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height and width of plot in maple 13...

Asked by: imparter 175
plot
July 05 2018
0  3

how to adjust the height and width of plot in maple 13

plot( x[3]^5, caption = typeset("\n A plot of %1.", x[3]^5), captionfont=[times, 20] );

caption size and font in plot...

Asked by: imparter 175
plot size caption
July 05 2018
0  3

hellow,

can any body help me to  increase the size of the caption in maple plot

plot( x[3]^5, caption = typeset("A plot of %1.", x[3]^5) );

dslove trigger time with rhs(SOL[1](last)...

Asked by: panke 145
ode events differential-equation
June 29 2018
0  6

I want to fetch the trigger time.
I use rhs function.
 

> 

restart; ode := diff(y(x), x) = 1/(y(x)+1); event := [[abs(y(x)+1)-0.1e-1, halt]]
> 

SOL := dsolve([ode, y(0) = 0], numeric, output = listprocedure, range = -10 .. 10, events = event):

Warning, cannot evaluate the solution further left of -.49995006, event #1 triggered a halt

  
> 

``
> 

tlast := rhs(SOL[1](last));

10.

 (1)
> 

NULL

x = 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 := eval(`dsolve/numeric/data/modules`[1]); _solnproc := _dat:-Get("soln_procedure"); _pars := map(rhs, _dat:-Get("params")); 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', "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[1] 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[1], 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", 1, 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", 1, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[1] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[1], 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:-Get("sysvars") end if; if procname <> unknown then return ('procname')(x) else _ndsol := `tools/gensym`("x"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat:-Get("soln_procedures")[1])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(x)))) end if end if; try _res := _solnproc(_xout); _res[1] catch: error end try end proc

 (2)
> 

``


 

Download RHS_TEST.mw

dsolve numeric error ...

Asked by: panke 145
dsolve numeric differential-equations
June 28 2018
1  0


 

> 

restart
> 

`ode&lambda;` := diff(lambda(tau), tau, tau)+2*a*Ep(tau)*(diff(lambda(tau), tau))/(Xi(tau)*a+1) = 0:
> 

th := algsubs((diff(lambda(tau), tau))^2 = (-1-(diff(xi(tau), tau))^2)/(-(xi(tau)*a+1)^2), `ode&xi;`):

a*(diff(xi(tau), tau))^2/(xi(tau)*a+1)+diff(diff(xi(tau), tau), tau)+a/(xi(tau)*a+1) = 0

  

a*(diff(xi(tau), tau))^2/(xi(tau)*a+1)+diff(diff(xi(tau), tau), tau)-a/(xi(tau)*a+1) = 0

 (1)
> 

ds2 := -(xi(tau)*a+1)^2*(diff(lambda(tau), tau))^2+(diff(xi(tau), tau))^2:
> 

`&lambda;p1` := 1:
> 

`ics&lambda;1` := lambda(0) = 0, (D(lambda))(0) = `&lambda;p1`:

xi(0) = (-1+2^(1/2))/a, (D(xi))(0) = 1

  

xi(0) = 1/a, (D(xi))(0) = 2

 (2)
> 

`lp&xi;1` := dsolve([`ode&xi;1`, `ics&xi;1`], numeric, output = listprocedure, range = teu .. te, events = event1); Xi := eval(xi(tau), `lp&xi;1`); `&Xi;p` := eval(diff(xi(tau), tau), `lp&xi;1`); `ode&lambda;`; `lp&lambda;1` := dsolve([`ode&lambda;`, `ics&lambda;1`], numeric, output = listprocedure, range = teu .. te, events = event1)

diff(diff(lambda(tau), tau), tau)+.6*Ep(tau)*(diff(lambda(tau), tau))/(.3*Xi(tau)+1) = 0

  

Error, (in dsolve/numeric/DAE/make_proc) number of unknown functions and equations must match, got 3 functions {Ep, Xi, lambda}, and 1 equations

  
> 

`lp&xi;1`(1)

[tau(1) = 1., (xi(tau))(1) = 2.20293901854199481, (diff(xi(tau), tau))(1) = .670856526448510904]

 (3)
> 

`&lambda;ep1` := eval(diff(lambda(tau), tau), lp1); `&xi;ep1` := eval(diff(xi(tau), tau), lp1); `&lambda;e1` := eval(lambda(tau), lp1); `&xi;e1` := eval(xi(tau), lp1)

proc (tau) 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](tau) else _xout := evalf(tau) end if; _dat := eval(`dsolve/numeric/data/modules`[1]); _solnproc := _dat:-Get("soln_procedure"); _pars := map(rhs, _dat:-Get("params")); if not type(_xout, 'numeric') then if member(tau, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(tau, '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(tau, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(tau, 'string')); if type(_res, 'list') then return _res[4] else return NULL end if elif member(tau, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(tau, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[4], 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(tau), 'string') = rhs(tau); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 4, 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", 4, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[4] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[4], 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(tau), 'string') = rhs(tau)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat:-Get("sysvars") end if; if procname <> unknown then return ('procname')(tau) else _ndsol := `tools/gensym`("xi(tau)"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat:-Get("soln_procedures")[4])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(tau)))) end if end if; try _res := _solnproc(_xout); _res[4] catch: error end try end proc

 (4)
> 

`&lambda;ep2` := eval(diff(lambda(tau), tau), lp2); `&xi;ep2` := eval(diff(xi(tau), tau), lp2); `&lambda;e2` := eval(lambda(tau), lp2); `&xi;e2` := eval(xi(tau), lp2)

proc (tau) 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](tau) else _xout := evalf(tau) end if; _dat := eval(`dsolve/numeric/data/modules`[2]); _solnproc := _dat:-Get("soln_procedure"); _pars := map(rhs, _dat:-Get("params")); if not type(_xout, 'numeric') then if member(tau, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(tau, '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(tau, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(tau, 'string')); if type(_res, 'list') then return _res[4] else return NULL end if elif member(tau, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(tau, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[4], 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(tau), 'string') = rhs(tau); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 4, 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", 4, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[4] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[4], 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(tau), 'string') = rhs(tau)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat:-Get("sysvars") end if; if procname <> unknown then return ('procname')(tau) else _ndsol := `tools/gensym`("xi(tau)"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat:-Get("soln_procedures")[4])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(tau)))) end if end if; try _res := _solnproc(_xout); _res[4] catch: error end try end proc

 (5)
> 

ds2h1 := subs([lambda(tau) = `&lambda;e1`(tau), xi(tau) = `&xi;e1`(tau), diff(lambda(tau), tau) = `&lambda;ep1`(tau), diff(xi(tau), tau) = `&xi;ep1`(tau)], ds2); dse1 := unapply(ds2h1, tau); ds2h2 := subs([lambda(tau) = `&lambda;e2`(tau), xi(tau) = `&xi;e2`(tau), diff(lambda(tau), tau) = `&lambda;ep2`(tau), diff(xi(tau), tau) = `&xi;ep2`(tau)], ds2); dse2 := unapply(ds2h2, tau)
> 

dse1(0); dse2(0)

-.999999999

  

1.000000000

 (6)
> 

> 

``
> 

> 

t := proc (xi, lambda) options operator, arrow; (xi+1/a)*sinh(a*lambda) end proc; x := proc (xi, lambda) options operator, arrow; (xi+1/a)*cosh(a*lambda) end proc; xi0 := 1; teg := 7

1

  

7

 (7)
> 

p1 := plot([[x(xi0, `&lambda;e1`(tau)), t(xi0, `&lambda;e1`(tau)), tau = teu .. te]], legend = ['ds' = -1], color = ["red"]); p2 := plot([[t(xi0, `&lambda;e2`(tau)), x(xi0, `&lambda;e2`(tau)), tau = teu .. te]], legend = ['ds' = 1], color = ["blue"]); p3 := plot([[tau, tau, tau = -teg .. teg], [tau, -tau, tau = -teg .. teg]], color = ["black", "black"], legend = ['ds' = 0, 'ds' = 0])
> 

with(plots); display([p1, p2, p3])

 
> 

> 

NULL
> 

``


 

Download Rindler_simulation_v2.mw

extracting coefficients of exponential functions...

Asked by: guras 100
solve exponential coefficients
June 20 2018
1  2

 

Consider for instance the following equation:

Eq:=(a-4)*exp(4*x)+(b+1)*exp(2*x)+(c-2)=0

How can I list the coefficients of the exponential functions and also solve the equation for the constant parameters 

a, b, and c?

I tried 

[coeffs(collect(lhs(EQ), exp), exp)] =~ 0;

but it did not work. Thank you for your help.

fetch the dsolve event time ...

Asked by: panke 145
events differential-equation dsolve
June 19 2018
1  1

1) How can i get the event time. This example 0.69313.

2) I don't want to see the Warning.How can i do it? 

 

Warning, cannot evaluate the solution further right of .69314729, event #1 triggered a halt

dsolve with event...

Asked by: panke 145
events differential-equation dsolve
June 12 2018
0  10

Why this event dose'nt work ?
S(t) is a state , a parameter
dsolve(...,numeric,events = [[[s(t), a*arcsinh(2/a) < s(t)], halt]]);

Having problems with expansion series (mtaylor)...

Asked by: Mark1993 0
series mtaylor
June 11 2018
0  5

Good evening!!!

Let me briefly describe the problem I've faced recently.

The program (attached) deals with a rather complicated function f depending on parametrs eps1, eps2, eps3, eps4 and variable w. The aim is to expand the function f(w1) into Taylor series with respect to all parametrs (eps1, eps2, eps3, eps4) in order to study its asymptotic behavior as function depending only on k; 0<k<1.

I decided to use mtaylor-function for that problem, which (as I've understood) is the only one to be applied in such cases, but the result was rather unsatisfactory, an error: 

Error, (in gcd/LinZip) input must be polynomials over the integers

Programm code: (1)-(12) only announcing functions....(((, see below
 

> 

f := proc (w) options operator, arrow; -B1+(A1-C1)*w+(B1-D1)*w^2-A1*w^3 end proc

proc (w) options operator, arrow; -B1+(A1-C1)*w+(B1-D1)*w^2-A1*w^3 end proc

 (1)
> 

f1 := proc (w) options operator, arrow; A1-C1+(2*B1-2*D1)*w-3*A1*w^2 end proc

proc (w) options operator, arrow; A1-C1+(2*B1-2*D1)*w-3*A1*w^2 end proc

 (2)
> 

w1 := (B1-D1+sqrt((B1-D1)^2+3*A1*(A1-C1)))/(3*A1)

(1/3)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))/A1

 (3)
> 

f(w1)

-B1+(1/3)*(A1-C1)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))/A1+(1/9)*(B1-D1)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))^2/A1^2-(1/27)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))^3/A1^2

 (4)
> 

s := eps4*sin(l*tau)+(4*(l*sqrt(k/(1-k))+l*eps3)+2*l*((1-2*k)/sqrt(k*(1-k))+eps1))/l^2

eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2

 (5)
> 

A1 := (2*(l*sqrt(k/(1-k))+l*eps3)+l*((1-2*k)/sqrt(k*(1-k))+eps1))/s

(2*l*(k/(1-k))^(1/2)+2*l*eps3+l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)

 (6)
> 

A1 := (2*(l*sqrt(k/(1-k))+l*eps3)+l*((1-2*k)/sqrt(k*(1-k))+eps1))/s

(2*l*(k/(1-k))^(1/2)+2*l*eps3+l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)

 (7)
> 

B1 := 4/s^2

4/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)^2

 (8)
> 

C1 := (((1-2*k)/sqrt(k*(1-k))+eps1)^2+(-(1-2*k)/sqrt(k*(1-k))+eps2)^2)/s^2

(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)^2

 (9)
> 

D1 := (2*((1-2*k)/sqrt(k*(1-k))+eps1))*(-(1-2*k)/sqrt(k*(1-k))+eps2)/s^2

2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)^2

 (10)
> 

l := 1

1

 (11)
> 

f(w1)

-4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(1/3)*((2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)-(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2)*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(16/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4-16*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+4*((1-2*k)/(k*(1-k))^(1/2)+eps1)^2*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)*(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^3)^(1/2))*(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)/(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)+(1/9)*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2)*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(16/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4-16*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+4*((1-2*k)/(k*(1-k))^(1/2)+eps1)^2*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)*(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^3)^(1/2))^2*(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2/(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2-(1/27)*(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(16/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4-16*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+4*((1-2*k)/(k*(1-k))^(1/2)+eps1)^2*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)*(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^3)^(1/2))^3/(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2

 (12)
> 

assume(0 < k and k < 1)
> 

mtaylor(f(w1), [eps1, eps2, eps3, eps4], 2)

Error, (in gcd/LinZip) input must be polynomials over the integers

  
> 

``


Wish you could give some advice on how to improve the situation.

Thanks a lot in advance.

Download res2.mw

 

 

Hold Maple Script...

Asked by: panke 145
pause
June 10 2018
0  7

How can I run Maple Script ,hold it and continue to run it ?
Somethink like Matlab pause statment

Tank you

protected variable...

Asked by: panke 145
assumptions assuming assume
June 08 2018
2  4

I have this maple code:
I want to change

back to α. How can i do it ? (it don't work with unprotect)

 

 

Stop the simulation according to event...

Asked by: panke 145
events differential-equation dsolve
June 08 2018
1  5

I do the numerical simulation with

lp:=dsolve(....,type = numeric, range = ta .. te)

The simulation stop at t=te .

I want to stop the simulation when e.g. x(t) < 0

How can i do it ?

 

Error with display and legend...

Asked by: panke 145
legend plotting display
June 08 2018
1  4

I use
lp1=dsolve(...,numeric)
p1 := odeplot(lp1,....)

new parameter

lp2=dsolve(...,numeric)
p2 := odeplot(lp2,....)

display([p1, p2], legend = ["step", "impulse"])

anf get the error

 

Error, (in plots:-display) display does not accept the legend option

 

 

 

 

Integral not evaluated...

Asked by: radaar 202
integration
June 04 2018
0  8


In the following file when p is a fraction other than 1/2 the integral is not evaluated. Please help

INTEGRAL2.mw
 

 

integral not giving result...

Asked by: radaar 202
integration
June 03 2018
0  5

 

> 

restart; Digits := 7; r := 2.5; Q := proc (n) options operator, arrow; int(simplify(1/(x*r^2*cos(x-y)+z*r^2*sin(z-y))^n, symbolic), y = 0 .. Pi) end proc; HH := eval(Q(5))

int(0.1048576e-3/(x^5*cos(x-1.*y)^5-5.*x^4*cos(x-1.*y)^4*z*sin(-1.*z+y)+10.*x^3*cos(x-1.*y)^3*z^2-10.*x^3*cos(x-1.*y)^3*z^2*cos(-1.*z+y)^2-10.*x^2*cos(x-1.*y)^2*z^3*sin(-1.*z+y)+10.*x^2*cos(x-1.*y)^2*z^3*sin(-1.*z+y)*cos(-1.*z+y)^2+5.*x*cos(x-1.*y)*z^4-10.*x*cos(x-1.*y)*z^4*cos(-1.*z+y)^2+5.*x*cos(x-1.*y)*z^4*cos(-1.*z+y)^4-1.*z^5*sin(-1.*z+y)+2.*z^5*sin(-1.*z+y)*cos(-1.*z+y)^2-1.*z^5*sin(-1.*z+y)*cos(-1.*z+y)^4), y = 0 .. Pi)

 (1)
> 

``


 

Download integral_unknown.mw

 

How to find the solution of differential equations...

Asked by: imparter 175
differential-equations
June 03 2018
0  5

Can any one help to find the value of sigma(r,z) and theta(r,z) from the differential equations analytically, 

ODEs:= <
      diff(theta(r),r$2) = -(1/r)*diff(theta(r),r) - diff(sigma(r),r)*diff(theta(r),r)-diff(theta(r),r)^2,  
   diff(sigma(r),r$2) = -(1/r)*diff(sigma(r),r) -diff(theta(r),r$2)-(1/r)*diff(theta(r),r)>;
boundary conditions

'diff((theta),r)=0','diff((sigma),r)=0'; # at r=0
and theta=0, sigma=0; #at r=h(z) 

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