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Maple 18 and LaTex...

Asked by: CakePie 30
latex export
April 13 2015
1  2

Hey

As a lot of people before me I'm severely dissappointed my Maple's ability to export a .mw file to .tex.

The output looks horrible and even disappears off the side of the page in some places.

I've searched far and wide on the internet but it's difficult for me to understand the few, outdated, results I've dug up.

 

Is it completely impossible to get my hands on a good (or just working) Maple 18 to LaTex exporter? It's not possible for me to begin coding my own.

anyone interested in collaborating on a Maple proj...

Asked by: mattcanderson1 35
procedure
April 11 2015
0  2

Hi Maple People,

I got stuck trying to write a procedue for my project today.  My topic is Prime Constellations.

If you want to help me, please read my primer on constellations

https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxwcmltZWNvbnN0ZWxsYXRpb25zfGd4OjNmOWZlNWQxZDY2ODY4YmQ

The procedure should refine an offset Vector and increase a multiplier scalar.

 

I want to delay putting the broken procedure until I can simplify it and try again.

Thanks,

Matt Anderson

Please help me to draw a plot...

Asked by: hooshmand 5
April 11 2015
0  5

hi friends

I encountered a problem and I can not draw the plot of this code

> sol := fsolve({diff(S, x) = 0, diff(S, y) = 0}, {x, y});



> with(VectorCalculus);
> with(linalg);
> s1 := evalf(subs(sol, linalg[grad](S, [x, y])));

> with(VectorCalculus);
> with(LinearAlgebra);
> s2 := evalf(subs(sol, linalg[hessian](S, [x, y]))); pmp0 := [x-subs(sol, x), y-subs(sol, y)]; sapprox := s0+evalm(`&*`(`&*`(transpose(pmp0), s2), pmp0));
> with(Statistics);
>
> with(stats); statevalf[icdf, chisquare[4]](.95);

> with(VectorCalculus);
> with(plottools);
> with(plots);
> with(linalg); ellips := {seq(stats*([statevalf[icdf, chisquare[4]]])(c) = sapprox, c = [.5, .95, .999])};
> plots(ellips(x, y), x = 950 .. 1000, y = 700 .. 750, grid = [50, 50], view = [950 .. 1000, 700 .. 750]);

 

 

can you helpe me?Thank you

dsolve method=lsode and range option...

Asked by: bogo 55
dsolve numeric
April 09 2015
0  2

Is it possible to use an option similar to range when using lsode method for dsolve? The ODEs I am trying to solve is stiff and will not work with the flag stiff=true or with method=rosenbrock unless i set Digits:=20. I want to avoid doing that as much as possible, since I believe wit will be very taxing, computationally. I have a very large systeom to solve. I found that method=lsode works with the default Digits=15. 

 

However I need to have the solutions in a given range stored for future access and manipulations. Using range gives me an error: 

Error, (in dsolve/numeric/an_args/lsode) lsode keyword was range, optional keyword must be one of 'ctrl', 'initial', 'itask', 'output', 'procedure', 'procvars', 'start', 'number', 'abserr', 'relerr', 'maxfun', 'minstep', 'maxstep', 'initstep', 'startinit', 'implicit', 'optimize', 'complex'

 

I cannot figure out how to use range or something similar with lsode. Anyone knows? 

pdsolve/Solve for derivatives algebraically (witho...

Asked by: jschulzb 150
pde pdsolve
April 07 2015
0  1

Hi, 

     I have a question regarding pdsolve, or Solve from the PDEtools package. I have a set of equations relating partial derivatives, and I'd like to isolate certain terms without explicitly known the functions. I can do this for a single equation, but not multiple ones. I'm curious if Maple can currently handle a system of eqns like these easily, since I will be increasing the number of eqns in the future. Here's the code 

 

 

> 

restart;
> 

PDEtools:-declare(H=H(x,y,t)):

H(x, y, t)*`will now be displayed as`*H

 (1)
> 

eq1:= H[tt](x,y,t) = H[xx](x,y,t) + H[yy](x,y,t);

H[tt](x, y, t) = H[xx](x, y, t)+H[yy](x, y, t)

 (2)
> 

eq2 := diff(H[tt](x,y,t), t) = diff(H[tx](x,y,t), x) + diff(H[ty](x,y,t), y);

diff(H[tt](x, y, t), t) = diff(H[tx](x, y, t), x)+diff(H[ty](x, y, t), y)

 (3)
> 

eq3 := diff(H[tx](x,y,t), t) = diff(H[xx](x,y,t), x) + diff(H[xy](x,y,t), y);

diff(H[tx](x, y, t), t) = diff(H[xx](x, y, t), x)+diff(H[xy](x, y, t), y)

 (4)
> 

eq4 :=diff(H[ty](x,y,t), t) = diff(H[xy](x,y,t), x) + diff(H[yy](x,y,t), y);

diff(H[ty](x, y, t), t) = diff(H[xy](x, y, t), x)+diff(H[yy](x, y, t), y)

 (5)
> 

PDEtools:-Solve(eq3, H[xy]);

H[xy](x, y, t) = Int(diff(H[tx](x, y, t), t)-(diff(H[xx](x, y, t), x)), y)+_F1(x, t)

 (6)
> 

PDEtools:-Solve({eq1, eq2, eq3, eq4}, H[xy]);

Error, (in pdsolve/sys) the input system cannot contain equations in the arbitrary parameters alone; found equation depending only on {H[tt](x,y,t), H[xx](x,y,t), H[yy](x,y,t)}: H[tt](x,y,t)-H[xx](x,y,t)-H[yy](x,y,t)

  
> 

 
> 

 

 

Download PDESolveHelp.mw

Combinations of numerical solutions from dsolve...

Asked by: bogo 55
dsolve stiff
April 07 2015
0  3

Hi! I am trying to plot and store in memory some specific combinations of the solutions of the systems of ODEs that I get numerically from dsolve for a particular range of the independent variable. 

A particular case for my problem is the following system of stiff ODEs for two unknown functions f[0,0](x) and f[1,0](x) beween xini (where the Initial conditions are defined) and xfin, an arbitrary value of x. Note that rosebrock method does not work, and I can only solve it with lsode[adamsfull] or lsode[backfull]. I am attaching a maple file that shows what I have done.


``

############## System of ODEs that needs to be solved ####################################

xini := .1

.1

 (1)

xfin := 2

2

 (2)

SystemToSolve := diff(f[0, 0](x), x)+(2./x^5+.5000000000/x)*f[0, 0](x) = -15.58845727*sin(.5773502693*x)/x^2+(46.76537182*(3.*sin(.5773502693*x)-1.732050808*x*cos(.5773502693*x)))/x^4, diff(f[1, 0](x), x)+(6./x^5+1.500000000/x)*f[1, 0](x)-1.*f[0, 0](x)/x = (-15.58845727*sin(.5773502693*x)/x^2+(46.76537182*(3.*sin(.5773502693*x)-1.732050808*x*cos(.5773502693*x)))/x^4)*(1.-1.*(1/x^4)^(1/4)*exp(1/x^4)*GAMMA(.7500000000, 1/x^4))-(1.*(-10.39230485*sin(.5773502693*x)/x^2+(31.17691454*(3.*sin(.5773502693*x)-1.732050808*x*cos(.5773502693*x)))/x^4+(4.*((.8660254040*(3.*sin(.5773502693*x)-1.732050808*x*cos(.5773502693*x)))/x+(.8660254040*((3.*(1.-6./x^2))*sin(.5773502693*x)+10.39230485*cos(.5773502693*x)/x))/x))/((1/x^4)^(1/4)*exp(1/x^4)*GAMMA(.7500000000, 1/x^4)*x^5)))*(1/x^4)^(1/4)*exp(1/x^4)*GAMMA(.7500000000, 1/x^4), f[0, 0](xini) = 1.503498546, f[1, 0](xini) = -.5011661819:

 

###################################################################################

 

``

ListProcs := dsolve({SystemToSolve}, numeric, method = lsode[backfull], output = listprocedure):

f00 := eval(f[0, 0](x), ListProcs);

proc (x) local _res, _dat, _solnproc, _xout, _ndsol, _pars, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x) else _xout := evalf(x) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _n, _y0, _ctl, _octl, _reinit, _errcd, _fcn, _i, _yini, _pars, _ini, _par; option `Copyright (c) 2002 by the University of Waterloo. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _ctl := array( 1 .. 34, [( 1 ) = (2), ( 2 ) = (.1), ( 3 ) = (.1), ( 4 ) = (1), ( 5 ) = (1), ( 6 ) = (22), ( 7 ) = (0), ( 9 ) = (-.5011661819), ( 8 ) = (1.503498546), ( 11 ) = (0.1e-6), ( 10 ) = (0.1e-6), ( 13 ) = (0), ( 12 ) = (0), ( 15 ) = (0), ( 14 ) = (0), ( 18 ) = (0), ( 19 ) = (0), ( 16 ) = (0), ( 17 ) = (0), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = (0), ( 21 ) = (0), ( 27 ) = (0), ( 26 ) = (0), ( 25 ) = (0), ( 24 ) = (0), ( 31 ) = (0), ( 30 ) = (0), ( 29 ) = (0), ( 28 ) = (0), ( 32 ) = (0), ( 33 ) = (-1), ( 34 ) = (0) ] ); _octl := array( 1 .. 34, [( 1 ) = (2), ( 2 ) = (.1), ( 3 ) = (.1), ( 4 ) = (1), ( 5 ) = (1), ( 6 ) = (22), ( 7 ) = (0), ( 9 ) = (-.5011661819), ( 8 ) = (1.503498546), ( 11 ) = (0.1e-6), ( 10 ) = (0.1e-6), ( 13 ) = (0), ( 12 ) = (0), ( 15 ) = (0), ( 14 ) = (0), ( 18 ) = (0), ( 19 ) = (0), ( 16 ) = (0), ( 17 ) = (0), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = (0), ( 21 ) = (0), ( 27 ) = (0), ( 26 ) = (0), ( 25 ) = (0), ( 24 ) = (0), ( 31 ) = (0), ( 30 ) = (0), ( 29 ) = (0), ( 28 ) = (0), ( 32 ) = (0), ( 33 ) = (-1), ( 34 ) = (0) ] ); _n := trunc(_ctl[1]); _yini := Array(0..2, {(1) = .1, (2) = 1.503498546}); _y0 := Array(0..2, {(1) = .1, (2) = 1.503498546}); _fcn := proc (N, X, Y, YP) option `[Y[1] = f[0,0](x), Y[2] = f[1,0](x)]`; YP[1] := -15.58845727*sin(.5773502693*X)/X^2+46.76537182*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X^4-(2./X^5+.5000000000/X)*Y[1]; if 1/X^4 < 0 then YP[1] := undefined; return 0 end if; if 1/X^4 < 0 then YP[1] := undefined; return 0 end if; YP[2] := (-15.58845727*sin(.5773502693*X)/X^2+46.76537182*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X^4)*(1.-1.*evalf((1/X^4)^(1/4))*exp(1/X^4)*GAMMA(.7500000000, 1/X^4))-1.*(-10.39230485*sin(.5773502693*X)/X^2+31.17691454*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X^4+4.*(.8660254040*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X+.8660254040*(3.*(1.-6./X^2)*sin(.5773502693*X)+10.39230485*cos(.5773502693*X)/X)/X)*evalf(1/(1/X^4)^(1/4))/(exp(1/X^4)*GAMMA(.7500000000, 1/X^4)*X^5))*evalf((1/X^4)^(1/4))*exp(1/X^4)*GAMMA(.7500000000, 1/X^4)-(6./X^5+1.500000000/X)*Y[2]+1.*Y[1]/X; 0 end proc; _pars := []; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then return _y0[0] elif _xout = "method" then return "lsode" elif _xout = "numfun" then return trunc(_ctl[24+trunc(_ctl[1])]) elif _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _ctl[2]-_y0[0] = 0. then error "no information is available on last computed point" else _xout := _ctl[2] end if elif _xout = "enginedata" then return eval(_octl, 1) elif _xout = "function" then return eval(_fcn, 1) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _yini) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n, _ini, _yini, _pars) end if; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; _octl[2] := _y0[0]; _octl[3] := _y0[0]; for _i to _n do _octl[_i+7] := _y0[_i] end do; for _i to nops(_pars) do _octl[2*_n+30+_i] := _y0[_n+_i] end do; for _i to 34 do _ctl[_i] := _octl[_i] end do; if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] else return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] end if else return "procname" end if end if; if _xout-_y0[0] = 0. then return [seq(_y0[_i], _i = 0 .. _n)] end if; _reinit := false; if _xin <> "last" then if 0 < 0 and `dsolve/numeric/checkglobals`(0, table( [ ] ), _pars, _n, _yini) then _reinit := true; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; for _i to _n do _octl[_i+7] := _y0[_i] end do; for _i to nops(_pars) do _octl[2*_n+30+_i] := _y0[_n+_i] end do end if; if _pars <> [] and select(type, {seq(_yini[_n+_i], _i = 1 .. nops(_pars))}, 'undefined') <> {} then error "parameters must be initialized before solution can be computed" end if end if; if not _reinit and _xout-_ctl[2] = 0 then [_ctl[2], seq(_ctl[_i], _i = 8 .. 7+_n)] else if sign(_xout-_ctl[2]) <> sign(_ctl[2]-_y0[0]) or abs(_xout-_y0[0]) < abs(_xout-_ctl[2]) or _reinit then for _i to 34 do _ctl[_i] := _octl[_i] end do end if; _ctl[3] := _xout; if Digits <= evalhf(Digits) then try _errcd := evalhf(`dsolve/numeric/lsode`(_fcn, var(_ctl))) catch: userinfo(2, `dsolve/debug`, print(`Exception in lsode:`, [lastexception])); if searchtext('evalhf', lastexception[2]) <> 0 or searchtext('real', lastexception[2]) <> 0 or searchtext('hardware', lastexception[2]) <> 0 then _errcd := `dsolve/numeric/lsode`(_fcn, _ctl) else error end if end try else _errcd := `dsolve/numeric/lsode`(_fcn, _ctl) end if; if _errcd < 0 then userinfo(2, {dsolve, `dsolve/lsode`}, `Last values returned:`); userinfo(2, {dsolve, `dsolve/lsode`}, ` t =`, _ctl[2]); _i := 8; userinfo(2, {dsolve, `dsolve/lsode`}, ` y =`, _ctl[_i]); for _i from _i+1 to 7+_n do userinfo(2, {dsolve, `dsolve/lsode`}, ` `, _ctl[_i]) end do; if _errcd+1. = 0. then if _ctl[14+trunc(_ctl[1])] <> 0 then error "an excessive amount of work was done, maxstep may be too small" else error "an excessive amount of work (greater than mxstep) was done" end if elif _errcd+2. = 0. then error "too much accuracy was requested for the machine being used" elif _errcd+3. = 0. then error "illegal input was detected" elif _errcd+4. = 0. then error "repeated error test failures on the attempted step" elif _errcd+5. = 0. then error "repeated convergence test failures on the attempted step" elif _errcd+6. = 0. then error "pure relative error control requested for a variable that has vanished" elif _errcd+7. = 0. then error "cannot evaluate the solution past %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_ctl[2]) else error "unknown error code returned from lsode %1", trunc(_errcd) end if end if; if _Env_smart_dsolve_numeric = true then if _y0[0] < _xout and procname("right") < _xout then procname("right") := _xout elif _xout < _y0[0] and _xout < procname("left") then procname("left") := _xout end if end if; [_xout, seq(_ctl[_i], _i = 8 .. 7+_n)] end if end proc, (2) = Array(1..3, {(1) = 18446744078356217278, (2) = 18446744078356217454, (3) = 18446744078356217630}), (3) = [x, f[0, 0](x), f[1, 0](x)], (4) = []}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(x, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(x, 'string')); if type(_res, 'list') then return _res[2] else return NULL end if elif member(x, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x), 'string') = rhs(x); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 2, rhs(_xout)]) end if elif not type(rhs(_xout), 'list') then error "initial and/or parameter values must be specified in a list" elif lhs(_xout) = "initial_and_parameters" and nops(rhs(_xout)) = nops(_pars)+1 then _res := _solnproc(lhs(_xout) = ["single", 2, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[2] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x), 'string') = rhs(x)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(x) else _ndsol := `tools/gensym`("f[0,0](x)"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat[2][2])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(x)))) end if end if; try _res := _solnproc(_xout); _res[2] catch: error end try end proc

 (3)

f10 := eval(f[1, 0](x), ListProcs);

proc (x) local _res, _dat, _solnproc, _xout, _ndsol, _pars, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x) else _xout := evalf(x) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _n, _y0, _ctl, _octl, _reinit, _errcd, _fcn, _i, _yini, _pars, _ini, _par; option `Copyright (c) 2002 by the University of Waterloo. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _ctl := array( 1 .. 34, [( 1 ) = (2), ( 2 ) = (.1), ( 3 ) = (.1), ( 4 ) = (1), ( 5 ) = (1), ( 6 ) = (22), ( 7 ) = (0), ( 9 ) = (-.5011661819), ( 8 ) = (1.503498546), ( 11 ) = (0.1e-6), ( 10 ) = (0.1e-6), ( 13 ) = (0), ( 12 ) = (0), ( 15 ) = (0), ( 14 ) = (0), ( 18 ) = (0), ( 19 ) = (0), ( 16 ) = (0), ( 17 ) = (0), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = (0), ( 21 ) = (0), ( 27 ) = (0), ( 26 ) = (0), ( 25 ) = (0), ( 24 ) = (0), ( 31 ) = (0), ( 30 ) = (0), ( 29 ) = (0), ( 28 ) = (0), ( 32 ) = (0), ( 33 ) = (-1), ( 34 ) = (0) ] ); _octl := array( 1 .. 34, [( 1 ) = (2), ( 2 ) = (.1), ( 3 ) = (.1), ( 4 ) = (1), ( 5 ) = (1), ( 6 ) = (22), ( 7 ) = (0), ( 9 ) = (-.5011661819), ( 8 ) = (1.503498546), ( 11 ) = (0.1e-6), ( 10 ) = (0.1e-6), ( 13 ) = (0), ( 12 ) = (0), ( 15 ) = (0), ( 14 ) = (0), ( 18 ) = (0), ( 19 ) = (0), ( 16 ) = (0), ( 17 ) = (0), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = (0), ( 21 ) = (0), ( 27 ) = (0), ( 26 ) = (0), ( 25 ) = (0), ( 24 ) = (0), ( 31 ) = (0), ( 30 ) = (0), ( 29 ) = (0), ( 28 ) = (0), ( 32 ) = (0), ( 33 ) = (-1), ( 34 ) = (0) ] ); _n := trunc(_ctl[1]); _yini := Array(0..2, {(1) = .1, (2) = 1.503498546}); _y0 := Array(0..2, {(1) = .1, (2) = 1.503498546}); _fcn := proc (N, X, Y, YP) option `[Y[1] = f[0,0](x), Y[2] = f[1,0](x)]`; YP[1] := -15.58845727*sin(.5773502693*X)/X^2+46.76537182*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X^4-(2./X^5+.5000000000/X)*Y[1]; if 1/X^4 < 0 then YP[1] := undefined; return 0 end if; if 1/X^4 < 0 then YP[1] := undefined; return 0 end if; YP[2] := (-15.58845727*sin(.5773502693*X)/X^2+46.76537182*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X^4)*(1.-1.*evalf((1/X^4)^(1/4))*exp(1/X^4)*GAMMA(.7500000000, 1/X^4))-1.*(-10.39230485*sin(.5773502693*X)/X^2+31.17691454*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X^4+4.*(.8660254040*(3.*sin(.5773502693*X)-1.732050808*X*cos(.5773502693*X))/X+.8660254040*(3.*(1.-6./X^2)*sin(.5773502693*X)+10.39230485*cos(.5773502693*X)/X)/X)*evalf(1/(1/X^4)^(1/4))/(exp(1/X^4)*GAMMA(.7500000000, 1/X^4)*X^5))*evalf((1/X^4)^(1/4))*exp(1/X^4)*GAMMA(.7500000000, 1/X^4)-(6./X^5+1.500000000/X)*Y[2]+1.*Y[1]/X; 0 end proc; _pars := []; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then return _y0[0] elif _xout = "method" then return "lsode" elif _xout = "numfun" then return trunc(_ctl[24+trunc(_ctl[1])]) elif _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _ctl[2]-_y0[0] = 0. then error "no information is available on last computed point" else _xout := _ctl[2] end if elif _xout = "enginedata" then return eval(_octl, 1) elif _xout = "function" then return eval(_fcn, 1) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _yini) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n, _ini, _yini, _pars) end if; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; _octl[2] := _y0[0]; _octl[3] := _y0[0]; for _i to _n do _octl[_i+7] := _y0[_i] end do; for _i to nops(_pars) do _octl[2*_n+30+_i] := _y0[_n+_i] end do; for _i to 34 do _ctl[_i] := _octl[_i] end do; if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] else return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] end if else return "procname" end if end if; if _xout-_y0[0] = 0. then return [seq(_y0[_i], _i = 0 .. _n)] end if; _reinit := false; if _xin <> "last" then if 0 < 0 and `dsolve/numeric/checkglobals`(0, table( [ ] ), _pars, _n, _yini) then _reinit := true; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; for _i to _n do _octl[_i+7] := _y0[_i] end do; for _i to nops(_pars) do _octl[2*_n+30+_i] := _y0[_n+_i] end do end if; if _pars <> [] and select(type, {seq(_yini[_n+_i], _i = 1 .. nops(_pars))}, 'undefined') <> {} then error "parameters must be initialized before solution can be computed" end if end if; if not _reinit and _xout-_ctl[2] = 0 then [_ctl[2], seq(_ctl[_i], _i = 8 .. 7+_n)] else if sign(_xout-_ctl[2]) <> sign(_ctl[2]-_y0[0]) or abs(_xout-_y0[0]) < abs(_xout-_ctl[2]) or _reinit then for _i to 34 do _ctl[_i] := _octl[_i] end do end if; _ctl[3] := _xout; if Digits <= evalhf(Digits) then try _errcd := evalhf(`dsolve/numeric/lsode`(_fcn, var(_ctl))) catch: userinfo(2, `dsolve/debug`, print(`Exception in lsode:`, [lastexception])); if searchtext('evalhf', lastexception[2]) <> 0 or searchtext('real', lastexception[2]) <> 0 or searchtext('hardware', lastexception[2]) <> 0 then _errcd := `dsolve/numeric/lsode`(_fcn, _ctl) else error end if end try else _errcd := `dsolve/numeric/lsode`(_fcn, _ctl) end if; if _errcd < 0 then userinfo(2, {dsolve, `dsolve/lsode`}, `Last values returned:`); userinfo(2, {dsolve, `dsolve/lsode`}, ` t =`, _ctl[2]); _i := 8; userinfo(2, {dsolve, `dsolve/lsode`}, ` y =`, _ctl[_i]); for _i from _i+1 to 7+_n do userinfo(2, {dsolve, `dsolve/lsode`}, ` `, _ctl[_i]) end do; if _errcd+1. = 0. then if _ctl[14+trunc(_ctl[1])] <> 0 then error "an excessive amount of work was done, maxstep may be too small" else error "an excessive amount of work (greater than mxstep) was done" end if elif _errcd+2. = 0. then error "too much accuracy was requested for the machine being used" elif _errcd+3. = 0. then error "illegal input was detected" elif _errcd+4. = 0. then error "repeated error test failures on the attempted step" elif _errcd+5. = 0. then error "repeated convergence test failures on the attempted step" elif _errcd+6. = 0. then error "pure relative error control requested for a variable that has vanished" elif _errcd+7. = 0. then error "cannot evaluate the solution past %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_ctl[2]) else error "unknown error code returned from lsode %1", trunc(_errcd) end if end if; if _Env_smart_dsolve_numeric = true then if _y0[0] < _xout and procname("right") < _xout then procname("right") := _xout elif _xout < _y0[0] and _xout < procname("left") then procname("left") := _xout end if end if; [_xout, seq(_ctl[_i], _i = 8 .. 7+_n)] end if end proc, (2) = Array(1..3, {(1) = 18446744078356217278, (2) = 18446744078356217454, (3) = 18446744078356217630}), (3) = [x, f[0, 0](x), f[1, 0](x)], (4) = []}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(x, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(x, 'string')); if type(_res, 'list') then return _res[3] else return NULL end if elif member(x, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[3], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x), 'string') = rhs(x); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 3, rhs(_xout)]) end if elif not type(rhs(_xout), 'list') then error "initial and/or parameter values must be specified in a list" elif lhs(_xout) = "initial_and_parameters" and nops(rhs(_xout)) = nops(_pars)+1 then _res := _solnproc(lhs(_xout) = ["single", 3, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[3] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[3], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x), 'string') = rhs(x)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(x) else _ndsol := `tools/gensym`("f[1,0](x)"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat[2][3])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(x)))) end if end if; try _res := _solnproc(_xout); _res[3] catch: error end try end proc

 (4)

ftoplot := unapply(f00(x)+0.45e-1*f10(x)/x^(3/2), x)

proc (x) options operator, arrow; f00(x)+0.45e-1*f10(x)/x^(3/2) end proc

 (5)

``

plot(ftoplot(x), x = xini .. xfin)

  

``


Download Test2ODEs.mw

The approach in that file works, however I have a question regarding the efficiency of my method, since I plan to extend the system to many more ODEs besides just 2 and also extend the range to a larger xfin. In this method, since I define the function to plot in terms of f01 and f02, wich are procedures, does this mean that for each x on the grid for the plot(ftoplot,x=xini..xfin) maple actually computes the solutions f00(x) and f01(x) and then forms the ftoplot combination and plots that specific point? If the default sampling of my interval is, say 1000 points, does it mean that the way I wrote it I will have 1000 invocations of the dsolve procedure, for each x in the sample? I am not sure, it seems to me that is the case. This would imply that instead of advancing the solution at each step maple starts over again from xini. How could I just avoid this behavior and instead have access to the values of ftoplot(x) in the range xini to xfin stored from one invocation of dsolve? 

 

The ideal scenario for me would be to have f[0,0](x) and f[0,1](x) stored as an interpolated function between xini and xfin from the solutions of one invocation of dsolve prior to defining ftoplot. Can this be achieved in principle? How? Remember, i have to use method=lsode and range is not accepted.  

 

Error, invalid input: with expects...

Asked by: bfathi 10
April 07 2015
0  6

hi friends

After this cods i see very error

 > restart;

read(orbit.sav ): whit(plots):
ax := -G*Mz*x/(x^2+y^2)^(3/2);
ay := -G*Mz*y/(x^2+y^2)^(3/2);
i := 'i'; j := i+1;
for k from 0 to 3 do
x := 7*10^6; Vx := 0;
y := 0; Vy := 9000;
dt := evalf(1/2^k);
for i from 0 to 328 do
X[i] := evalf(x); Y[i] := evalf(y);
for n to 40*2^k do
x := evalf((1/2)*ax*dt^2+Vx*dt+x); y := evalf((1/2)*ay*dt^2+Vy*dt+y);
Vx := evalf(ax*dt+Vx); Vy := evalf(ay*dt+Vy)
od;
if i mod 41= 0 then
dX[k, i] := X[i]-XS[j]; dY[k, i] := Y[i]-YS[j]
fi
od;
p[k] := plot([seq([(X[i]-XS[j])*(1/1000), (Y[i]-YS[j])*(1/1000)], i = 0 .. 328)], color = green) end do;
p1 := display({seq(p[k], k = 0 .. 3)}, thickness = 3)
SI := [seq(41*i, i = 0 .. 8)]
p2 := plot({seq([seq([(1/1000)*dX[k, i], (1/1000)*dY[k, i]], k = 0 .. 1), [0, 0]], i = SI)}, color = black)
display({p1, p2}, scaling = constrained, labels = ['dx', 'dy'])
display({p1, p2}, view = [-.1 .. .5, -.4 .. .2], scaling = constrained, labels = ['dx', 'dy'])

can you help me Please?

Thank you

 

 

 

how to using maple code convert to mathematica cod...

Asked by: candy898 60
convert mathematica
April 06 2015
0  2

Does anyone know how to using some softward convert ?  for example  I have maple code , but I want to using mathematica code .I need fast way.

There is no Startup Code Menu Item in Maple 13...

Asked by: mapleatha 160
startup
April 05 2015
1  3

There is no menu item called "Startup Code"

in the "Edit" menu item of my Maple 13.

Please help!

 

Thanks!

Why does Maple not use the +C at the end of an ind...

Asked by: Brent Williams 40
April 04 2015
0  4

We're starting on indefinite integrals in my 1st year calculus class.

 

A quick example would be int(sin(x), x);=-cos(x)+C

 

Maple doesn't add the +C on the end of it's solution. Can someone explain or point me to a resource? I've tried searching but I can't find an answer. 

Request to provide Maple procedure for iterated in...

Asked by: ANANDMUNAGALA 175
April 04 2015
0  5

compute the cdf of a piecewise probability distrib...

Asked by: GPY 80
April 01 2015
1  1

This should be trivial but I am not able to figure out the right syntax to execute it

The pdf is given by :

f_X(x)={ 1/25 *x, 0<=x<5

             2/5 -x/25, 5<=x<10

             0, otherwise

I have tried to use the "CumulativeDistributiveFunction" so far

Most Optimal dsolve method for the following syste...

Asked by: bogo 55
dsolve stiff
April 01 2015
1  4

Hi!

 

I am trying to solve a large nxl system of coupled differential equations. Maple seems to have trouble even for small n's so I wanted to know if anyone has any suggestions. Take the case of the following system of ODEs for my unknown functions f[0,0](x) and f[1,0](x). 

 

ODEs:= {diff(f[0, 0](x), x)+2.*f[0, 0](x)/x^5+.5000000000*f[0, 0](x)/x = -15.58845727*sin(.5773502693*x)/x^2+140.2961154*sin(.5773502693*x)/x^4-81.*cos(.5773502693*x)/x^3, diff(f[1, 0](x), x)+6.*f[1, 0](x)/x^5+1.500000000*f[1, 0](x)/x-1.*f[0, 0](x)/x = -15.58845727*sin(.5773502693*x)/x^2+25.98076212*sin(.5773502693*x)*(1/x^4)^(1/4)*exp(1/x^4)*GAMMA(.7500000000, 1/x^4)/x^2+140.2961154*sin(.5773502693*x)/x^4-233.8268591*sin(.5773502693*x)*(1/x^4)^(1/4)*exp(1/x^4)*GAMMA(.7500000000, 1/x^4)/x^4-81.*cos(.5773502693*x)/x^3+135.*cos(.5773502693*x)*(1/x^4)^(1/4)*exp(1/x^4)*GAMMA(.7500000000, 1/x^4)/x^3-20.78460970*sin(.5773502693*x)/x^6+6.000000004*cos(.5773502693*x)/x^5+62.35382908*sin(.5773502693*x)/x^8-36.00000002*cos(.5773502693*x)/x^7, f[0, 0](.1) = 1.503497680, f[1, 0](.1) = -.5011660086}

 

 

Following Preben Alsholm's suggestion from my previous thread I am using lsode[adamsfull], since no other method i have tried worked for this problem. I am currently using:

 

Sollsodefull:=dsolve({ODEs}, numeric, method = lsode[adamsfull])

 

and it seems to work. I am wondering if there is a way to optimize this, as I will be extending my problem to n and l much larger than order unity numbers, therefore my system will contain about 10^4-10^5 equations. Solving this symple system of 2 equations takes a bit less than a second, but still it takes some time for the processor on my MBP. I am affraid it will be a nightmare for the full problem. Whats the most optimal dsolve option for this kind of problem? Any ideas?

 

I have also attempted dverk78, rkf45,rosenbrock, lsode(without the adamsfull option), and all failed for this particular system. Errors were:

1. For rkf45: Error, (in f00) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

2. For dverk78: Error, (in Soldverk78) cannot evaluate the solution past .1, step size < hmin, problem may be singular or error tolerance may be too small

3. For rosenbrock: Error, (in dsolve/numeric/SC/firststep) unable to evaluate the partial derivatives of f(x,y) for stiff solution

4. For lsode without [adamsfull]: Error, (in Sollsode) an excessive amount of work (greater than mxstep) was done

5. For default method with stiff=true and inplicit=true options: Error, (in dsolve/numeric/SC/firststep) unable to evaluate the partial derivatives of f(x,y) for stiff solution

Compiler "Error, (in Compiler:-Compile) compiler e...

Asked by: jockoflocko 35
compiler
April 01 2015
0  3

Dear all,

I want to use the Maple Compiler to improve the performance of some of my codes. To get used to it, I tried doing the examples from the ?Compiler help-page, but everytime I run the compiler, I get the error message:

"Error, (in Compiler:-Compile) compiler exited with nonzero status 1: 

Do some of you know a possible reason for this?

Thank you all.

Download test.mw

Shared variables between Maplesim and Maple...

Asked by: EngM 60
March 31 2015
1  1

Hello, 

is there a way I can use data (variables) from Maple environment in the Maplesim environment. 

I have a scirpt in maple that generates the robots joints angles and need to use them in the 3D robot built in maplesim. I know I can export/Import data, but this sounds redundant. Is there a way to simply use an input block as a source of the data in maplesim and have the variable name generated in maple used int. Similar to what Matlab/Simulink does.. 

 

 

thanks.

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