MaplePrimes Questions

i want to plot this equations for P and t for  t= 0 t0 600 seconds..can u provide me how?

time-dependent_aerodynamic_pressure.mw

restart

k := 0.1e-1;

0.1e-1

 

5

(1)

`P₀₀` := 100;

100

(2)

V := 25;

25

(3)

rho := 1;

1

 

.5

(4)

eq := diff(P(t), t) = -k*P(t)+rho*Cp*(int(V*sin(alpha), t));

diff(P(t), t) = -0.1e-1*P(t)+12.5*sin(5)*t

(5)

solution := dsolve({eq, P(0) = `P₀₀`}, P(t));

P(t) = 1250*sin(5)*t-125000*sin(5)+exp(-(1/100)*t)*(100+125000*sin(5))

(6)

``

Download time-dependent_aerodynamic_pressure.mw

Hi!

I hope everyone is fine. I have a square matrix like the following form
A := Matrix([[10, -1, 2, 0], [-1, 11, -1, 3], [2, -1, 10, -1], [0, 3, -1, 8]]);
How to split A into three matrices D, L and U as:

D:= Matrix([[10, 0, 0, 0], [0, 11, 0, 0], [0, 0, 10, 0], [0, 0, 0, 8]]);
L := Matrix([[0, 0, 0, 0], [-1, 0, 0, 0], [2, -1, 0, 0], [0, 3, -1, 0]]);
U := Matrix([[0, -1, 2, 0], [0, 0, -1, 3], [0, 0, 0, -1], [0, 0, 0, 0]]);

I am waiting for your positive response. Please take care

Hello Everyone;

I need to solve the following nonlinear ODE

C*diff(y(x), x) + (-B0*y(x)^3 - B1*y(x)^2 - B2*y(x) - B3) = 0, y(0)=B4

where B0,B1,B2,B3 and B4 are constants. I am trying in Maple 2021, but receiving solution in the form of integral. Is that any other ways that I will be able exact solution. Maple sheet is atatched. I am waiting for your kind respose.

Thanks

Question1.mw

restart

 

infolevel[dsolve] := 4

4

(1)

ode22 := C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

(2)

solll := dsolve(ode22, implicit, useInt)

Methods for first order ODEs:

 

--- Trying classification methods ---

 

trying a quadrature

 

trying 1st order linear

 

trying Bernoulli

 

trying separable

 

<- separable successful

 

x-Intat(C/(B0*_a^3+B1*_a^2+B2*_a+B3), _a = y(x))+_C1 = 0

(3)

ode[257] := C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

(4)

dsolve(ode[257], implicit)

Methods for first order ODEs:

 

--- Trying classification methods ---

 

trying a quadrature

 

trying 1st order linear

 

trying Bernoulli

 

trying separable

 

<- separable successful

 

x-Intat(C/(B0*_a^3+B1*_a^2+B2*_a+B3), _a = y(x))+_C1 = 0

(5)

NULL

Download Question1.mw

Hello,

I want to create an product expression from all list elements,

e.g.

expr := createproduct([a,b,c,d,1]);

expr:= a*b*c*d

Context; I'd like to apply a function on all factos of a polynomial. I can easily map(fun,factors(apolynomial)) which will output a list. However I do not know how to get back.

Thanks for your comments!

When i try to log on to my maplesoft acount on Maple 2023 i get a messeage saying "Sign in Error: Please check your credentials and try again." i have done this multiple time double checked my password and everything, but it won't let me log on... what do i do?

Hi @Acer, and of course also hi to the whole mapleprimes comunnity.

I have a problem with the Phasors module. Very often I have to use the evalc in calculations involving phasors. Sometimes it might make sense, since one of the involved variables are not defined as a phasor.

May I suggest that you upgrade the phasors module to a package Acer? I'd be honored to help in the testing.

Besides I have the same experience as mentioned in this question (bear over with me it's years since already): Maple 2020 Sheet now opening in 2021, 2022, and 2023 results in errors.

 

attached some examples:

Eksempel_8.2.mw

Example_12.3.mw

Eksempel_14.5.mw

Opgave_4_-_SHS_-_RA_ref-UL1.mw

Opgave_4_-_SHS_-_RA_ref-UL1_using_context_menu.mw

Hi everyone.

Could you please help me to obtain the results by 'solve'?

Is there any way such as numerical methods in this regard?

Fung.mws

Hi,

I'm just working on som electricity tasks and have to calculate thre phase power in alternating current systems. I use the SI system and have checked that with UsingSystem() -> SI and GetUnits() -> voltampere[power], voltampere_reactive[power] among others, so everything should be alright, but why can't I then choose theese units from neither the Units Palette, the Context Panel or right click menu option Convert Output Units?

convert(expr, units, var) and convert(expr, units, VA) works but my students and colleagues won't be satisfied with that.

Thank you for any help.

Is there a way to delete frames arround the legend in a plot?

Hi,

I'm trying to figure out how to get the HermitianTranpose vector to distribute over a sum of vectors. Maple seems to want to ignore the linearity of the conjugate operation.

See the example code attached.

Thanks.
 

alp := [a, b, c, d, e]

[a, b, c, d, e]

(1)

u[a] := Vector(5, proc (m) options operator, arrow; u[alp[m], a] end proc)

u[b] := Vector(5, proc (m) options operator, arrow; u[alp[m], b] end proc)

u[c] := Vector(5, proc (m) options operator, arrow; u[alp[m], c] end proc)

u[d] := Vector(5, proc (m) options operator, arrow; u[alp[m], d] end proc)

u[e] := Vector(5, proc (m) options operator, arrow; u[alp[m], e] end proc)

NULL

NULL

NULL

N := r[a]*u[a]+r[b]*u[b]+r[c]*u[c]+r[d]*u[d]+r[e]*u[e]

Vector[column](%id = 36893490335086041316)

(2)

``

LinearAlgebra:-HermitianTranspose(N)

Vector[row](%id = 36893490335105454316)

(3)

NULL


 

Download DistributeHermitian.mw

Hi,

Just to inform me about the technical possibility of copying this continued fraction in Word?

Thanks

ContFrac.mw

I have a calculation sheet that used to work in Maple 2020 and earlier, but with an upgrade to versions 2021 to 2023 the same errors are appearing. The sheet still functions fine in 2020 but unknown why these errors appear when using 2021 thru 2023.

Does anyone know what might have changed with the later versions to result in these types of errors?

Hi . My question is about writing a gravity equation, which I explained comprehensively I  explain in the PDF linked below, and I need the code for this equation in Maple.

My_Question2.pdf

list:= [[-12, 3, 5], [-11, -2, 5], [-11, -1, 2], [-11, -1, 8], [-11, 0, 
        1], [-11, 0, 9], [-11, 3, 0], [-11, 3, 10], [-11, 6, 1], [-11, 6, 
        9], [-11, 7, 2], [-11, 7, 8], [-11, 8, 5], [-4, -9, 5], [-4, 
        3, -7], [-4, 3, 17], [-4, 15, 5], [-3, -9, 2], [-3, -9, 8], [-3, 
        0, -7], [-3, 0, 17], [-3, 6, -7], [-3, 6, 17], [-3, 15, 2], [-3, 15,
        8], [-2, -9, 1], [-2, -9, 9], [-2, -1, -7], [-2, -1, 17], [-2, 
        7, -7], [-2, 7, 17], [-2, 15, 1], [-2, 15, 9], [1, -10, 5], [1, -9, 
        0], [1, -9, 10], [1, -2, -7], [1, -2, 17], [1, 3, -8], [1, 3, 
        18], [1, 8, -7], [1, 8, 17], [1, 15, 0], [1, 15, 10], [1, 16, 
        5], [4, -9, 1], [4, -9, 9], [4, -1, -7], [4, -1, 17], [4, 
        7, -7], [4, 7, 17], [4, 15, 1], [4, 15, 9], [5, -9, 2], [5, -9, 
        8], [5, 0, -7], [5, 0, 17], [5, 6, -7], [5, 6, 17], [5, 15, 2], [5, 
        15, 8], [6, -9, 5], [6, 3, -7], [6, 3, 17], [6, 15, 5], [13, -2, 
        5], [13, -1, 2], [13, -1, 8], [13, 0, 1], [13, 0, 9], [13, 3, 
        0], [13, 3, 10], [13, 6, 1], [13, 6, 9], [13, 7, 2], [13, 7, 
        8], [13, 8, 5], [14, 3, 5]];
These points are lies on the sphere (x - 1)^2 + (y - 3)^2 + (z - 5)^2 = 13^2. How to write the equation of the planes tangent to the sphere at the points in the list? This is some equations.
I tried

restart;
with(geom3d);
L := [[-12, 3, 5], [-11, -2, 5], [-11, -1, 2], [-11, -1, 8], [-11, 0, 1], [-11, 0, 9], [-11, 3, 0], [-11, 3, 10], [-11, 6, 1], [-11, 6, 9], [-11, 7, 2], [-11, 7, 8], [-11, 8, 5], [-4, -9, 5], [-4, 3, -7], [-4, 3, 17], [-4, 15, 5], [-3, -9, 2], [-3, -9, 8], [-3, 0, -7], [-3, 0, 17], [-3, 6, -7], [-3, 6, 17], [-3, 15, 2], [-3, 15, 8], [-2, -9, 1], [-2, -9, 9], [-2, -1, -7], [-2, -1, 17], [-2, 7, -7], [-2, 7, 17], [-2, 15, 1], [-2, 15, 9], [1, -10, 5], [1, -9, 0], [1, -9, 10], [1, -2, -7], [1, -2, 17], [1, 3, -8], [1, 3, 18], [1, 8, -7], [1, 8, 17], [1, 15, 0], [1, 15, 10], [1, 16, 5], [4, -9, 1], [4, -9, 9], [4, -1, -7], [4, -1, 17], [4, 7, -7], [4, 7, 17], [4, 15, 1], [4, 15, 9], [5, -9, 2], [5, -9, 8], [5, 0, -7], [5, 0, 17], [5, 6, -7], [5, 6, 17], [5, 15, 2], [5, 15, 8], [6, -9, 5], [6, 3, -7], [6, 3, 17], [6, 15, 5], [13, -2, 5], [13, -1, 2], [13, -1, 8], [13, 0, 1], [13, 0, 9], [13, 3, 0], [13, 3, 10], [13, 6, 1], [13, 6, 9], [13, 7, 2], [13, 7, 8], [13, 8, 5], [14, 3, 5]];
eqS := Equation(sphere(S, (x - 1)^2 + (y - 3)^2 + (z - 5)^2 - 169 = 0, [x, y, z], 'centername' = T));
k := [seq](sort(Equation(TangentPlane(P, S, point(A, pt[])), [x, y, z])), pt in L);
seq([L[i], k[i]], i = 1 .. nops(L));


I get

With each equation has the form a*x  + b*y + c*x + d=0, how can I get in the form igcd(a,b,c,d) = 1 and a >0. If a = 0, then b>0; If b = 0, then c>0. 

PS. I use this expr := sort(primpart(3*x + 6*y + 12));
expr*signum(lcoeff(expr)) = 0;

But I do not know use it in the seq k

restart``

with(plots); with(RealDomain)

``

c := 1; cr := 0.3e-1*c; u := 1; sExp := 0.6e-1*c; s := .65*c

v := 3*c

``

NULL``

FirmModelHmax := proc (alpha, beta, delta) local q, p, pr, FirmpfSiS, F1, G1, G2, G3, RecpfSiS, sol, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi, h, ps, qs, prs, prof1, prof2; xi := 1; prs := ps-delta*v; prof1 := qs*(ps-c)+(1/2)*(beta^2*xi^2*qs^2/(1-alpha)-(1+beta*xi)^2*qs^2)(ps-s)/u+(prs-sExp)(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))); prof2 := qs*(ps-c)-(1/2)*(ps-s)*qs^2*(prs-sExp)(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha)))/(alpha*u); if alpha <= 1/(1+beta*xi) then [p, q] := solve({diff(prof1, qs) = 0, qs = alpha*u*(v-ps)/(v-s), 0 < ps}, [ps, qs]); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof1, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := G3-(1-alpha)*G2; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 else [p, q] := solve({diff(prof2, qs) = 0, qs = alpha*u*(v-ps)/(v-s), 0 < ps}, [ps, qs]); q := alpha*u*(v-p)/(v-s); F1 := beta*xi*q/(u*(1-alpha)); G1 := (1/2)*q^2/(u*alpha^2); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof2, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := alpha*G1; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 end if; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, h, UnsoldSiS, OldSoldPrim, xi end proc

``

NULL

``

WhyNot3 := proc (alpha, delta) if not [alpha, delta]::(list(numeric)) then return ('procname')(args) end if; FirmModelHmax(alpha, .2, delta)[3] end proc:

pltHmax1 := plot(
  [seq(WhyNot3(alpha, delta),delta=0.1..0.5,0.2)]  
  , alpha=0..2/(2 + 0.2*(1 - sqrt((c - s)/(v - s))))     
  , linestyle=[dot,dashdot,dash]    
  , legend=[seq('delta'=delta,delta=0.1..0.5,0.2)]    
  , legendstyle=[location=left]    
  , labels=["alpha","Firm profit"]    
  , labeldirections =["horizontal", "vertical"]  
  , legendstyle=[location=bottom]
):

display(pltHmax1)

Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 

 

NULL

Download HmaxProc.mw

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