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Hi everybody!

I am trying to find explicitely the relations between the columns of a matrix

of non-maximal rank. For example, if I have the matrix

M := Matrix([<1,2,3>, <2,4,6>, <5,6,7>]);

I would like that Maple finds that the second column is twice the first one: v_2 = 2*v_1.

How can I do?

Hello All,

(I also sent this fact to Maplesoft Support).

Since I updayed to 2016.1 the F1 key does bring a menu witch send to..F5 only.

No way to have a "full" Help Menu.(See the attached file)

I guess a silly bug jumped in :)

Kind regards,

 

Jean-Michel

 

When Maple 2016 hit the road, I finally relegated my printed Mollier charts and steam tables to a filing cabinet, and moved my carefully-curated spreadsheets of refrigerant properties to a distant part of my hard drive. The new thermophysical data engine rendered those obsolete.

Other than making my desk tidier, what I find exciting is that I can compute with fluid properties in a tool that has numerical integrators, ODE solvers, optimizers, programmatic visualisation and more.

Here are several small examples that demonstrate how you can use fluid properties with Maple’s math and visualization tools (this worksheet contains the complete examples).

Work Done in Compressing a Gas

The work done (per unit mass) in compressing a fluid at constant temperature is

where V1 and V2 are specific volumes and p is pressure.

You need a relationship between pressure and specific volume (either theoretical or experimental) to calculate the work done.

Assuming the ideal gas law, the work done becomes

where R is the ideal gas constant, T is the temperature (in K) and M is the molecular mass (in kg mol-1), and V is the volume.

 Ideal gas constant

Molecular mass of propane

Hence the work done predicted by the Ideal Gas Law is

Let’s now use real fluid properties instead and numerical integrators to compute the work done.

Here, the work done predicted with the Ideal Gas Law and real fluid properties is similar. This isn’t, however, always the case for all gases (try experimenting with ammonia – its strong intermolecular forces result in non-ideal behavior).

Minimum Specific Heat Capacity of Water

The specific heat capacity of water varies with temperature like so.

Let's find the temperature at which the specific heat capacity of water is the lowest.

The lowest specific heat capacity occurs at 309.4 K; this is the temperature at which water requires the least energy to raise or lower its temperature.

Incidentally, this isn’t that far from the standard human body temperature of 310.1 K (given that the human body is largely water, one might hazard a guess why we have evolved to maintain this temperature).

Temperature-Entropy Plot for Water

Maple 2016 generates pressure-enthalpy-temperature charts and psychrometric charts out of the box. However, you can create your own customized thermodynamic visualizations.

This, for example, is a temperature-entropy chart for water, together with the two-phase vapor dome (the worksheet contains the code to generate this plot).

I'm also working on a lumped-parameter heat exchanger model with fluid properties (and hence heat transfer coefficients) that change with temperature. That'll be more complex than these simple examples, and will use Maple's numeric ODE solver.

 

Hello

 

I will try to be as specific as possible.

On my Ti nspire it is possible for me to calculate polar equations like on the buttom picture with the settings on the upper picture. But when I try this in Maple It is not possible. I have worked my way try for two days now and it does not work for me.

Does any body know how to get this solved? 

Regards

Heide

 

An update to Maple 2016 is now available. Maple 2016.1 provides:

  • Updated translations for Simplified and Traditional Chinese,  French, Greek, Japanese, Brazilian Portuguese, and Spanish
  • Updates to the new Maple Workbook
  • Enhancements to Maple’s context-sensitive menus
  • A variety of improvements to the math engine and interface

 

To get this update, use Tools>Check for Updates from within Maple, or visit the Maple 2016.1 downloads page.

 

eithne

Hi,

I'm not sure that I mean datatable component corectly.

I also consider that I was done somthing wrong

Thank you for advanced for any help.

restart

with(DocumentTools):

Oryginaly DataTable was inserted as a 3 x 3. I will traing to push maple to obtain 4 x 4 with specific row and column name.

``

SetProperty("DataTable0", visibleRows, 4);

DocumentTools:-SetProperty("DataTable0", visibleColumns, 4);

DocumentTools:-SetProperty("DataTable0", columnWidths, [20, 40, 80, 80]);

DocumentTools:-SetProperty("DataTable0", rowNames, [r1, r2, r3, r4]);

DocumentTools:-SetProperty("DataTable0", columnNames, [c1, c2, c3, c4]);

DocumentTools:-SetProperty("DataTable0", update)

``

``

``


wzel

Download datatable_problem.mw

The attached worksheet shows a small selection of new and improved results in integration for Maple 2016. Note that integration is a vast topic, so there will always be more improvements that can be made, but be sure that we are working on them.

Maple2016_Integration.mw

A selection of new and improved integration results for Maple 2016

New answers in Maple 2016

 

 

Indefinite integrals:

 

int(sqrt(1+sqrt(z-1)), z);

(4/5)*(1+(z-1)^(1/2))^(5/2)-(4/3)*(1+(z-1)^(1/2))^(3/2)

(1.1)

int(arctan((-1+sec(x))^(1/2))*sin(x), x);

-arctan((-(1/sec(x)-1)*sec(x))^(1/2))/sec(x)+(1/2)*(-1+sec(x))^(1/2)/sec(x)+(1/2)*arctan((-1+sec(x))^(1/2))

(1.2)

int(((1+exp(I*x))^2+(1+exp(-I*x))^2)/(1-2*c*cos(x)+c^2), x);

-x-2*x/c-x/c^2+I*exp(I*x)/c-I*exp(-I*x)/c-I*c*ln(exp(I*x)-1/c)/(c-1)-I*ln(exp(I*x)-1/c)/(c-1)-I*ln(exp(I*x)-1/c)/(c*(c-1))-I*ln(exp(I*x)-1/c)/(c^2*(c-1))+I*c*ln(-c+exp(I*x))/(c-1)+I*ln(-c+exp(I*x))/(c-1)+I*ln(-c+exp(I*x))/(c*(c-1))+I*ln(-c+exp(I*x))/(c^2*(c-1))

(1.3)

int(x^4/arccos(x)^(3/2),x);

(1/4)*(-x^2+1)^(1/2)/arccos(x)^(1/2)-(1/4)*2^(1/2)*Pi^(1/2)*FresnelC(2^(1/2)*arccos(x)^(1/2)/Pi^(1/2))+(3/8)*sin(3*arccos(x))/arccos(x)^(1/2)-(3/8)*2^(1/2)*Pi^(1/2)*3^(1/2)*FresnelC(2^(1/2)*3^(1/2)*arccos(x)^(1/2)/Pi^(1/2))+(1/8)*sin(5*arccos(x))/arccos(x)^(1/2)-(1/8)*2^(1/2)*Pi^(1/2)*5^(1/2)*FresnelC(2^(1/2)*5^(1/2)*arccos(x)^(1/2)/Pi^(1/2))

(1.4)

 

Definite integrals:

int(arcsin(sin(z)), z=0..1);

1/2

(1.5)

int(sqrt(1 - sqrt(1+z)), z=0..1);

((4/5)*I)*(2^(1/2)-1)^(3/2)*2^(1/2)+((8/15)*I)*(2^(1/2)-1)^(3/2)

(1.6)

int(z/(exp(2*z)+4*exp(z)+10),z = 0 .. infinity);

(1/20)*dilog((I*6^(1/2)-3)/(-2+I*6^(1/2)))-((1/60)*I)*6^(1/2)*dilog((I*6^(1/2)-3)/(-2+I*6^(1/2)))+(1/20)*dilog((I*6^(1/2)+3)/(2+I*6^(1/2)))+((1/60)*I)*6^(1/2)*dilog((I*6^(1/2)+3)/(2+I*6^(1/2)))+((1/120)*I)*6^(1/2)*ln(2+I*6^(1/2))^2-((1/120)*I)*6^(1/2)*ln(2-I*6^(1/2))^2+(1/40)*ln(2+I*6^(1/2))^2+(1/40)*ln(2-I*6^(1/2))^2+(1/60)*Pi^2

(1.7)

simplify(int(sinh(a*abs(x-y)), y=0..c, 'method'='FTOC'));

(1/2)*(piecewise(x < 0, 0, 0 <= x, 2*exp(-a*x))+piecewise(x < 0, 0, 0 <= x, -4)+2*piecewise(c <= x, -cosh(a*(-x+c))/a, x < c, (cosh(a*(-x+c))-2)/a)*a-exp(-a*x)+piecewise(x < 0, 0, 0 <= x, 2*exp(a*x))+4-exp(a*x))/a

(1.8)

int(ln(x+y)/(x^2+y), [x=0..infinity, y=0..infinity]);

infinity

(1.9)


Definite integrals with assumptions on the parameters:

int(x^(-ln(x)),x=0..b) assuming b > 0;

(1/2)*erf(ln(b)-1/2)*Pi^(1/2)*exp(1/4)+(1/2)*Pi^(1/2)*exp(1/4)

(1.10)

int(exp(-z)*exp(-I*n*z)*cos(n*z),z = -infinity .. infinity) assuming n::integer;

undefined

(1.11)


Integral of symbolic integer powers of sin(x) or cos(x):

int(sin(x)^n,x) assuming n::integer;

` piecewise`(0 < n, -(Sum((Product(1+1/(n-2*j), j = 1 .. i))*sin(x)^(n-2*i-1), i = 0 .. ceil((1/2)*n)-1))*cos(x)/n+(Product(1-1/(n-2*j), j = 0 .. ceil((1/2)*n)-1))*x, n < 0, (Sum((Product(1-1/(n+2*j+1), j = 0 .. i))*sin(x)^(n+2*i+1), i = 0 .. -ceil((1/2)*n)-1))*cos(x)/n+(Product(1+1/(n+2*j-1), j = 1 .. -ceil((1/2)*n)))*ln(csc(x)-cot(x)), x)

(1.12)

int(cos(x)^n,x) assuming n::negint;

-(Sum((Product(1-1/(n+2*j+1), j = 0 .. i))*cos(x)^(n+2*i+1), i = 0 .. -ceil((1/2)*n)-1))*sin(x)/n+(Product(1+1/(n+2*j-1), j = 1 .. -ceil((1/2)*n)))*ln(sec(x)+tan(x))

(1.13)

int(cos(x)^n,x) assuming n::posint;

(Sum((Product(1+1/(n-2*j), j = 1 .. i))*cos(x)^(n-2*i-1), i = 0 .. ceil((1/2)*n)-1))*sin(x)/n+(Product(1-1/(n-2*j), j = 0 .. ceil((1/2)*n)-1))*x

(1.14)

Improved answers in Maple 2016

 

int(sqrt(1+sqrt(x)), x);

(4/5)*(1+x^(1/2))^(5/2)-(4/3)*(1+x^(1/2))^(3/2)

(2.1)

int(sqrt(1+sqrt(1+z)), z= 0..1);

-(8/15)*2^(1/2)-(8/15)*(1+2^(1/2))^(3/2)+(4/5)*(1+2^(1/2))^(3/2)*2^(1/2)

(2.2)

int(signum(z^k)*exp(-z^2), z=-infinity..infinity) assuming k::real;

(1/2)*(-1)^k*Pi^(1/2)+(1/2)*Pi^(1/2)

(2.3)

int(2*abs(sin(x*p)*sin(x)), x = 0 .. Pi) assuming p> 1;

-2*(sin(Pi*p)*signum(sin(Pi*p))*cos(Pi/p)-p*sin(Pi/p)*cos(Pi*(floor(p)+1)/p)+sin(Pi*(floor(p)+1)/p)*cos(Pi/p)*p-sin(Pi*p)*signum(sin(Pi*p))-sin(Pi*(floor(p)+1)/p)*p+sin(Pi/p)*p)/((cos(Pi/p)-1)*(p^2-1))

(2.4)

int(1/(x^4-x+1), x = 0 .. infinity);

-(sum(ln(-_R)/(4*_R^3-1), _R = RootOf(_Z^4-_Z+1)))

(2.5)


In Maple 2016, this multiple integral is computed over 3 times faster than it was in Maple 2015.

int(exp(abs(x1-x2))*exp(abs(x1-x3))*exp(abs(x3-x4))*exp(abs(x4-x2)), [x1=0..R, x2=0..R, x3=0..R, x4=0..R], AllSolutions) assuming R>0;

(1/8)*exp(4*R)-29/8+(7/2)*exp(2*R)-5*R*exp(2*R)+2*exp(2*R)*R^2-(5/2)*R

(2.6)

Austin Roche
Mathematical Software, Maplesoft


with(PDEtools, casesplit, declare)
``

L := 1651.12; m := 3205.12; r1 := .1875; r2 := 2; z1 := 0; z2 := 12; ld := 4.5

NULL

declare(u(r, z), w(r, z))``

with(DEtools, gensys)

rr := (L+2*m)*(diff(u(r, z), r))+L*(diff(w(r, z), z))+L*u(r, z)/r

zz := L*(diff(u(r, z), r))+(L+2*m)*(diff(w(r, z), z))+L*u(r, z)/r

rz := m*(diff(u(r, z), z))+m*(diff(w(r, z), r))

BCS := {rr(r1, ld) = 0, rz(r1, z) = T, w(r, 0) = 0, zz(r, z2) = 0}

{3205.12*(diff(u(r, z), z))(.1875, z)+3205.12*(diff(w(r, z), r))(.1875, z) = T, 8061.36*(diff(u(r, z), r))(.1875, 4.5)+1651.12*(diff(w(r, z), z))(.1875, 4.5)+1651.12*(u(r, z))(.1875, 4.5)/r(.1875, 4.5) = 0, 1651.12*(diff(u(r, z), r))(r, 12)+8061.36*(diff(w(r, z), z))(r, 12)+1651.12*(u(r, z))(r, 12)/r(r, 12) = 0, w(r, 0) = 0}

(1)

``

NULL

sys3 := [(L+2*m)*(diff(u(r, z), r, r))+(L+m)*(diff(w(r, z), r, z))+(L+2*m)*(diff(u(r, z), r))/r-(L+2*m)*u(r, z)/r^2+m*(diff(u(r, z), z, z)) = 0, (L+m)*(diff(u(r, z), r, z))+m*(diff(w(r, z), r, r))+(L+2*m)*(diff(w(r, z), z, z))+(L+m)*(diff(u(r, z), z))/r+m*(diff(w(r, z), r))/r = 0]

pdsolve(sys3, BCS, numeric)

 

 

``

``


Download PDE_equation2.mw

Hi all,

I have the following PDE, is it solveable by Maple or not. Do I need a boundary condition and how many or I can get a general solution? I am new to Maple. Any help will be appreciated.

Thank you.

 

 

 

Can we get it in MapleSim, not in exactly this form, but in substance? (Not in Maple)
The line of intersection of surfaces:
(x1-0.5) ^ 4 + x2 ^ 4 + x 3 ^ 4-1. ^ 2 = 0.;
x1 ^ 2 + (x2-0.25) ^ 2 + x3 ^ 2-1. ^ 2 = 0.;
(Red) rotates about an axis oX3. During rotation, the line intersects with the fixed sphere ((0., 1.5, 0 .5); R = 1.725). One of the points of intersection is drawn in green. Green Dot and the center of the sphere connected to the blue segment.  In the sphere  of  fixed  trajectory of  the green point.
In other words, the geometric model  3d  cam mechanism and its kinematics.


Here is a simple program.

t:=(a/b)^2*x*y;

st:=cat(``,`t:=`,t,`;`);

fprintf(`outfile`,"%A\n",st);

Running this on Maple 2015 gives a correct Maple statement for t in outfile which can be read into another Maple session.

Running on another computer with Maple 17 gives

t:= || (a^2/b^2*x*y) || ;

in outfile which is not a valid statement.

I know that I can avoid this problem by using the save statement but I want to understand why the code gives the wrong result in Maple 17 and how to change it so it works on both versions.

Thanks.

Hello All.

Why Maple can’t do this Simple indefinite integral?

I'm have a integral :

 

Please compare to Mathematica:

Thanks in advance for your help.

 

I_Mariusz

test.mw

In addition to the Maple 2015.2 and MapleSim 2015.2 updates for Mac, we have just released updates to both Maple and MapleSim for Windows and Linux.

Maple 2015.2a provides a fix for the sum bug reported here.

MapleSim 2015.a provides a variety of interface improvements, and updates to the MapleSim Battery Library and MapleSim CAD Toolbox.

For Mac users, these improvements are included with the Maple 2015.2/MapleSim 2015.2 updates.

All updates are available through the Check for Updates system, and are also available from our website on the downloads section of our website.

eithne

We have just released updates to Maple 2015 and MapleSim 2015 that fix the problems on Mac OS X 10.11 (El Capitan).  If you want to use the new OS, you should update your products.

Updates are available through Check for Updates and from the Downloads section of our website. See Maple 2015.2 and MapleSim 2015.2 for details. MapleSim users, please note that this update also gives you all the new features in MapleSim 2015.2.

If you are using earlier versions of these products, please read the  Maple and MapleSim on Mac OS X 10.11 FAQ for more information about your options.

 

eithne

This is really weird.

restart;
eq:=phi(f(x,y(x),diff(y(x),x)),g(x,y(x),diff(y(x),x)));

Does any one see a "||" in the above? I do not. Then why Maple shows this:

r := cat("dsolve(",eq,",y(x))");

       r:="dsolve("||phi(f(x,y(x),y'(x)),g(x,y(x),y'(x)))||",y(x))"

This is Maple 2015 on windows. Running in worksheet mode

Here is screen shot

 

This problem does not show up all the time. For example, this works ok:

 

No "||" added. The problem with all the above, is that I can't make it all as a string in the first example above. I am trying to make a string of   "dsolve(" + ode + "),y(x)"

Here is the display options

 

thank you

Hello,

 

I'm trying to solve the integral u/(1-u) with Maple and noticed that it returned a result that doesn't accord to the solution I found by hand or the solution from WolframAlpha. This is a screenshot of the weird behaviour:

Does Maple do any weird conversions? Or did I do something wrong or is Maple wrong?

Thanks in advance,

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