## 245 Reputation

5 years, 143 days

## Re: Substituting an expression (differen...

Maple 2023

Hello there,

This is another issue, associated with substitution. In the following Maple expressions, I tried to substitutte the denominator of 'eq_K1_m4' in order to make it as 'eq_K1_m4_desired', but did not get any success (yet).

Therefore, would you have a look at this issue to see if the intended goal can be achieved?

 > 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);
 (1)
 > eq_K1_m4_desired := K__1 = E__q0*(R__T*E__B*sin(delta) + X__Td*E__B*cos(delta))/Dx + (X__q - X__dp)*i__q0*(X__Tq*E__B*sin(delta) - R__T*E__B*cos(delta))/Dx;
 (2)
 > eq_Dx := Dx = 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)
 > 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.
 (6)
 > # 2
 > subs(eq_Dx, eq_K1_m4); # did not work.
 (7)
 > # 3
 > simplify(eq_K1_m4, {Dx = 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}, [Dx]); # did not work.
 (8)
 > # 4
 > algsubs(eq_Dx, eq_K1_m4); # did not work.
 (9)
 > # 5
 > applyrule(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 = Dx, eq_K1_m4); # did not work.
 (10)
 >

## Re: Substituting an expression...

Maple 2023

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);
 (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);
 (2)
 > ######
 >

## RE: LieDerivative...

Maple 2022

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);
 (1)
 >
 M > f := evalDG((x2)*D_x1 + (c1 * (1 - x1^2) * x2 - c2 * x1)*D_x2);
 (2)
 M > h := evalDG((x1)*D_x1 + (0)*D_x2);
 (3)
 M >
 M > LieDerivative(f, h);
 (4)
 M >

## RE: simplifying a numerical representati...

Maple 2022

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]]);
 (1)
 > Eigenvalues(Amat);
 (2)
 > Desired := sqrt((2.000000000*10^(-10))^2 * (1.275510203*10^17*K__D^2 - 1.019733868*10^21));
 (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,

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

Maple

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):
 (1)