Is there any chance to see that the 'eq_5_22_desired' expression shown below can be derived from a collection of the commands. similar to what's given in the 'eq_5_22a'? In other words, is it possible to make Maple aware of the point that 'L__ad/(L__ad + L__fd)' can be interpreted as 'L__ad*L__fd/(L__ad + L__fd) * 1/L__fd'?

> 

restart;
> 

with(LinearAlgebra):
> 

interface(imaginaryunit=j):
> 

eq_5_22 := Psi__ad = -L__ad*L__fd*i__d*1/(L__ad + L__fd) + L__ad*Psi__fd*1/(L__ad + L__fd);

Psi__ad = -L__ad*L__fd*i__d/(L__ad+L__fd)+L__ad*Psi__fd/(L__ad+L__fd)

 (1)
> 

eq_5_23x := L__ad__p = 1 / (1/L__ad + 1/L__fd);

L__ad__p = 1/(1/L__ad+1/L__fd)

 (2)
> 

eq_5_23 := L__ad__p = evala(rhs(eq_5_23x));

L__ad__p = L__ad*L__fd/(L__ad+L__fd)

 (3)
> 

eq_5_22a := Psi__ad = collect(expand(solve(eq_5_18x, Psi__ad)), rhs(eq_5_23)); # error

Error, invalid input: expand expects 1 argument, but received 0

  
> 

eq_5_22_desired := Psi__ad = -L__ad__p*i__d + L__ad__p*Psi__fd/L__fd;

Psi__ad = -L__ad__p*i__d+L__ad__p*Psi__fd/L__fd

 (4)
> 

 

Download Q20220812.mw

Re: How to collect using a term by multi...

pik1432 240 Maple 2022
multiplication syntax collect
June 02 2022
2 6

Hello there, 

Would you allow me to ask this question?

Is there any way to apply 'collect' command using a term by multiplication of variables?

The following worksheet shows an example. What I wanted to see is the 'desired' expression, while multiple attempts with 'collect' command failed. 


 

> 

restart;
> 

eq_e5_10z := Psi[q0]*Delta*delta = 1/(omega[0])*p(Delta*Psi[q])+Delta*Psi[d]+Psi[d0]*1/(omega[0])*p(Delta*delta);

Psi[q0]*Delta*delta = p(Delta*Psi[q])/omega[0]+Delta*Psi[d]+Psi[d0]*p(Delta*delta)/omega[0]

 (1)
> 

eq_e5_10za := Delta*Psi[d] = Psi[q0]*Delta*delta - op(1, rhs(eq_e5_10z)) - op(3, rhs(eq_e5_10z));

Delta*Psi[d] = Psi[q0]*Delta*delta-p(Delta*Psi[q])/omega[0]-Psi[d0]*p(Delta*delta)/omega[0]

 (2)
> 

eq_e5_10zb := subs({p(Delta*Psi[q])=0}, eq_e5_10za);

Delta*Psi[d] = Psi[q0]*Delta*delta-Psi[d0]*p(Delta*delta)/omega[0]

 (3)
> 

collect(rhs(eq_e5_10zb), {Delta*delta});# error

Error, (in collect) cannot collect Delta*delta

  
> 

collect(rhs(eq_e5_10zb), [Delta*delta]);# error

Error, (in collect) cannot collect Delta*delta

  
> 

collect(rhs(eq_e5_10zb), [Delta, delta]);# did not work  

Psi[q0]*Delta*delta-Psi[d0]*p(Delta*delta)/omega[0]

 (4)
> 

Desired := (psi__q0 - psi__d0*p/omega__0)*(Delta*delta);

(psi__q0-psi__d0*p/omega__0)*Delta*delta

 (5)
> 

 


 

Download Q20220602.mw

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