pik1432

Thank you for the clarification....

Answered: pik1432 245

June 08 2023

0 0

@acer Sorry, I missed that point. Thank you for bringing up the difference.

Thank you for the answers!...

Answered: pik1432 245

June 07 2023

0 0

Thank you all for your attention and the ways to make it work!

For the sake of reference, here is the collection of all the answers above.

>

restart;

>	with(LinearAlgebra):

>	with(DynamicSystems):

>	interface(imaginaryunit=j):

>

eq_K1_m4 := K__1 = E__q0*(R__T*E__B*sin(delta) + X__Td*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) + (X__q - X__dp)*i__q0*(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);

K__1 = E__q0*(R__T*E__B*sin(delta)+X__Td*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)+(X__q-X__dp)*i__q0*(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)

(1)

>	eq_K1_m4_desired := K__1 = E__q0(R__TE__Bsin(delta) + X__TdE__Bcos(delta))/Dx + (X__q - X__dp)i__q0(X__TqE__Bsin(delta) - R__TE__B*cos(delta))/Dx;

(2)

>	eq_Dx := Dx = L__aqsL__l + L__aqsX__E + L__aqsL__ads_p + L__l^2 + 2L__lX__E + L__lL__ads_p + R__E^2 + 2R__ER__a + R__a^2 + X__E^2 + X__E*L__ads_p;

(3)

>	denom(op(1, rhs(eq_K1_m4))) - rhs(eq_Dx); # checking to see if the denominator expression is the same as the expression of Dx

(4)

>	denom(op(2, rhs(eq_K1_m4))) - rhs(eq_Dx); # checking to see if the denominator expression is the same as the expression of Dx

(5)

>

# 1

>	map2(applyrule, eq_Dx, eq_K1_m4); # did not work.

K__1 = E__q0*(R__T*E__B*sin(delta)+X__Td*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)+(X__q-X__dp)*i__q0*(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)

(6)

>

# 2

>	subs(eq_Dx, eq_K1_m4); # did not work.

K__1 = E__q0*(R__T*E__B*sin(delta)+X__Td*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)+(X__q-X__dp)*i__q0*(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)

(7)

>

# 3

>	simplify(eq_K1_m4, {Dx = L__aqsL__l + L__aqsX__E + L__aqsL__ads_p + L__l^2 + 2L__lX__E + L__lL__ads_p + R__E^2 + 2R__ER__a + R__a^2 + X__E^2 + X__E*L__ads_p}, [Dx]); # did not work.

K__1 = -E__B*((-R__T*(-X__q+X__dp)*i__q0-E__q0*X__Td)*cos(delta)+sin(delta)*(X__Tq*(-X__q+X__dp)*i__q0-R__T*E__q0))/(L__l^2+(L__aqs+L__ads_p+2*X__E)*L__l+X__E^2+(L__aqs+L__ads_p)*X__E+L__aqs*L__ads_p+(R__E+R__a)^2)

(8)

>

# 4

>	algsubs(eq_Dx, eq_K1_m4); # did not work.

K__1 = E__q0*(R__T*E__B*sin(delta)+X__Td*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)+(X__q-X__dp)*i__q0*(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)

(9)

>

# 5

>	applyrule(L__aqsL__l + L__aqsX__E + L__aqsL__ads_p + L__l^2 + 2L__lX__E + L__lL__ads_p + R__E^2 + 2R__ER__a + R__a^2 + X__E^2 + X__E*L__ads_p = Dx, eq_K1_m4); # did not work.

K__1 = E__q0*(R__T*E__B*sin(delta)+X__Td*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)+(X__q-X__dp)*i__q0*(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)

(10)

>	# answer by ecterrab

>	Physics:-Substitute((rhs=lhs)(eq_Dx), eq_K1_m4);

(11)

>	# answer by Carl Love

>	subs(1/rhs(eq_Dx)= 1/Dx, eq_K1_m4);

(12)

>	# answer by acer

>	subs(denom(rhs(eq_K1_m4))=Dx,eq_K1_m4);

(13)

>

Download Q20230606_w_answer.mw

Thank you for the answers!...

Answered: pik1432 245

June 02 2023

0 0

Thank you for all your answers.

For a referece, the following worksheet shows all the answers above:

>

restart;

>	with(LinearAlgebra):

>	with(DynamicSystems):

>	interface(imaginaryunit=j):

>	eq_m1 := m1 = (X__TqE__Bsin(delta) - R__TE__Bcos(delta))/(R__E^2 + 2R__aR__E + R__a^2 + X__E^2 + X__EL__adsL__fd/(L__fd + L__ads) + 2X__EL__l + L__aqsX__E + L__aqsL__adsL__fd/(L__fd + L__ads) + L__aqsL__l + L__lL__adsL__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__TqE__Bsin(delta) - R__TE__Bcos(delta))/(R__E^2 + 2R__aR__E + R__a^2 + X__E^2 + X__EL__ads_p + 2X__EL__l + L__aqsX__E + L__aqsL__ads_p + L__aqsL__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));

>	# by sursumCorda

>	map2(applyrule, L__ads*L__fd/(L__fd + L__ads) = L__ads_p, eq_m1);

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)

(3)

>	# by tomleslie

>	simplify(subs(L__ads = L__ads_p*L__fd/(L__fd - L__ads_p), eq_m1));

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

(4)

>

Download Q20230602_w_answer.mw

Thank you for the answers!...

Answered: pik1432 245

January 10 2023

0 0

Hello all,

Thank you for all your answers. The attached worksheet is the recap of them.

@Thomas Richard , yes there are different ways of addressing the issue. The last portion of the attached worksheet shows one possbiel way

>

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)

>	A_eig := 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((2.00000000010^(-10))^2 (1.27551020310^17K__D^2 - 1.019733868*10^21));

(3)

>

# by C_R

>	(identify@expand@factor)~(A_eig);

$Vector(2, {(1) = -(1/14)*`#msub(mi("K"),mi("D",fontstyle = "normal"))`+(1/14)*sqrt(`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-7994.713532), (2) = -(1/14)*`#msub(mi("K"),mi("D",fontstyle = "normal"))`-(1/14)*sqrt(`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-7994.713532)})$

(4)

>

# by Acer

>	evalindets(A_eig, &(float,`+`^(1/2)),u->signum(op(1,u))(op([2,1],u)*op(1,u)^2)^(1/2));

$Vector(2, {(1) = -0.7142857140e-1*`#msub(mi("K"),mi("D",fontstyle = "normal"))`+sqrt(0.5102040812e-2*`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-40.78935472), (2) = -0.7142857140e-1*`#msub(mi("K"),mi("D",fontstyle = "normal"))`-sqrt(0.5102040812e-2*`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-40.78935472)})$

(5)

>	# for Thomas Richard

>

restart;

>	with(LinearAlgebra):

>	with(DynamicSystems):

>	interface(imaginaryunit=j):

>	A11 := -K__D / (2*H_gen);

(6)

>	A12 := -K__S / (2*H_gen);

(7)

>	A21 := omega__0;

(8)

>

A22 := 0;

(9)

>	Amat := <<A11\|A12>,<A21\|A22>>;

$Matrix(2, 2, {(1, 1) = -(1/2)*K__D/H_gen, (1, 2) = -(1/2)*K__S/H_gen, (2, 1) = `ω__0`, (2, 2) = 0})$

(10)

>	Bmat := <1/(2*H_gen), 0>;

$Vector(2, {(1) = (1/2)/H_gen, (2) = 0})$

(11)

>	sys_gen := StateSpace(Amat, Bmat);

>	Amat_eigenVals := Eigenvalues(Amat);

$Vector(2, {(1) = -(1/4)*(K__D-sqrt(-8*H_gen*K__S*`ω__0`+K__D^2))/H_gen, (2) = -(1/4)*(K__D+sqrt(-8*H_gen*K__S*`ω__0`+K__D^2))/H_gen})$

(12)

>	char_poly_gen := CharacteristicPolynomial(sys_gen);

(13)

>	# Given system parameters

>	Freq := 60;

(14)

>	sys_MVA_base := MVA * 4;

(15)

>	H_genx := 3.5;

(16)

>	omega__0x := evalf(2PiFreq);

(17)

>	P_gen := 0.9; # in pu

(18)

>	Q_gen := 0.3; # in pu

(19)

>	E__t := polar(1.0, convert(36*degrees, radians));

(20)

>	E__b := polar(0.995, convert(0*degrees, radians));

(21)

>	Xd__p := j * 0.3;

(22)

>	Xtr := j * 0.15;

(23)

>	Xckt1 := j * 0.5;

(24)

>	Hgen := 3.5;

(25)

>

######

>	I__t := conjugate(P_gen +j*Q_gen) / abs(E__t);

(26)

>	Xd__p * I__t;

(27)

>	abs(E__t) + Xd__p * I__t;

(28)

>	E__p := convert(abs(E__t) + Xd__p * I__t, polar);

(29)

>	temp := convert(argument(E__p), degrees);

(30)

>	delta__0 := 36*degrees + temp;

(31)

>	X__T := Xd__p + Xtr + Xckt1;

(32)

>	# from eq. 12.76

>	K__Sx := (abs(E__p) * abs(E__b) / abs(X__T)) * cos (convert(delta__0, radians));

(33)

>	Amat_eigenValsNumeric := subs({H_gen=H_genx, K__S=K__Sx, omega__0 = omega__0x}, Amat_eigenVals);

$Vector(2, {(1) = -0.7142857142e-1*K__D+0.7142857142e-1*sqrt(K__D^2-7994.713520), (2) = -0.7142857142e-1*K__D-0.7142857142e-1*sqrt(K__D^2-7994.713520)})$

(34)

>

Download Q20230110_m1_answers.mw

I tried.

Thank you!...

Answered: pik1432 245

August 12 2022

0 0

Thank you for your valuable answers, Carl Love and Christian Wolinski!

Here is the recap of your answers.

>

restart;

>	with(LinearAlgebra):

>	interface(imaginaryunit=j):

>	eq_5_22 := Psi__ad = -L__adL__fdi__d1/(L__ad + L__fd) + L__adPsi__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__pi__d + L__ad__pPsi__fd/L__fd;

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

(4)

>	# from Carl Love - 1

>	solve(eq_5_23, {L__ad}); # step 1

${L__ad = L__ad__p*L__fd/(L__fd-L__ad__p)}$

(5)

>	eval(eq_5_22, %); # step 2

Psi__ad = -L__ad__p*L__fd^2*i__d/((L__fd-L__ad__p)*(L__ad__p*L__fd/(L__fd-L__ad__p)+L__fd))+L__ad__p*L__fd*Psi__fd/((L__fd-L__ad__p)*(L__ad__p*L__fd/(L__fd-L__ad__p)+L__fd))

(6)

>	simplify(%); # step 3

Psi__ad = -(L__fd*i__d-Psi__fd)*L__ad__p/L__fd

(7)

>	expand(%); # step 4

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

(8)

>	expand(simplify(eval(eq_5_22, solve(eq_5_23, {L__ad})))); # single line - combined

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

(9)

>	# from Carl Love - 2

>	expand(simplify(eq_5_22, {eq_5_23}, [L__ad])); # using simplify/siderels

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

(10)

>	# from Christian Wolinski

>	convert(eliminate({eq_5_23, eq_5_23x, eq_5_22}, {Psi__ad, L__ad})[1], parfrac, L__fd);

${L__ad = L__ad__p+L__ad__p^2/(L__fd-L__ad__p), Psi__ad = -L__ad__p*i__d+L__ad__p*Psi__fd/L__fd}$

(11)

>

Download Q20220812_w_Answers2.mw

Sorry!...

Answered: pik1432 245

June 05 2022

0 0

@acer You are absolutely right. It does matter!

Thank you!...

Answered: pik1432 245

June 04 2022

0 0

@acer Thank you for the answer and the way of using the collect command with no recursion. As noted in the answer to 'tomleslie', it did not matter to me whether the notation 'p' is treated as a function call or a standalone multiplicative factor.

Thank you!...

Answered: pik1432 245

June 04 2022

0 0

@tomleslie Thank you for the extra note. The purpose is to check the steps of deriving the final expression, from a series of expressions given in a text book, there is practically no distinction between the two. In other words, if a way becomes preferrable, then it would be utilized for the necessary facilitation.

Thank you for the answer!...

Answered: pik1432 245

June 02 2022

0 0

Yes. the p() with the 'Delta*delta' causes the blockage. Perhaps one way to go around it is to re-write that part from p(Delta*delta) as p*(Delta*delta), which worked with the nested 'collect' command.

Sorry and Thank you...

Answered: pik1432 245

April 28 2022

0 0

@Carl Love Thank you for your correction and sorry for my misunderstanding.

Here is the comparison. '1' is your correction, while '2' shows my misunderstanding.

>

######

>

# 1

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools):

>	_Envdiffopdomain:=[Dt,t]:

>	eq_e5_9 := psi__d0Delta__delta(t) + psi__q0DtDelta__delta(t)/omega__0 = p_Delta__psi__d(t)/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*Dt*Delta__delta(t)/omega__0 = p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t)

(1)

>	diffop2de(eq_e5_9, f(t));

psi__d0*Delta__delta(t)*f(t)+psi__q0*Delta__delta(t)*(diff(f(t), t))/omega__0 = (p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t))*f(t)

(2)

>

######

>

# 2

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools):

>	_Envdiffopdomain:=[Dt,t]:

>	eq_e5_9 := psi__d0Delta__delta(t) + psi__q0DDelta__delta(t)/omega__0 = p_Delta__psi__d(t)/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0 = p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t)

(3)

>	diffop2de(eq_e5_9, f(t));

(psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0)*f(t) = (p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t))*f(t)

(4)

>

Download Q20220428.mw

Thank you!...

Answered: pik1432 245

April 27 2022

0 0

@Carl Love : Thank you for your answer. I was able to re-iterate it by using the attached worksheet (below).

However, still, my question is not fully addressed yet. What I wanted to achieve is the expression labeled as '(e5.13p) ' in the attached PDF file('Ex5_1_simple.pdf'). Then, if the differentiator operator works as expected, those differentiations associated with constants would go away by themselves.

>

######

>

# 1

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools):

>	_Envdiffopdomain:=[Dt,t]:

>	eq_e5_9 := psi__d0Delta__delta(t) + psi__q0DDelta__delta(t)/omega__0 = p_Delta__psi__d(t)/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0 = p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t)

(1)

>	diffop2de(eq_e5_9, f(t));

(psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0)*f(t) = (p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t))*f(t)

(2)

>

######

>

# 2

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools):

>	eq_e5_9 := psi__d0Delta__delta(t) + psi__q0DDelta__delta(t)/omega__0 = p_Delta__psi__d(t)/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0 = p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t)

(3)

>	diffop2de(eq_e5_9, f(t));

Error, (in DEtools/diffop2de) differential algebra not specified

>

######

>

# 3

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools):

>	_Envdiffopdomain:=[Dx,x]:

>	eq_e5_9 := psi__d0Delta__delta(t) + psi__q0DDelta__delta(t)/omega__0 = p_Delta__psi__d(t)/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0 = p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t)

(4)

>	diffop2de(eq_e5_9, f(t));

(psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0)*f(x) = (p_*Delta__psi__d(t)/omega__0-Delta__psi__q(t))*f(x)

(5)

>

Download Q20220427.mw

Ex5_1_simple.pdf

Sorry!...

Answered: pik1432 245

April 26 2022

0 0

@acer: Thank you for your point. I should have thought that when I posted the question.

Regarding the desired form, please have a look at the following worksheet.

>

######

>	# E5.13 - 3

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools): _Envdiffopdomain:=[Dt,t]:

>	eq_e5_9 := psi__d0Delta__delta(t) + psi__q0DDelta__delta(t)/omega__0 = DDelta__psi__d(t)/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0 = D*Delta__psi__d(t)/omega__0-Delta__psi__q(t)

(1)

>	diffop2de(eq_e5_9, f(t));

(psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0)*f(t) = (D*Delta__psi__d(t)/omega__0-Delta__psi__q(t))*f(t)

(2)

>	eq_e5_9_disired := psi__d0Delta__delta(t) + psi__q0/omega__0diff(Delta__delta(t),t) = 1/omega__0*diff(Delta__psi__d(t),t) - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*(diff(Delta__delta(t), t))/omega__0 = (diff(Delta__psi__d(t), t))/omega__0-Delta__psi__q(t)

(3)

>

Download Q20220426.mw

Sorry!...

Answered: pik1432 245

April 25 2022

0 0

@acer Thank you for your message and sorry for that missing worksheet. I thought I attached it, but perhaps something went wrong. Here is the worksheet file.

>

######

>	# E5.13 - 2

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools): _Envdiffopdomain:=[Dt,t]:

>	eq_e5_9 := psi__d0Delta__delta(t) + psi__q0DDelta__delta(t)/omega__0 = DDelta__psi__d(t)/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0 = D*Delta__psi__d(t)/omega__0-Delta__psi__q(t)

(1)

>	diffop2de(eq_e5_9, f(t));

(psi__d0*Delta__delta(t)+psi__q0*D*Delta__delta(t)/omega__0)*f(t) = (D*Delta__psi__d(t)/omega__0-Delta__psi__q(t))*f(t)

(2)

>

Download Q20220425.mw

Thank you!...

Answered: pik1432 245

April 20 2022

0 0

@Carl Love Thank you for the further explanation. Sorry, I should have noticed that the 'unprotect/protect' commands should precede the 'with(DEtools)', Now it works.

>

restart;

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	with(DEtools): _Envdiffopdomain:=[Dt,t]:

>

>	xxx := psi__d0 + psi__q0*Dt/omega__0 = 1/omega__0 - 1;

psi__d0+psi__q0*Dt/omega__0 = 1/omega__0-1

(1)

>	xxx_1 := lhs(xxx) - rhs(xxx);

psi__d0+psi__q0*Dt/omega__0-1/omega__0+1

(2)

>

>	xxx_a := diffop2de(xxx, f(t));

psi__d0*f(t)+psi__q0*(diff(f(t), t))/omega__0 = (1/omega__0-1)*f(t)

(3)

>	xxx_1_a := diffop2de(xxx_1, f(t));

(psi__d0-1/omega__0+1)*f(t)+psi__q0*(diff(f(t), t))/omega__0

(4)

>

Download LDOs_m3.mw

Thank you!...

Answered: pik1432 245

April 20 2022

0 0

@Carl Love Thank you for the informative answer. However, I'm afraid the error still persists. The attached worksheet is my attempt with the suggested routine.

>

restart;

>	with(DEtools): _Envdiffopdomain:=[Dt,t]:

>

>	xxx := psi__d0 + psi__q0*Dt/omega__0 = 1/omega__0 - 1;

psi__d0+psi__q0*Dt/omega__0 = 1/omega__0-1

(1)

>	xxx_1 := lhs(xxx) - rhs(xxx);

psi__d0+psi__q0*Dt/omega__0-1/omega__0+1

(2)

>	unprotect(DEtools): DEtools[diffop2de]:= L-> `if`(L::algebraic, `DEtools/diffop2de`, curry(map, procname))(args): protect(DEtools):

>	xxx_a := diffop2de(xxx, f(t));

Error, (in DEtools/diffop/to_eqn) unable to compute coeff

>

>	xxx_1_a := diffop2de(xxx_1, f(t));

(psi__d0-1/omega__0+1)*f(t)+psi__q0*(diff(f(t), t))/omega__0

(3)

>

Download LDOs_m2.mw

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