Maple 13 Questions and Posts

These are Posts and Questions associated with the product, Maple 13

Hi all,

We want to find a curve fit for an integer sequence.

We have n such that n^2+n+17 is a prime number.

See oeis.org/A007635 and comments.

Use the Maple CurveFitting package.

I tried with(CurveFitting).

We do not know if this is best represented by a polynomial or exponential curve fit.

 

n2_and_n_and_17_in_OEIS_007635.mw

n2_and_n_and_17_in_OEIS_007635.pdf

Regards,

Matt

Since I am a mathematician, I am wondering how Maple goes about solving an identity for 3 functions.
Let's say we have af1(t)+bf_2(t)+cf_3(t) = 0 for all t. How does maple actually find a triplet a,b,c that works for all real t?
It does with solve(identity( ),[a,b,c]). But what is the theory behind it?
We know, of course, a priori, that such a triplet exists.

Thank you!

mapleatha

 



 

I am trying to calculate the following integra   
r*rr*g1^2*h1^2*f1^2*fh1^2*exp(-2*t)/t

here g1 is a kummerM functin in s, and also h1 is another kummerM function  in ss, and f1 and fh1 are the HeunB functions with complex arguments in r and rr. and t=sqrt((r-rr)^2+(s-ss)^2).I would like to integte over dr drr ds dss

How should wirte a while loop for solve nonlinear equations by newton raphson method

why i can not evaluate 29 polynomial. maple try to evaluate last 7hr, how many time required too solve it?

 

hai, 
greetings,

I require help to plot graphs by changing differernt parameters. i am enclosing my codes and sample codes,

 my_codes.mw

nanofluid_sample.mw

Thanks in advance.

How can I activate my maple 13?

I have no activatIon left but installed maple

once

My purchase Code is BNN7VMT4BPFN7ESG

Thank. You 

Hello everyone! I have just started to using Maple 13. I want to solve complex eauation systems.

When I am working on Maple, If I write simple mathematical calculation and then press right click, the context menu open. However, I want to use solve command. Therefore I wrote an eauation after than press right click the context menu will not open. 

What is the reason of this problem? 

In the following problem at two example are given. For Z=2 the sum is converging whereas at Z=4 it is not converging. Thank you

 

PROBLEM.mw


 

restart

`odeλ` := 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), `odeξ`):

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:

`λp1` := 1:

`icsλ1` := lambda(0) = 0, (D(lambda))(0) = `λp1`:

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

 

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

(2)

`lpξ1` := dsolve([`odeξ1`, `icsξ1`], numeric, output = listprocedure, range = teu .. te, events = event1); Xi := eval(xi(tau), `lpξ1`); `Ξp` := eval(diff(xi(tau), tau), `lpξ1`); `odeλ`; `lpλ1` := dsolve([`odeλ`, `icsλ1`], 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

 

`lpξ1`(1)

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

(3)

`λep1` := eval(diff(lambda(tau), tau), lp1); `ξep1` := eval(diff(xi(tau), tau), lp1); `λe1` := eval(lambda(tau), lp1); `ξe1` := 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

I need some help. I'm trying to solve this system of equations, but maple says the solutions may have been lost.

I don't know why. Here are the equations:

I have four equations,very unknown variables in the equation.

I am trying to solve for any 4 unknowns ,not must had be Zoo1.Zoo2.th1.th2,it can be Za1.Za2.Zb1.Zb2.  

Any help  would be greatly appreciated.

I was calculating the total derivative of a function but maple does not respond to the commands like alias,diff,totaldiff etc.

please see the attached pdf.multiplier.pdfmultiplier.pdf

The summation takes too long time. Please help me
 

 

 

 

 

We conjecture that the polynomial h(n) = n^2 + n + 41 is prime for an infinite number of values n.
We furthur conjecture that p(n) = n^2 + 1 is prime an infinite number of times.

I have shown that the set (x,y) with h(y) mod x is congruent to 0 can be written down.  It is p(x,y).  p(x,y) is the set of all divisors of h(n).  See

https://sites.google.com/site/primeproducingpolynomial/

landau.mw

Regards,

Matt

  how can I find equation discribing elliptic intersections and use lagrange to show the higest and lowest value ?    g 

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