## How to map an expression to x-axis and another exp...

Asked by:

Hello there,

Would you allow me to ask this question?

What I tried in the worksheet below is to map an expression to x-axis and another expression to y-axis, while both expressions have the same input (or independent variable). However, the resulting plot still shows those two expressions as two separate curves. Would you tell me how to map or assign the expressions to each axis?

 > restart;
 > with(LinearAlgebra):
 > Digits := 6:
 > j := I:
 > L__adpu := 1.66; L__aqpu := 1.61; L__lpu := 0.15; R__apu := 0.003; E__tpu := 1.0; MVA := 555;      (1)
 > A__sat := 0.0312500: B__sat := 6.93147:
 > I__tpu_compare := (P__t - j* Q__t) / E__tpu; (2)
 > I__tpu_a := abs(I__tpu_compare); (3)
 > Phi := arccos(P__t / (I__tpu_a * E__tpu)); (4)
 > E__a__tilde := E__tpu + (R__apu + j * L__lpu) * I__tpu_compare; (5)
 > psi__at := abs(E__a__tilde); (6)
 > psi__I := A__sat * exp(B__sat * (psi__at - 0.8)); (7)
 > K__sd := psi__at / (psi__at + psi__I); (8)
 > K__sq := K__sd; (9)
 > X__ad := K__sd * L__adpu:
 > X__d := X__ad + L__lpu:
 > X__aq := K__sq * L__aqpu:
 > X__q := X__aq + L__lpu:
 > delta__i := arctan((X__q * I__tpu_a * cos(Phi) - R__apu * I__tpu_a * sin(Phi))/(E__tpu + R__apu * I__tpu_a * cos(Phi) + X__q * I__tpu_a * sin(Phi))):
 > e__q := E__tpu * cos(delta__i):
 > i__d := I__tpu_a * sin(delta__i + Phi):
 > i__q := I__tpu_a * cos(delta__i + Phi):
 > i__fd := (e__q + R__apu * i__q + X__d * i__d)/(X__ad):
 > i_armature := sqrt(i__d^2 + i__q^2):
 > i_armature2 := subs(P__t = 0, i_armature):
 > i_armature3 := subs(P__t = 0.5, i_armature):
 > i_armature4 := subs(P__t = 1.0, i_armature):
 > plotA := plot(i_armature2, Q__t = -0.6..0.6):
 > plotB := plot(i_armature3, Q__t = -0.6..0.6):
 > plotC := plot(i_armature4, Q__t = -0.6..0.6):
 > plots:-display([plotA, plotB, plotC]); > i__fd2 := subs(P__t = 0, i__fd):
 > i__fd3 := subs(P__t = 0.5, i__fd):
 > i__fd4 := subs(P__t = 1.0, i__fd):
 >
 > plotD := plot(i__fd2, Q__t = -0.6..0.6):
 > plotE := plot(i__fd3, Q__t = -0.6..0.6):
 > plotF := plot(i__fd4, Q__t = -0.6..0.6):
 > plots:-display([plotD, plotE, plotF]); > plot([i__fd2, i_armature2, Q__t = -0.6..0.6]); #failed, two expressions are plotted seperately. >
 >

Best Regards,

In Kwon Park

Download Q20210416.mw

## How to solve dx/f(x,y,z)=dy/g(x,y,z)=dz/h(x,y,z)=d...

Asked by:

How to solve the Linear first-order partial differential equation by the Lagrange method. Suppose u and v are dependent variables and x,y,z are independent variables of a partial differential equation of the form:

dx/f(x,y,z)=dy/g(x,y,z)=dz/h(x,y,z)=du/k(x,y,z)=dv/s(x,y,z). I need its solution in the form of u and v . How to find it ?

## How to get the plot of the system of equation...

Asked by:

Hi!

How to get the plot of the system of the equation below: Tau >=0.Plot.mw

I did not succeed.

Thanks

## How to treat differentiation as an operator...

Asked by:

Hello there,

Would you tell me how to treat differentiation as an operator?

Here is a simple example:

(The content of the worksheet is supposed to be here, but that did not work)

Download Q20210407.mw

The 'coeff' operation shows 'psi__d0' as the only coefficient of 'Delta__delta(t)', while what I wanted to see is the 'Desired' expression in the worksheet, '(psi__d0 + psi__q0 / omega__0 * D)' as the coefficients. Here, 'D' represents the differentiation.

Thank you,

In Kwon Park

## Am I solving for x properly?...

Asked by:

Hi!

I am double checking some textbook methods involving the arc length of a parabolic function of y.  I need to calculate the x coordinate that represents half the arc length of the parabola from x=0 to x=1

I have included my work in the form of a maple worksheet.  Help on this would be appreciated.

Have a great day!Test_solve_for_x.mw

## Can we find Lie Subalgebra by vector fields in Lie...

Asked by:

I am trying to find Lie subalgebra for finding optimal solutions directly with the help of MAPLE.  Please help me to find it. Share MAPLE code please.

## Frequency Differentiation of Fourier Transform + A...

Asked by:

Just A Simple Fouier Transform Example:

Given x(t) = exp(-2*t) u(t) and X(ω) is equal to 1/(j*omega + 2);

Use The Frequency Differentiation of Fourier Transform to the Given Problem and Plot With An Amplitude Spectrum Graph:

Sorry Everyone: I am trying To Learn This Software and Need A Bit Of Help: I am Trying To Solve & Plot With An Amplitude Spectrum Graph #A & Problem #B. Can Anyone Help:

Sorry I Do Not Know How & I Can Find Very Little Via Google a Google Search and Thank You A Million Times For Anyone That Can Help Me With Problems.

#A). t*x(t)
#B). t^2*X(t)

#Solution To Example Problem #A 't*x(t)':

(t)^nX(t)->(j)^n*((&DifferentialD;)^n)/((&DifferentialD;)^( )omega^n)(X(omega));

n := -1;

X := omega -> 1/(2 + j*omega);

diff([j^n*diff(X(omega), [omega \$ n])], omega);

## How do I solve this improper integral involving ex...

Asked by:

Greetings!

I am unable to evaluate an improper integral involving rational, exponential and Bessel functions. Can Maple do it? if not is there a way around.

test.mw

## Maximal paths via breadth-first search

by: Maple 2019

Yesterday, user @lcz , while responding as a third party to one of my Answers regarding GraphTheory, asked about breadth-first search. So, I decided to write a more-interesting example of it than the relatively simple example that was used in that Answer. I think that this is general enough to be worthy of a Post.

This application generates all maximal paths in a graph that begin with a given vertex. (I'm calling a path maximal if it cannot be extended and remain a path.) This code requires Maple 2019 or later and 1D input. This works for both directed and undirected graphs. Weights, if present. are ignored.

```restart:

AllMaximalPaths:= proc(G::GRAPHLN, v)
description
"All maximal paths of G starting at v by breadth-first search"
;
option `Author: Carl Love <carl.j.love@gmail.com> 2021-Mar-17`;
uses GT= GraphTheory;
local
P:= [rtable([v])], R:= rtable(1..0),
VL:= GT:-Vertices(G), V:= table(VL=~ [\$1..nops(VL)]),
Departures:= {op}~(GT:-Departures(G))
;
while nops(P) <> 0 do
P:= [
for local p in P do
local New:= Departures[V[p[-1]]] minus {seq}(p);
if New={} then R,= [seq](p); next fi;
(
for local u in New do
local p1:= rtable(p); p1,= u
od
)
od
]
od;
{seq}(R)
end proc
:
#large example:
GT:= GraphTheory:
K9:= GT:-CompleteGraph(9):
Pa:= CodeTools:-Usage(AllMaximalPaths(K9,1)):
memory used=212.56MiB, alloc change=32.00MiB,
cpu time=937.00ms, real time=804.00ms, gc time=312.50ms

nops(Pa);
40320
#fun example:
P:= GT:-SpecialGraphs:-PetersenGraph():
Pa:= CodeTools:-Usage(AllMaximalPaths(P,1)):
memory used=0.52MiB, alloc change=0 bytes,
cpu time=0ns, real time=3.00ms, gc time=0ns

nops(Pa);
72

Pa[..9]; #sample paths
{[1, 2, 3, 4, 10, 9, 8, 5], [1, 2, 3, 7, 8, 9, 10, 6],
[1, 2, 9, 8, 7, 3, 4, 5], [1, 2, 9, 10, 4, 3, 7, 6],
[1, 5, 4, 3, 7, 8, 9, 2], [1, 5, 4, 10, 9, 8, 7, 6],
[1, 5, 8, 7, 3, 4, 10, 6], [1, 5, 8, 9, 10, 4, 3, 2],
[1, 6, 7, 3, 4, 10, 9, 2]}

```

Notes on the procedure:

The two dynamic data structures are

• P: a list of vectors of vertices. Each vector contains a path which we'll attempt to extend.
• R: a vector of lists of vertices. Each list is a maximal path to be returned.

The static data structures are

• V: a table mapping vertices (which may be named) to their index numbers.
• Departures: a list of sets of vertices whose kth set is the possible next vertices from vertex number k.

On each iteration of the outer loop, P is completely reconstructed because each of its entries, a path p, is either determined to be maximal or it's extended. The set New is the vertices that can be appended to the (connected to vertex p[-1]). If New is empty, then p is maximal, and it gets moved to R

The following code constructs an array plot of all the maximal paths in the Petersen graph. I can't post the array plot, but you can see it in the attached worksheet: BreadthFirst.mw

```#Do an array plot of each path embedded in the graph:
n:= nops(Pa):
c:= 9:
plots:-display(
(PA:= rtable(
(1..ceil(n/c), 1..c),
(i,j)->
if (local k:= (i-1)*ceil(n/c) + j) > n then
plot(axes= none)
else
GT:-DrawGraph(
GT:-HighlightTrail(P, Pa[k], inplace= false),
stylesheet= "legacy", title= typeset(Pa[k])
)
fi
)),
titlefont= [Times, Bold, 12]
);

#And recast that as an animation so that I can post it:
plots:-display(
[seq](`\$`~(plots:-display~(PA), 5)),
insequence
);

``` ## RE: rewriting an expression with substitution...

Asked by:

Hello there,

Would you allow me to ask this (perhaps simple) question?

My goal is to express an equation as 'desired', but with no success with algsubs()/subs()/simplify().

Would you please show me the correct way?

 > restart:
 > PowerBalanceEq := 0 = e1(t) * i1(t) + e2(t) * i2(t) + e3(t) * i3(t); (1)
 > eq_i1 := i1(t) = solve(PowerBalanceEq, i1(t)); (2)
 > n21eq := n21 = e2(t) / e1(t); (3)
 > eq_i2 := algsubs(n21eq, eq_i1); (4)
 > eq_i3 := subs(n21eq, eq_i1); (5)
 > eq_i4 := simplify(eq_i1, {e2(t) / e1(t) = n21}); (6)
 > desired := i1(t) = -n21*i2(t) - e3(t)*i3(t)/e1(t); (7)
 >

Best Regards,

In Kwon Park

Download Q20210316.mw

## Detect and print the operating system....

Asked by:

Is there a means of getting Maple to detect and print the operating system which it is being run on? Searching for this topic is awkward as it returns page after page of troubleshooting guides on how to get Maple running on different operating systems.

Conventionally in Bash I would use something like: echo \$(uname)

## how to find Derivative in loop?...

Asked by:

PLs, correct my code about how to find the derivative by using the loop concept in maple?

help_derivative_in_loop.mw

## indefinite definite easily evaluated, definite int...

Asked by:

Can anyone look at this worksheet, and explain why maple seems to complicate an easily evaluated integral? Hyper.mw

## system hanged on doing integration...

Asked by:

Hi, I am trying to integrate a lengthy-expression but maple does not give a result and got hanged even after waiting 1 hour and more, pls help me to handle this or is this any other way to get a result?

Help_of_Integration.mw

## how to write loop and solve the algebric expressi...

Asked by:

Hi, how to write a loop and solve the algebraic expression? is the loop and do loop are the same thing? if different then pls mention how to solve the same question by using do loop?

solution_loop_help.mw

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