Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

DEAR SIR,

 

GOOD EVENING.

 

HOW TO FIND THE AREA BETWEEN THE CURVES  USING MAPLE? 

How I can edit and apply the following conditions to my plot functions 

`######   I want to change q  (starting from 0.3) from 0.3 by .001 to 0.377 and plot 2D (u-q) ,(v,q), (u,v) and  plot3D (u,v,q)`

 

`######   I want to change q (starting from 0.37727) from 0.37727 by .001 to 0.390059 and h from 0.1 by .001 to 0.138462  and plot 2D (h-q)  and  plot3D (u,h,q),(v,h,q)`

I couldn't attach my file here, so I uploaded that here

https://drive.google.com/file/d/17purRxEdDqrTJeFDcF1-d9J7b3LkuJnF/view?usp=sharing

 

Hi,

I am studying nonlinear differential equations, and came across an interesting one on maple's help page.  I made a post about this equation already, but I have decided to make a new post because the topic is slightly different than from the previous post.

The topic of this post is:

"Can numerical methods and exact, implicit techniques find false solutions?"

To make the discussion clearer, the rest of this post can be found in the maple file I created.

Hi to all community. I am trying to integrate a lengthy-expression but could not get the result after waiting of 1 and 2 hours even. is there any way to control such integration


 

Integration_Help.mw

 

 

A very simple question (by example):

Consider two polynomials g and h:

with(PolynomialTools):

g:=FromCoefficientList([1,2,3],x);

h:=FromCoefficientList([4,5,6,7],x);

 

What is the syntax for computing the composition of g with h? (As a polynomial.)

For instance, I would like to use CoefficientList on the result.

 

I know the @ operator and the subs command and have tried using them in various ways, but with no success.

(Of course, my question is general; the above is just an example.)

---

Edit: Additional question (which is my real question):

I'm writing a procedure that takes two polynomials g and h, and in which I define an unknown polynomial f. I want to compute its coefficients so that

f "composition" g = h

I write:

fCoeff:=seq(a[i],i=0..t) (to define the unknown coefficients. I can compute t.)

f := FromCoefficientList([fCoeff],x);

Then I would like to do something like:

comCoeff:=CoefficientList(f "composition" g,x)

If I have this, then I know how to solve for the unkown coefficients in f.

Given a metric, to compute quantities in the NP formalism one needs to specify a null tetrad. In the various examples in the help pages, sometimes the tetrad is specified simply as a list of 4 vectors, e.g., NT := [...] and sometimes evalDG is applied as in NT := evalDG({...]). Using the first format, Maple accepted NT as argument in NPSpinCoefficients but  NPCurvatureScalars(SpinCoefficients,NT) complained that the second argument wasn't a list of four vectors. When I used the second format, both commands returned the expected results. Why the difference?

RobinsonTrautmanSpinDG.mw

How I can plot3d function s. in the domain x ,y from -1300 to 200.

Thanks

if.mw
 

"restart;   #`    x__A`=-1300..200,      `y__A`=-1300..200    u1:=(((`x__A`-200)^(2)+(`y__A`^())^(2))*0.001)/(960000);   if  u1<=0.001  then w(u1):=-0.5772-ln(u1);  else if u1>0.001  then w(u1):=-0.5772-ln(u1)+u1-((u1)^(2))/(2*2!)+((u1)^(3))/(3*3!)-((u1)^(4))/(4*4!)+((u1)^(5))/(5*5!)-((u1)^(6))/(6*6!)+((u1)^(7))/(7*7!)-((u1)^(8))/(8*8!)+((u1)^(9))/(9*9!)-((u1)^(10))/(10*10!)+((u1)^(11))/(11*11!)-((u1)^(12))/(12*12!);     end if"

Error, invalid 'if' statement

"restart;      u1:=(((`x__A`-200)^2+(`y__A`)^2)*0.001)/960000;   if u1<=0.001  then w:=(u1)->-0.5772-ln(u1);  elseif u1>0.001  then w(u1):=-0.5772-ln(u1)+u1-((u1)^2)/(2*2!)+((u1)^3)/(3*3!)-((u1)^4)/(4*4!)+((u1)^5)/(5*5!)-((u1)^6)/(6*6!)+((u1)^7)/(7*7!)-((u1)^8)/(8*8!)+((u1)^9)/(9*9!)-((u1)^10)/(10*10!)+((u1)^11)/(11*11!)-((u1)^12)/(12*12!);     end if"

 

s := 6.87*10^(-3)*w(u1); plot3d(s, x__A = -1300 .. 200, y__A = -1300 .. 200)


 

Download if.mw

 

Hello. I want to use the command verify but with two variables. For example:

verify(x^2 + y^2, 0, {'greater_equal'});

but I get FAIL as an answer. I tried adding before the verify command assume(x, 'real'); assume(y, 'real');

but notihng changed.

 

Thanks for any help.

Dear people in mapleprims,

I haven't used maple for a long time.
By the way, I tried to modify a denominator part in an fractional expression, but I couldn't.

Original expression is 

a:=-(I__22-X__2)/(I__11*I__22-I__11*X__2-I__12*I__21-I__22*X__1+X__1*X__2);

#And, I want to change this to the form

b:=(X__2-I__22)/((x__1-I__11)*(X__2-I__22)-I__12*I__21);

How can I do this?

Thank you in advance.

taro yamada

 

Hi,

I have managed to create the following plot.  It won't plot on the site's plotter:

fieldplot([1, y^2 + x], x = -10 .. 10, y = -6 .. 6, fieldstrength = fixed, color = abs(y^2 + x + 1))

I am trying to assign a colour gradient to the different vectors based on vector magnitude.  In the color option, I entered color= expresssion for the magnitude of the vectors

 

This only half worked.  It currently scales the colours such that the largest and smallest vectors are the same colour.  How do I assign a gradient such that the small magnitude vectors are one colour, and they then transition to another colour as their magnitude gets larger?

 

 

Hello. I am trying to solve this system of equations but I can't get Maple to show all solutions.

I have solve the system by hand and there are two more solutions (x=x, y=1) and (x=x, y=-1).

 

Thanks for any help !

 

Hello. I want to solve a 2X2 system using Maple. I have written this code but I do not get expected results.

restart;
with(DEtools);
with(plottools);
with(plots);
with(Algebraic);

F := -1 - y - exp(x);
G := x^2 + y*(exp(x) - 1);

sol1 := eliminate({F, G}, {x, y});

sol1 := [{x = RootOf(-exp(_Z)^2 + _Z^2 + 1), y = -exp(RootOf(-exp(_Z)^2 + _Z^2 + 1)) - 1}, {}]

But, the solutions are x=0 and y=-2 (I have solved the system by hand).

 

Any help?!

I have a parametric polynomial which is defined based on the multiplication of different variables and I want to rearrange the polynomial based on specific variables. For example, suppose the polynomial is defined as follows:

a:= (1+x+y)(2x-yx+z)(y^2-zy)

and I want to have a based on first, and second orders of x, or even other variables. Thanks

Hi so ive been working on a few codes making Eulers method and RungeKutta and Taylor Series (second order) and I cant figure out why my code is giving me a weird output? I will attach my maple files here, I can post more information if you'd like. Also have no idea how to start for taylor series so any help with code on that would be appreciated!

 


 

euler1 := proc (f, a, b, alpha, h, N) local i, t, w; i := 1; t := a; w := alpha; while i <= N do w := w+h*f(t, w); t := a+i*h; i := i+1 end do; [w] end proc

proc (f, a, b, alpha, h, N) local i, t, w; i := 1; t := a; w := alpha; while i <= N do w := w+h*f(t, w); t := a+i*h; i := i+1 end do; [w] end proc

(1)

euler1(e^(5*3-y), 0, 3, .5, .2, 2)

[.5+.2*e(0, .5)^(15-y(0, .5))+.2*e(.2, .5+.2*e(0, .5)^(15-y(0, .5)))^(15-y(.2, .5+.2*e(0, .5)^(15-y(0, .5))))]

(2)

NULL

NULL

NULL


 

Download p5one.mw
 

RK4 := proc (f, a, b, alpha, h, N) local t, w, i, k1, k2, k3, k4; i := 1; t := a; w := alpha; while i <= N do k1 := h*f(t, w); k2 := h*f(t+(1/2)*h, w+(1/2)*k1); k3 := h*f(t+(1/2)*h, w+(1/2)*k2); k4 := h*f(t+h, w+k3); w := w+(1/6)*k1+(1/3)*k2+(1/3)*k3+(1/6)*k4; t := a+i*h; i := i+1 end do; [w] end proc

proc (f, a, b, alpha, h, N) local t, w, i, k1, k2, k3, k4; i := 1; t := a; w := alpha; while i <= N do k1 := h*f(t, w); k2 := h*f(t+(1/2)*h, w+(1/2)*k1); k3 := h*f(t+(1/2)*h, w+(1/2)*k2); k4 := h*f(t+h, w+k3); w := w+(1/6)*k1+(1/3)*k2+(1/3)*k3+(1/6)*k4; t := a+i*h; i := i+1 end do; [w] end proc

(1)

RK4(exp(5*3-y), 0, 3, .5, .2, 1)

[.5+0.3333333333e-1*(exp(15-y))(0, .5)+0.6666666667e-1*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(0, .5))+0.6666666667e-1*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(0, .5)))+0.3333333333e-1*(exp(15-y))(.2, .5+.2*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(0, .5))))]

(2)

``


 

Download rk4new.mw

 

I have an assignment for Q that after subsequent other assignments and substitutions  results in 

-XC1*R1^2/((R1^2 + XC1^2)*(R1*XC1^2/(R1^2 + XC1^2) + 12960.54302))

 

when I type Q.

 

I would like to solve this for XC1, for values of Q that make  XC1 is real. 

How do I do this?  Can I rearrange this assignment?   

I guess I could do something like this:

eq1:= -XC1*R1^2/((R1^2 + XC1^2)*(R1*XC1^2/(R1^2 + XC1^2) + 12960.54302))

solve(eq1=Q,XC1)

but Q as a function of XC1 is a derived from other relationships.

 

The worksheet probably makes what I'm asking more clear.    I was able to get the result, but I'm sure there is a better, more elegant  way to do what I needed to do...

 

Thanks
 

``

restart

Series-Parallel Conversion Equations as a function of Q

• 

Q = Xs/Rs = Rp/Xp;

• 

Rp := Rs*(Q^2 + 1);

``

``

Impedance Transpormation Equations

Rp := proc (Rs, Xs) options operator, arrow; (Rs^2+Xs^2)/Rs end proc

Xp := proc (Rs, Xs) options operator, arrow; (Rs^2+Xs^2)/Xs end proc

Rs := proc (Rp, Xp) options operator, arrow; Rp*Xp^2/(Rp^2+Xp^2) end proc

Xs := proc (Rp, Xp) options operator, arrow; Xp*Rp^2/(Rp^2+Xp^2) end proc

``

zL := 1.343+I*131.925

1.343+131.925*I

(1)

``

XL0p := Xp(Re(zL), Im(zL))

131.9386717

(2)

RLp := Rp(Re(zL), Im(zL))

12960.54302

(3)

QLp := RLp/XLp

12960.54302/XLp

(4)

XC2 := -XL0p

-131.9386717

(5)

Q := XL1/(R1s+RLp)

XL1/(R1s+12960.54302)

(6)

R1s := Rs(R1, XC1)

R1*XC1^2/(R1^2+XC1^2)

(7)

XC1s := Xs(R1, XC1)

XC1*R1^2/(R1^2+XC1^2)

(8)

XL1 := -XC1s

-XC1*R1^2/(R1^2+XC1^2)

(9)

Q

-XC1*R1^2/((R1^2+XC1^2)*(R1*XC1^2/(R1^2+XC1^2)+12960.54302))

(10)

``

tmp1 := solve(-XC1*R1^2/((R1^2+XC1^2)*(R1*XC1^2/(R1^2+XC1^2)+12960.54302)) = Tmp, XC1)

(-25000.*R1+(-0.3240135755e14*R1*Tmp^2+625000000.*R1^2-0.4199391884e18*Tmp^2)^(1/2))*R1/(Tmp*(50000.*R1+648027151.)), -1.*(25000.*R1+(-0.3240135755e14*R1*Tmp^2+625000000.*R1^2-0.4199391884e18*Tmp^2)^(1/2))*R1/(Tmp*(50000.*R1+648027151.))

(11)

"solve(indets(numer(tmp1[1]))"

{R1, Tmp, (-0.3240135755e14*R1*Tmp^2+625000000.*R1^2-0.4199391884e18*Tmp^2)^(1/2)}

(12)

simplify(solve(op(3, indets(numer(tmp1[1])))^2 > 0, Tmp, parametric))

piecewise(R1 <= -8398783768000/648027151, [[Tmp = Tmp]], R1 < 0, [[50*5^(1/2)*R1/(648027151*R1+8398783768000)^(1/2) < Tmp, Tmp < -50*5^(1/2)*R1/(648027151*R1+8398783768000)^(1/2)]], R1 = 0, [], 0 < R1, [[-50*5^(1/2)*R1/(648027151*R1+8398783768000)^(1/2) < Tmp, Tmp < 50*5^(1/2)*R1/(648027151*R1+8398783768000)^(1/2)]])

(13)

``


 

Download pi-filter_anal_copy.mw

 

 

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