Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

sys := {diff(b(t),t) = 0,diff(c(t),t) = -b(t)/a(t)};
DEplot(sys, [b(t),c(t)], t=0..5, x=-5..5, y=-5..5);
Error, (in DEtools/DEplot) Option keyword (x) was not in the allowed set of options, consisting of: iterations, arrows, dirgrid, obsrange, scene, colour, linecolour, stepsize, a dependent variable range, a list of initial conditions or one of the allowed plot options: {animate, axes, color, colour, coords, font, scaling, style, symbol, title, view, animatecurves, animatefield, axesfont, dirfield, labelfont, linestyle, numframes, resolution, thickness, tickmarks, titlefont, xtickmarks, ytickmarks}, or one of the allowed dsolve/numeric options: {abserr, control, ctrl, initial, itask, maxder, maxfun, maxkop, maxord, maxpts, maxstep, method, mi..

diff(a(t), t) = diff(a(t), t);
diff(b(t),t) = 0;
diff(c(t),t) = -b(t)/a(t);

[diff(rhs(sol[1][2]), a(t)),diff(rhs(sol[1][2]), b(t)),diff(rhs(sol[1][2]), c(t))];
Error, (in VectorCalculus:-diff) invalid input: diff received a(t), which is not valid for its 2nd argument

 

 

 

eq2 := b(t)*(diff(c(t), t))*(diff(a(t), t))+b(t)*(diff(a(t), t))+a(t)*(diff(c(t), t));
eq3 := a(t)*(diff(b(t), t))(diff(a(t), t))+b(t)*(diff(b(t), t))*(diff(c(t), t));
eq4 := b(t)*(diff(c(t), t))(diff(b(t), t))+a(t)*(diff(b(t), t))+b(t)*(diff(c(t), t));
dfieldplot([eq2,eq3,eq4],[t,x],t=0..5,a=-5..5,b=-5..5,c=-5..5);
dfieldplot([eq2,eq3],[t,x],t=0..5,a=-5..5,b=-5..5);
eq2a := eval(subs(c(t)=exp(t), eq2));
eq3a := eval(subs(c(t)=exp(t), eq3));
eq4a := eval(subs(c(t)=exp(t), eq4));
dfieldplot([eq2a,eq3a], [a(t), b(t)], t = -5 .. 5, a = -5 .. 5, b = -5 .. 5, arrows = SLIM, color = black, dirfield = [10, 10]);

I'm trying to export a worksheet to Latex. I'm able to exprot it. But the long equations are not broken into multiple lines. I have used Mathlinebreaking width 5.0 inch in the export option. But it still does not work. I can see the linebreaking command (\\) in the tex file. But when I compile my latex code the pdf does not have any linebreak. The equation just overflows. Any help will be appreciated. 

Hey,

I think I found a bug concerning the useage of assume and alias:

restart:

alias(a=a(t),b=b(t));

a, b

(1)

assume(a(t),real);

getassumptions(a(t));

{((a(t))(t))::real}

(2)

assume(b(t),real);

getassumptions(a(t));

{((b(t))(t))::real}

(3)

getassumptions(b(t));

{((b(t))(t))::real}

(4)

 

 

 

Commenting out the alias command produces correct results. I am on linux with build 922027.

alias_bug.mw

 from determinant's polynomial?                                                                                                       

I am trying to find a general solution to the 1D-wave equation

Eq1:=diff(u(x,t),t$2)=diff(u(x,t),x$2);

pdsolve(Eq1,HINT=f(x)*g(t)); # Hinting pdsolve gives general solution using separation of variables

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)}); # without HINT and using intial conditions, I get travelling wave solution

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)},HINT=f(x)*g(t)); # Now when I try to use hint and ICs both, pdsolve return nothing.

I want to use separation of variables to find solution to the wave equation.

Any comment?

Thanks

without _Y(t) and DESol?

f := diff(u(t), t$2) + (2/t-1/t^2*p(1/t))*diff(u(t),t) + 1/t^4*q(1/t)*u(t) = 0;
dsolve(f,u(t));
u(t) = DESol({q(1/t)*_Y(t)/t^4+(2/t-p(1/t)/t^2)*(diff(_Y(t), t))+diff(_Y(t), t, t)}, {_Y(t)})

just would like to find u1 and u2 solution

 from galois group function's result?                                     

g[1] := (diff(a(t), t))/(t^2-1) = 1;
g[2] := (diff(a(t), t))*(diff(b(t), t)) = 1;
dsolve({eq2, eq3});
with(DynamicSystems):
sys := DiffEquation([g[1]=1, g[2]=1], inputvariable = [b(t)], outputvariable = [a(t), b(t)]):
ts := 0.1:
t_sim := 10.0:
#in_t := Sine(1, 1, 0, 0):
#in_z := Sine(1, 1, 0, 0, samplecount = round(t_sim/ts), sampletime = ts, discrete):
in_t := t:
sol := Simulate(sys, [in_t]):
p1 := plots[odeplot](sol, [[t, a(t)]], t = 0 .. t_sim, numpoints = 200, color = red):
Error, (in DEtools/convertsys) unable to convert to an explicit first-order system
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

would like to draw the graph of x^2-1

with below sys instead of x^2-1 

sys := {-(1/2)*(-x-1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), b))/x^2+(diff(y(a, b), a))*(diff(y(a, b), b)), (1/2)*(x+1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), a))/x^2+(x^2+x+1)/x^4, (1/2)*(x+1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), a))/x^2-(1/2)*(-x-1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), b))/x^2+(x^2+x+1)/x^4};
IBC:={x=1,y(a,3)=(3-1)*(3+1),y(0,b)=0,y(1,b)=0}:
pds:=pdsolve(sys,IBC,numeric,spacestep=140);
plots[display]([seq(pds:−plot(v,t=i10),i=0..5)]):

 

I'm having trouble with using constrained optimization to solve a problem.

The problem is set up as:

Max: w=x1/2 y1/4

Subject to: K=x+4. K is a constant.

 

I'm not sure where to start.

 from permutation group to permutation group and inverse this mapping?

how to do?

how to find [[1,3,2,4],[1,2]] and [2,3][[1,3,2,4],[1,2]] and [2,4],[[1,3,2,4],[1,2]]?

and why Orbits(G) put permutation group into power, how to display the result of this power group?

i use this or quartic polynomials' resolvent

with(GroupTheory):
G := SpecialUnitaryGroup(3, 1);
Orbits(G);
Orbit(1,G);
Orbit(3,G);

with(GroupTheory):
G := Group({[[1, 2]], [[3, 4]]});
Orbit(G);
G := Group({[[1, 2], [3, 4]]});
Orbit(G);

 

GroupTheory:-PermutationGroup(

{module () local cycles, p, d, work; option object; end module,

module () local cycles, p, d, work; option object; end module},

degree = 4)
Error, invalid input: GroupTheory:-Orbit expects its 1st argument, point, to be of type posint, but received module () local labels, minSupp, maxSupp, suppSize, AtkinsonsAlgorithm, IsSimpleGroupOrder, doDerivedSeries, doLowerCentralSeries, Intersection2, RightCosetRepresentatives, LeftCosetRepresentatives, PRA, `Giant?`, `Even?`, doStab1, doStab, CycleIndexMonomial; export generator_list, n, supergroup, Sylows, pCores, ModulePrint, ModuleDeconstruct, Generators, Orbit, Orbits, IsTransitive, Transitivity, IsPrimitive, GroupOrder, Elements, IsAbelian, IsElementary, IsSimple, ConjugacyClass, ConjugacyClasses, CayleyTable, Centre, DerivedSubgrou...
GroupTheory:-PermutationGroup(

{module () local cycles, p, d, work; option object; end module},

degree = 4)
Error, invalid input: GroupTheory:-Orbit expects its 1st argument, point, to be of type posint, but received module () local labels, minSupp, maxSupp, suppSize, AtkinsonsAlgorithm, IsSimpleGroupOrder, doDerivedSeries, doLowerCentralSeries, Intersection2, RightCosetRepresentatives, LeftCosetRepresentatives, PRA, `Giant?`, `Even?`, doStab1, doStab, CycleIndexMonomial; export generator_list, n, supergroup, Sylows, pCores, ModulePrint, ModuleDeconstruct, Generators, Orbit, Orbits, IsTransitive, Transitivity, IsPrimitive, GroupOrder, Elements, IsAbelian, IsElementary, IsSimple, ConjugacyClass, ConjugacyClasses, CayleyTable, Centre, DerivedSubgrou...

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