Maple 2024 Questions and Posts

How make a system of equation by using special fa...

Asked by: salim-barzani 1670

January 06 2025

0 4

i want to factoring the (m+G'/G) in my long equation but i use some trick but still i can't get the exactly system and still G will remain in my system what should i factoring for remove this G(xi) from my system is all about factoring , my system of equation are wrong contain G(xi) How i can remove it by taking a factoring or any other technique,

not parameter is arbitrary except V and sigma''

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Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`. See ?protect for details.

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F := sum(e[i]*(m+(diff(G(xi), xi))/G(xi))^i, i = -1 .. 1)

e[-1]/(m+(diff(G(xi), xi))/G(xi))+e[0]+e[1]*(m+(diff(G(xi), xi))/G(xi))

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-e[-1]*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)

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-e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)

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NULL

>	# rewritting rule RR := isolate(m+diff(G(xi), xi)/(G(xi))=Phi, diff(G(xi), xi)/G(xi));

(diff(G(xi), xi))/G(xi) = Phi-m

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>	# Apply RR and collect wrt Phi subs(RR, L): normal(%): PhiN := collect(numer(lhs(%)), phi): PhiD := denom(lhs(%%));

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>	with(LargeExpressions): LLE := collect(PhiN, Phi, Veil[phi] ): LLE / PhiD = 0;

(Phi^6*phi[1]+3*Phi^5*phi[2]-Phi^4*phi[3]-Phi^3*phi[4]-Phi^2*phi[5]+Phi*phi[6]-phi[7])/(Phi^3*G(xi)^4) = 0

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>	# phi[i] coefficients phis := [ seq( phi[i] = simplify(Unveil[phi](phi[i]), size), i=1..LastUsed[phi] ) ]: print~( phis ):

phi[3] = -3*e[1]*G(xi)^4*(-(1/3)*a[1]*k^2+(-e[-1]*(gamma-sigma)*e[1]+(-gamma+sigma)*e[0]^2+(1/3)*w*a[2]-(1/3)*alpha)*k+b*e[-1]*e[1]+b*e[0]^2-(1/3)*w)

phi[4] = (2*e[1]*(V*a[2]-a[1])*(diff(G(xi), xi))^3+3*e[1]*G(xi)*(2*m*mu+lambda)*(V*a[2]-a[1])*(diff(G(xi), xi))^2+e[1]*(V*a[2]-a[1])*G(xi)*((2*m*mu+lambda)^2*G(xi)+3*mu)*(diff(G(xi), xi))+G(xi)^2*(-(6*e[-1]*((-gamma+sigma)*k+b)*e[1]-a[1]*k^2+k*w*a[2]+((-gamma+sigma)*k+b)*e[0]^2-k*alpha-w)*e[0]*G(xi)+e[1]*mu*(2*m*mu+lambda)*(V*a[2]-a[1])))*G(xi)

phi[5] = -3*e[-1]*G(xi)^4*(-(1/3)*a[1]*k^2+(-e[-1]*(gamma-sigma)*e[1]+(-gamma+sigma)*e[0]^2+(1/3)*w*a[2]-(1/3)*alpha)*k+b*e[-1]*e[1]+b*e[0]^2-(1/3)*w)

phi[6] = 4*((1/2)*(V*a[2]-a[1])*(diff(G(xi), xi))^3+(3/2)*(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*G(xi)*(diff(G(xi), xi))^2+(V*a[2]-a[1])*((m*mu+(1/2)*lambda)^2*G(xi)+(3/4)*mu)*G(xi)*(diff(G(xi), xi))+(1/2)*((3/2)*e[0]*((-gamma+sigma)*k+b)*e[-1]*G(xi)+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*mu)*G(xi)^2)*e[-1]*G(xi)

phi[7] = 8*e[-1]*((1/4)*(V*a[2]-a[1])*(diff(G(xi), xi))^4+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*G(xi)*(diff(G(xi), xi))^3+(V*a[2]-a[1])*((m*mu+(1/2)*lambda)^2*G(xi)+(1/2)*mu)*G(xi)*(diff(G(xi), xi))^2+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*mu*G(xi)^2*(diff(G(xi), xi))+(1/4)*(-(1/2)*((-gamma+sigma)*k+b)*e[-1]^2*G(xi)^2+mu^2*(V*a[2]-a[1]))*G(xi)^2)

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>	# WATCHOUT: you have 9 coefficients and so its desirable to have the same number of unknowns unknowns := indets(rhs~(phis), {e[-1],e[0],e[1],'identical'(mu),'identical'(lambda),'identical'(a[1]),'identical'(alpha)}); COEFFS := solve(rhs~(phis), unknowns)

${alpha = alpha, lambda = lambda, mu = mu, a[1] = a[1], e[-1] = 0, e[0] = 0, e[1] = 0}, {alpha = alpha, lambda = lambda, mu = mu, a[1] = -(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2, e[-1] = 0, e[0] = e[0], e[1] = 0}, {alpha = (1/2)*(-G(xi)^4*gamma*k^3*e[-1]^2+G(xi)^4*k^3*sigma*e[-1]^2-4*G(xi)^2*(diff(G(xi), xi))*V*k^2*m*mu^2*a[2]+4*G(xi)*(diff(G(xi), xi))^3*V*k^2*m*mu*a[2]+G(xi)^4*b*k^2*e[-1]^2+4*G(xi)^2*(diff(G(xi), xi))*k*m*mu^2*w*a[2]-4*G(xi)*(diff(G(xi), xi))^3*k*m*mu*w*a[2]-2*G(xi)^2*V*k^2*mu^2*a[2]+2*G(xi)*(diff(G(xi), xi))^2*V*k^2*mu*a[2]-2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*V*k^2*mu*a[2]+2*(diff(G(xi), xi))^4*V*k^2*a[2]+2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*V*k^2*a[2]-4*G(xi)^2*(diff(G(xi), xi))*m*mu^2*w+2*G(xi)^2*k*mu^2*w*a[2]+4*G(xi)*(diff(G(xi), xi))^3*m*mu*w-2*G(xi)*(diff(G(xi), xi))^2*k*mu*w*a[2]+2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*k*mu*w*a[2]-2*(diff(G(xi), xi))^4*k*w*a[2]-2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*k*w*a[2]-2*G(xi)^2*mu^2*w+2*G(xi)*(diff(G(xi), xi))^2*mu*w-2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*mu*w+2*(diff(G(xi), xi))^4*w+2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*w)/((2*m*mu^2*(diff(G(xi), xi))*G(xi)^2-2*m*mu*(diff(G(xi), xi))^3*G(xi)+mu*(diff(G(xi), xi))*G(xi)*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)-(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)+mu^2*G(xi)^2-mu*(diff(G(xi), xi))^2*G(xi)-(diff(G(xi), xi))^4)*k), lambda = RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)/G(xi), mu = mu, a[1] = -(1/2)*(-G(xi)^4*gamma*k*e[-1]^2+G(xi)^4*k*sigma*e[-1]^2-4*G(xi)^2*(diff(G(xi), xi))*V*m*mu^2*a[2]+4*G(xi)*(diff(G(xi), xi))^3*V*m*mu*a[2]+G(xi)^4*b*e[-1]^2-2*G(xi)^2*V*mu^2*a[2]+2*G(xi)*(diff(G(xi), xi))^2*V*mu*a[2]-2*mu*G(xi)*(diff(G(xi), xi))*V*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*a[2]+2*(diff(G(xi), xi))^4*V*a[2]+2*(diff(G(xi), xi))^3*V*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*a[2])/(2*m*mu^2*(diff(G(xi), xi))*G(xi)^2-2*m*mu*(diff(G(xi), xi))^3*G(xi)+mu*(diff(G(xi), xi))*G(xi)*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)-(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)+mu^2*G(xi)^2-mu*(diff(G(xi), xi))^2*G(xi)-(diff(G(xi), xi))^4), e[-1] = e[-1], e[0] = 0, e[1] = 0}$

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>	case1 := COEFFS[2]

${alpha = alpha, lambda = lambda, mu = mu, a[1] = -(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2, e[-1] = 0, e[0] = e[0], e[1] = 0}$

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(-a[2]*V-(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2)*(diff(diff(U(xi), xi), xi))+U(xi)*(((-gamma+sigma)*k+b)*U(xi)^2+k*e[0]^2*gamma-k*e[0]^2*sigma-b*e[0]^2-k*w*a[2]+k*alpha+(w*a[2]-alpha)*k) = 0

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E := diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

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Download G-factoring.mw

system of 1-D PDEs numerically...

Asked by: mayzal 25

January 05 2025

1 8

I’m trying to solve a stiff system 1-D PDEs numerically in Maple but I’m getting the following error:

“Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence”

I included a picture of the PDEs and their BCs in the attached maple file. For easy reading, the attached file includes highlighted sections for parameters and variables. You can skip those to PDEs, BCs and ICs sections at the end of the document to reach the error I’m facing.

For reference, I used another software to solve the system and I was able to get the results in few seconds, so I think it is solvable. However, personally I prefer to use Maple so any inputs, insights, workarounds that I could use to handle the system in Maple would be of great help to me. Thank you.

question.mw

Bug report: Error, (in dsolve) invalid subscript s...

Asked by: nm 11538

December 27 2024

0 2

I do not remember if I reported this before or not. Can't find it. Just in case, I am posting this.

If someone find it is duplicate, feel free to delete this. But this is in latest Maple 2024.2. May be this can be fixed in time by Maple 2025 version.

>

restart;

>	interface(version);

>	Physics:-Version();

>

libname;

$"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"$

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0;

(diff(y(x), x))/y(x)-(3/2)*(4*x^2+y(x)^2+1)/(x*(4*x^2+y(x)^2-2-2*x)) = 0

>	DEtools:-odeadvisor(ode);

>	dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

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restart;

>	infolevel[dsolve]:=5;

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0:

>	dsolve(ode,y(x));

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

trying inverse linear

trying homogeneous types:

trying Chini

differential order: 1; looking for linear symmetries

trying exact

Looking for potential symmetries

trying inverse_Riccati

trying an equivalence to an Abel ODE

equivalence obtained to this Abel ODE: diff(y(x),x) = 3/2*(4*x^2+1)/x/(2*x^2-x-1)*y(x)-(x^2+2*x+3)/x/(2*x^2-x-1)^2*y(x)^2+3/8*(2*x+3)/(2*x^2-x-1)^3/x*y(x)^3

trying to solve the Abel ODE ...

The relative invariant s3 is: -1/432*(8*x^4+40*x^3+45*x^2-270*x+135)/x^3/(x-1)^6/(2*x+1)^4

The first absolute invariant s5^3/s3^5 is: 729/16*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^3/(2*x+1)^4/(8*x^4+40*x^3+45*x^2-270*x+135)^5

The second absolute invariant s3*s7/s5^2 is: 1/3*(8*x^4+40*x^3+45*x^2-270*x+135)*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^2

...checking Abel class AIL (45)

...checking Abel class AIL (310)

...checking Abel class AIR (36)

...checking Abel class AIL (301)

...checking Abel class AIL (1000)

...checking Abel class AIL (42)

...checking Abel class AIL (185)

...checking Abel class AIA (by Halphen)

...checking Abel class AIL (205)

...checking Abel class AIA (147)

...checking Abel class AIL (581)

...checking Abel class AIL (200)

...checking Abel class AIL (257)

...checking Abel class AIL (400)

...checking Abel class AIA (515)

...checking Abel class AIR (1001)

...checking Abel class AIA (201)

...checking Abel class AIA (815)

Looking for potential symmetries

... changing x -> 1/x, trying again

Looking for potential symmetries

The third absolute invariant s5*s7/s3^4 is: 243/16*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(2*x+1)^4*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)/(8*x^4+40*x^3+45*x^2-270*x+135)^4

-> ======================================

-> ...checking Abel class D (by Appell)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {4/27} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class B (by Liouville)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {1, 4, 1/4} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class A (by Abel)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -1/4} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class C (by Abel)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {2, -11676447873119/75975070592769, 9/5, 15632211369872/75439744512117, 46273613050865/52325357771027, 75312059745574/25138886548531} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = 9/5 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.6

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-4, 16} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.8

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -116457391291688/45108305127449, -96869842492381/35485755507516, -36964550865207/94238117721032, -32286830321303/11596568583712, 32286830321303/11596568583712, 36964550865207/94238117721032, 96869842492381/35485755507516, 116457391291688/45108305127449} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.9

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-2/9, -1/9} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.51

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -94917840318055/84247876515289, -85939756880989/51399391393709, -82210125508529/36853933366676, -74381886667083/82545981233858, -41168492684238/33804146399567, -15658703496425/19275443365317, -9175348901453/101481647952193, 3/4, 15/4, 5568553686203/113599855351490, 12774469621703/63437040534358, 17836021821409/102823494563886, 39657708622139/74009717243016, 82495450887526/27663991325651, 86656182727564/45157560524183, 90074893410229/54954593917906, 100200889070747/32282555481919, 113612565327585/103754255779069} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = 15/4 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.5

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-1, 1, -113553630998996/78694251194667, -112790344818825/35834119404842, -104905620984375/18860524785743, -95409943222181/78810323073434, -77648002983645/31218435062578, -67259194033608/9576982470445, -46892223838816/86694928762723, -45901561561111/29768419326991, -34674701564566/6522678435631, 26154715634141/21099761863911, 42841215778132/81925179545457, 52638927823233/15127919203723, 54069389554571/5444364811188, 54445812264368/10328928623117, 56815569067370/40738034746481, 75614540760757/62881656939350, 76459718737483/64786816765621, 85896394925571/88677987470966, 90623073438172/24246571690325, 103628692054633/17857341616628, 117754725919014/60191028908095} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = -1 leads to a useless solution (F does not depend on x)

_____________________________

C = -113553630998996/78694251194667 leads to a useless solution (F does not depend on x)

_____________________________

C = -112790344818825/35834119404842 leads to a useless solution (F does not depend on x)

_____________________________

C = -104905620984375/18860524785743 leads to a useless solution (F does not depend on x)

_____________________________

C = -95409943222181/78810323073434 leads to a useless solution (F does not depend on x)

_____________________________

C = -77648002983645/31218435062578 leads to a useless solution (F does not depend on x)

_____________________________

C = -67259194033608/9576982470445 leads to a useless solution (F does not depend on x)

_____________________________

C = -46892223838816/86694928762723 leads to a useless solution (F does not depend on x)

_____________________________

C = -45901561561111/29768419326991 leads to a useless solution (F does not depend on x)

_____________________________

C = -34674701564566/6522678435631 leads to a useless solution (F does not depend on x)

_____________________________

C = 26154715634141/21099761863911 leads to a useless solution (F does not depend on x)

_____________________________

C = 42841215778132/81925179545457 leads to a useless solution (F does not depend on x)

_____________________________

C = 52638927823233/15127919203723 leads to a useless solution (F does not depend on x)

_____________________________

C = 54069389554571/5444364811188 leads to a useless solution (F does not depend on x)

_____________________________

C = 54445812264368/10328928623117 leads to a useless solution (F does not depend on x)

_____________________________

C = 56815569067370/40738034746481 leads to a useless solution (F does not depend on x)

_____________________________

C = 75614540760757/62881656939350 leads to a useless solution (F does not depend on x)

_____________________________

C = 76459718737483/64786816765621 leads to a useless solution (F does not depend on x)

_____________________________

C = 85896394925571/88677987470966 leads to a useless solution (F does not depend on x)

_____________________________

C = 90623073438172/24246571690325 leads to a useless solution (F does not depend on x)

_____________________________

C = 103628692054633/17857341616628 leads to a useless solution (F does not depend on x)

_____________________________

C = 117754725919014/60191028908095 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.52

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-5, -4, -3, 0, 1, 2, -3/2} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.53

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-3, -1, 1, 2, -3/2, -2/3, -1/2} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = -3 leads to a useless solution (F does not depend on x)

_____________________________

C = -3/2 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

trying to map the Abel into a solvable 2nd order ODE

...checking Abel class AIA 2-parameter, reducible to Riccati

Error, (in dsolve) invalid subscript selector

>

restart;

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0:

>	dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

>	tracelast;

Error, (in dsolve) invalid subscript selector

Download dsolve_invalid_subscript_dec_27_2024.mw

why taking double derivative with two different in...

Asked by: salim-barzani 1670

December 27 2024

0 6

I did a lot of time but this time i don't know why not run any one have idea?

>

(1)

>

(2)

>

(3)

>

(4)

>

(5)

>

Download why.mw

Error, (in dsolve) type `System` does not exist wh...

Asked by: nm 11538

December 26 2024

1 4

I am trying to see if I can get speed up by using dsolve inside thread.

I made very simple example of global list of two differential equations to start with.

Next, created two threads where each picks one ode from the global list to process. So they should in theory run in parallel. The list of ode's is a global list in the worksheet for now.

But I keep getting error when calling dsolve

Error, (in dsolve) type `System` does not exist

I tried also passing the actual ode to the thread, still, same error.

Next, I did not pass anything, but called dsolve directly from inside thread proc on same ode. The ode is local variable inside the proc. I still get same error.

Does this mean dsolve is not supported by threads?

But when I searched this subject, AI says it works in threads:

Everything works OK when I run dsolve in worksheet outside thread (i.e. normally).

I will show below worksheet showing these cases. I must not be doing something right. But what? Can one not pass data from global worksheet to the thread this way? Or does one needs to load something in each thread to make this work?

>	interface(version);

>	Physics:-Version();

>

libname;

$"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"$

Example 1. Passing index of list to thread

>

restart;

>	g_list:=[sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2x(t)=0, diff(y(x),x)=lambdasin(lambdax)y(x)^2+acos(lambdax)^ny(x)-acos(lambda*x)^(n-1)]:

>	work_func:=proc(i::posint) :-dsolve(g_list[i]): end proc:

>	Threads:-Wait( seq( Threads:-Create( work_func(i)), i=1..2) );

Error, (in dsolve) type `System` does not exist

Example 2. Passing actual ode itself to thread

>

restart;

>	g_list:=[sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2x(t)=0, diff(y(x),x)=lambdasin(lambdax)y(x)^2+acos(lambdax)^ny(x)-acos(lambda*x)^(n-1)]:

>	work_func:=proc(ode::`=`) :-dsolve(ode): end proc:

>	Threads:-Wait( seq( Threads:-Create( work_func(g_list[i])), i=1..2) );

Error, (in dsolve) type `System` does not exist

>

Example 3. Normal processing. No threads

>

restart;

>	g_list:=[sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2x(t)=0, diff(y(x),x)=lambdasin(lambdax)y(x)^2+acos(lambdax)^ny(x)-acos(lambda*x)^(n-1)]:

>	work_func:=proc(ode::`=`) :-dsolve(ode): end proc:

>	for item in g_list do work_func(item); od:

>

#no error

>

Example 4. do not pass anything. Just call dsolve

>

restart;

>	work_func:=proc(i::posint) local x,t; local ode:=sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2*x(t)=0; :-dsolve(ode): end proc:

>	Threads:-Wait( seq( Threads:-Create( work_func(i)), i=1..2) );

Error, (in dsolve) type `System` does not exist

>

Download error_dsolve_using_threads_dec_26_2024.mw

implicitplot misbehaves in Maple 2024...

Asked by: Rouben Rostamian 8586

December 26 2024

3 5

>

restart;

Here are the graphs of a parabola and a straight line:

>	plots:-display( plot(x^2, x=-1..1), plot((x+1)/2, x=-1..1), color=["Red","Green"]);

Suppose I want to plot the part of the parabola that lies below

the straight line, and suppose, just to be nasty, I choose to do it

with implicitplot:

>	plots:-implicitplot(y=x^2, x=-1..1, y=0..(x+1)/2);

That is not a parabola at all. [And where does the "ynew" label come from?]

This behavior was introduced in Maple 2022.

In Maple 2021 we get the expected result:

plots:-implicitplot(y=x^2, x=-1..1, y=0..(x+1)/2);

Download mw.mw

How is the simplification achieved...

Asked by: Ronan 1371

December 20 2024

0 2

2024-12-20_Q_simplification_Question.mw
Solve the general cubic. Apply values and simplify.

Could someone show how Maple simplifies to the value of X=3? I tried doing it manually and I could not figure it out.

Also is there a Help assistant to see the setps?

>

restart

>

X^3+a*X=b

(1)

>

>	sol:=solve(X^3+a*X=b,[X])

(2)

>	vals:=[a=6,b=45]

(3)

>	Nans:=(map(eval,sol,vals))

[[X = (1/6)*(4860+12*166617^(1/2))^(1/3)-12/(4860+12*166617^(1/2))^(1/3)], [X = -(1/12)*(4860+12*166617^(1/2))^(1/3)+6/(4860+12*166617^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/6)*(4860+12*166617^(1/2))^(1/3)+12/(4860+12*166617^(1/2))^(1/3))], [X = -(1/12)*(4860+12*166617^(1/2))^(1/3)+6/(4860+12*166617^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/6)*(4860+12*166617^(1/2))^(1/3)+12/(4860+12*166617^(1/2))^(1/3))]]

(4)

>	simplify(Nans)

[[X = 3], [X = (1/4)*(I*3^(1/2)*(180+44*17^(1/2))^(2/3)+(8*I)*3^(1/2)-(180+44*17^(1/2))^(2/3)+8)/(180+44*17^(1/2))^(1/3)], [X = -3/2-((1/2)*I)*51^(1/2)]]

(5)

Download 2024-12-20_Q_simplification_Question.mw

How remove error when changing delta parameter in ...

Asked by: salim-barzani 1670

December 17 2024

0 16

This is my first time working with plotting data from a matrix. However, with the help of a friends on MaplePrimes, I learned how to plot the data in both Maple and MATLAB. Despite this, I am having trouble with visualization. When I change the delta value, my function experiences vibrations or noise, which is clearly visible in the plot. But when I change delta, I encounter errors with my matrix data. How can I fix this problem? and there is any way for get better visualization by Explore ? also How show this vibration or noise in 2D?

>

restart;

>	randomize():

>	local gamma;

(1)

>

T3 := (B[1]*(tanh(2*n^2*(delta^2-w)*k*t/((k*n-1)*(k*n+1))+x)-1))^(1/(2*n))*exp(I*(-k*x+w*t+delta*W(t)-delta^2*t))

(B[1]*(tanh(2*n^2*(delta^2-w)*k*t/((k*n-1)*(k*n+1))+x)-1))^((1/2)/n)*exp(I*(-k*x+w*t+delta*W(t)-delta^2*t))

(2)

>

>	params := {B[1]=1,n=2,delta=1,w=1,k=3 };

(3)

>

insert numerical values

>	solnum :=subs(params, T3);

(4)

>

Warning, the function names {W} are not recognized in the target language

cg = ((tanh(x) - 0.1e1) ^ (0.1e1 / 0.4e1)) * exp(i * (-0.3e1 * x + W(t)));

>	N := 100: use Finance in: Wiener := WienerProcess(): P := PathPlot(Wiener(t), t = 0..10, timesteps = N, replications = 1): end use:

>	W__points := plottools:-getdata(P)[1, -1]: t_grid := convert(W__points[..,1], list): x_grid := [seq(-2..2, 4/N)]:

>	T, X := map(mul, [selectremove(has, [op(expand(solnum))], t)])[]: ST := unapply(eval(T, W(t)=w), w)~(W__points[.., 2]): SX := evalf(unapply(X, x)~(x_grid)): STX := Matrix(N$2, (it, ix) -> ST[it]*SX[ix]);

_rtable[36893490640185799852]

(5)

>

opts := axis[1]=[tickmarks=[seq(k=nprintf("%1.1f", t_grid[k]), k=1..N, 40)]],
        axis[2]=[tickmarks=[seq(k=nprintf("%1.1f", x_grid[k]), k=1..N, 40)]],
        style=surface:

DocumentTools:-Tabulate(
  [
    plots:-matrixplot(Re~(STX), opts),
    plots:-matrixplot(Im~(STX), opts),
plots:-matrixplot(abs~(STX), opts)
  ]
  , width=60
)

(6)

>

(7)

Download data-analysis.mw

Techniques for Simplifying Differential Equations...

Asked by: salim-barzani 1670

December 11 2024

0 0

I'm trying to transform a partial differential equation (PDE) into an ordinary differential equation (ODE) as demonstrated in the paper. However, I find some steps confusing and difficult to follow. The process often feels chaotic, and managing the complexity of the equations is overwhelming. Could you suggest an effective and systematic method to handle such transformations more easily?

>

(1)

>

(2)

>	$tr := {t = tau, x = tauc[0]+xi, Omega(x, t) = U(xi)exp(I(-k(tauc[0]+xi)+wtau+deltaW(tau)-delta^2tau))}$

${t = tau, x = tau*c[0]+xi, Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))}$

(3)

>

Omega(x, t)^m*m*(diff(Omega(x, t), t))/Omega(x, t)

(4)

>

(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m*(-((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))*c[0]+I*U(xi)*(-k*c[0]+w+delta*(diff(W(tau), tau))-delta^2)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))/(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))

(5)

>

pde1 := I*(diff(Omega(x, t)^m, t))+alpha*(diff(Omega(x, t)^m, `$`(x, 2)))+I*beta*(diff(abs(Omega(x, t))^(2*n)*Omega(x, t)^m, x))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*(diff(Omega(x, t)^m, x))+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

(6)

>

(7)

>

(8)

Download transform-pde-to-ode-hard_example.mw

questions about mapole...

Asked by: StudentOne 0

December 10 2024

0 2

Hello sir, how are you?
Sorry to bother you, I needed your help. I have the script from your textbook "3D Graph Equation of Motorcycle run on Maple Software". It's not working. I'd appreciate it if you could take a look.

with(plots);
implicitplot3d(((49.80*x + 19.44*y + 133.2300 - 19.08*sqrt(x^2 + 8.30*x + 19.8469 + y^2 + 3.24*y) - 66.6150*abs(-3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + 0.5625*abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2) = ((((((((((((2 + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(y^2 - 3.18)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24)) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24) + 0.42*abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2) and ((((((((((((2 + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(y^2 - 3.18)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24)) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24) + 0.42*abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2) = 0, x = -7 .. 7, y = -4 .. 3, z = -3 .. 3, numpoints = 350000, style = surface, color = "Niagara Azure");

Why cant I animate images like this? usingdisplay ...

Asked by: nmacsai 280

December 08 2024

0 3

I am trying to animate images generated in a do loop using display and insequence. I get an output but there is no flipping of the image even while I see the frames count flip through the frames. What am I doing wrong? See attached code. Thanks!

Why_cant_I_animate_still_images_like_this.mw

Why do I get this error when solving a union of tw...

Asked by: Saalehorizontale 55

December 08 2024

0 3

Hey guys,

in the attached file you can see my problem. Since Maple was not able to calculate my set with 8 equations, 8 variables and 13 inequalities I had to split in into two steps. Here you can see how I try to take one solutions of what I got with solve onto 8 equations with 8 variables and to solve this together with my inequalities. It never was a problem before. So ow I get a weird error I dont understand.

>

$restart; inequalities := {0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(p-1)*s, 0 < (m*y-1)*n+(m*x-m+1)*(1-p), 0 < (m*x-m-s+1)*p+m*y*(s-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; solve(`union`({k = (x*(1-sqrt(x))+sqrt(x)-2*x)/((x^2-3*x+1)*x), m = (sqrt(x)+x)/(x-1), n = (sqrt(x)+x)/(x-1), p = (-1-sqrt(x))/(x-1), s = (-1-sqrt(x))/(x-1), t = (2*x*(1-sqrt(x))+1+sqrt(x)-5*x)/(x^2-3*x+1), y = 1-sqrt(x)}, inequalities)); inequalities := {0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(p-1)*s, 0 < (m*y-1)*n+(m*x-m+1)*(1-p), 0 < (m*x-m-s+1)*p+m*y*(s-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}$

Error, (in unknown) invalid input: SolveTools:-Inequality expects its 1st argument, eqns, to be of type {list, set}({`<`, `<=`, `=`}), but received [p < 1, -p < 0, And(2*argument((p-1)/p) <= Pi,-Pi < 2*argument((p-1)/p))]

>	$restart; solve(`union`({k = (x(1-sqrt(x))+sqrt(x)-2x)/((x^2-3x+1)x), m = (sqrt(x)+x)/(x-1), n = (sqrt(x)+x)/(x-1), p = (-1-sqrt(x))/(x-1), s = (-1-sqrt(x))/(x-1), t = (2x(1-sqrt(x))+1+sqrt(x)-5x)/(x^2-3x+1), y = 1-sqrt(x)}, {0 < x, 0 < y}))$

${k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), 3/2+(1/2)*5^(1/2) < p}, {k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), 1 < p, p < 3/2+(1/2)*5^(1/2)}, {k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), 1/2 < p, p < (1/2)*5^(1/2)-1/2}, {k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), p < 1, (1/2)*5^(1/2)-1/2 < p}$

(1)

>	$restart; solve(`union`({k = (x(1-sqrt(x))+sqrt(x)-2x)/((x^2-3x+1)x), m = (sqrt(x)+x)/(x-1), n = (sqrt(x)+x)/(x-1), p = (-1-sqrt(x))/(x-1), s = (-1-sqrt(x))/(x-1), t = (2x(1-sqrt(x))+1+sqrt(x)-5x)/(x^2-3x+1), y = 1-sqrt(x)}, {0 < s, 0 < x, 0 < y}))$

Error, (in unknown) invalid input: SolveTools:-Inequality expects its 1st argument, eqns, to be of type {list, set}({`<`, `<=`, `=`}), but received [-p < 0, And(2*argument((p-1)/p) <= Pi,-Pi < 2*argument((p-1)/p))]

So my question is why does this error occur? And what does it mean? the "but received..." argument in the error makes no sense to me. Why does it happen when I add 0<s but 0<x,0<y is okay?

Thank you in advance

Download Why_this_error.mw

Apply Bilinear form for some PDE...

Asked by: salim-barzani 1670

December 03 2024

0 1

I try to get some Bilinear form for some PDE equation and already i have algorithm by writing in lecture but i can't apply i don't what is mistake i did, and i didn't seen some of this lecture code in maple like (myint(expr,var))
i do upload PIcture of algorithm and example which they get Bilinear form

Bilinear.mw

thanks for any help

dsolve gets stuck...

Asked by: Scot Gould 1039

December 02 2024

1 4

dsolve gets stuck on a problem. Attached is the worksheet.

In Case I, dsolve solves the two ODEs separately. In Case II, dsolve solves them together, but only if I define a constant. In Case III the constant is not defined. dsolve never returns, and I have to hit the stop sign. The question I have: Is there a consistent method to the failure so that I can avoid the problem in the future with other ODEs?

dsolve_bug.mw

What "style" are the icons?...

Asked by: Scot Gould 1039

December 01 2024

1 0

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