Product Suggestions

Post your suggestions on new features and products.

Let us look in RealDomain and then in the RealDomain:-solve command. One is addressed to the usual solve command. The commands of the RealDomain package are not still documented since Maple 7 when the package was introduced. There is a general description only 

  • By default, Maple performs computations under the assumption that the underlying number system is the complex field. The RealDomain package provides an environment in which computations are performed under the assumption that the basic underlying number system is the field of real numbers.
  • Results returned by procedures are postprocessed by discarding values containing any detectable non-real answers or replacing them with undefined where appropriate.

The above is not enough. Here is an example which confuses me: 

RealDomain:-solve(exp(I*x) = -1, AllSolutions);
NULL

though 

solve(exp(I*x) = -1, AllSolutions);
                         Pi (2 _Z1 + 1)

and 

RealDomain:-solve(exp(I*x) = -1);
                               Pi

I lie awake thinking about that. Maplesoft staff help me!


 

I found a strange bug in int.
For some functions f(x), Maple is able to compute the antiderivative (correctly) but refuses to compute the definite integral.
Or, computes the integral over 0..1  and  0..2  but refuses to compute over 1..2.

int(exp(x^3), x);  #ok

-(1/3)*(-1)^(2/3)*((2/3)*x*(-1)^(1/3)*Pi*3^(1/2)/(GAMMA(2/3)*(-x^3)^(1/3))-x*(-1)^(1/3)*GAMMA(1/3, -x^3)/(-x^3)^(1/3))

(1)

int(exp(x^3), x=1..2); #?

int(exp(x^3), x = 1 .. 2)

(2)

int(exp(x^3), x=1..2, method=FTOC); #??

int(exp(x^3), x = 1 .. 2, method = FTOC)

(3)

int(exp(x^3), x=0..2); #?

int(exp(x^3), x = 0 .. 2)

(4)

int(exp(-x^3), x);  #ok

(3/4)*x*exp(-(1/2)*x^3)*WhittakerM(1/6, 2/3, x^3)/(x^3)^(1/6)+exp(-(1/2)*x^3)*WhittakerM(7/6, 2/3, x^3)/(x^2*(x^3)^(1/6))

(5)

int(exp(-x^3), x=0..2);  #ok

(3/4)*2^(1/2)*exp(-4)*WhittakerM(1/6, 2/3, 8)+(1/8)*2^(1/2)*exp(-4)*WhittakerM(7/6, 2/3, 8)

(6)

int(exp(-x^3), x=0..1);  #ok

(3/4)*exp(-1/2)*WhittakerM(1/6, 2/3, 1)+exp(-1/2)*WhittakerM(7/6, 2/3, 1)

(7)

int(exp(-x^3), x=1 .. 2);  #???

int(exp(-x^3), x = 1 .. 2)

(8)


 

Download !strange-bug-int.mw

Correct computatiton for

for reasonable expressions f(x,y), g(x,y) would be very useful in double integrals.

For the moment this is not possible. Too many bugs:

int(Heaviside(1-x^2-y^2), x=-infinity..infinity, y=-infinity..infinity); #should be Pi
                           undefined
int(Heaviside(1-x^2-y^2), x=-1..1, y=-1..1); #should be Pi
                               0
int(Heaviside(y-x^2), x=-1..1, y=-1..1); #should be 4/3
                               -2

int(Heaviside(y-x^2), y=-1..1, x=-1..1); #This one is OK!
                              4/3

 

 

 

 

In order to change Maple for the better, I use to submit SCRs. However, as i was kindly
informed by Bryon (a copy of his e-letter on demand), MaplePrimes are under reconstruction and do not
work properly. At least my three messages sent through the Contact button were lost.
I have  unsuccessfully tried to reach beta.maplesoft.com (see the result of ping in the screen screen.29.08.16.docx).
Please, help me!

Hi,

In the following example I introduce some commutation rules that are standard in Quantum Mechanics. A major feature of the Maple Physics Package, is that it is possible to define tensors as Quantum Operators. This is of great interest because powerful tensor simplification rules can then be used in Quantum Mechanics. For an example, see the commutation rules of the components of the angular momentum operator in ?Physics,Examples. Here, I focus on a possible issue: when destroying all quantum operators, the pre-defined commutation rules still apply, which should not be the case. As shown in the post, this is link to the fact that these operators are also tensors.
 

NULL

 

Physics:-Version()[2]

`2016, August 16, 18:56 hours`

(1)

NULL

NULL

restart; with(Physics); interface(imaginaryunit = I)

First, set a 3D Euclidian space

Setup(mathematicalnotation = true, dimension = 3, signature = `+`, spacetimeindices = lowercaselatin, quiet)

[dimension = 3, mathematicalnotation = true, signature = `+ + +`, spacetimeindices = lowercaselatin]

(2)

Define two rank 1 tensors

Define(x[k], p[k])

`Defined objects with tensor properties`

 

{Physics:-Dgamma[a], Physics:-Psigma[a], Physics:-d_[a], Physics:-g_[a, b], p[k], x[k], Physics:-KroneckerDelta[a, b], Physics:-LeviCivita[a, b, c]}

(3)

Now, further define these tensors as quantum operators and gives the usual commutation rule between position and momentum operators (Quantum Mechanics).

Setup(hermitianoperators = {p, x}, algebrarules = {%Commutator(p[k], p[n]) = 0, %Commutator(x[k], p[l]) = I*`ℏ`*KroneckerDelta[k, l], %Commutator(x[k], x[l]) = 0}, realobjects = {`ℏ`})

[algebrarules = {%Commutator(p[k], p[n]) = 0, %Commutator(x[k], p[l]) = I*`ℏ`*Physics:-KroneckerDelta[k, l], %Commutator(x[k], x[l]) = 0}, hermitianoperators = {p, x}, realobjects = {`ℏ`}]

(4)

As expected:

(%Commutator = Commutator)(p[a], x[b])

%Commutator(p[a], x[b]) = -I*`ℏ`*Physics:-KroneckerDelta[a, b]

(5)

Now, reset all the Hermitian operators, so that all quantum operators are destroyed. This is useful if, for instance, one needs to compare some the result with the commutative case.

Setup(redo, hermitianoperators = {})

[hermitianoperators = none]

(6)

As expected, there are no quantum operators anymore...

Setup(quantumoperators)

[quantumoperators = {}]

(7)

...so that the following expressions should commute (result should be true)

Library:-Commute(p[a], x[b])

false

(8)

Result should be 0NULL

Commutator(p[a], x[b])

-I*`ℏ`*Physics:-KroneckerDelta[a, b]

(9)

p[a], x[b]

p[a], x[b]

(10)

NULL

NULL

``

NULLNULL

Below is just a copy & paste of the above section. The only difference, is that "Define(x[k], p[k])" has been commented, so that x[k]and p[k] are not a tensor. In that case, everything behaves as expected (but of course, the interesting feature of tensors is not available).

````

NULL

restart; with(Physics); interface(imaginaryunit = I)

First, set a 3D Euclidian space

Physics:-Setup(mathematicalnotation = true, dimension = 3, signature = `+`, spacetimeindices = lowercaselatin, quiet)

[dimension = 3, mathematicalnotation = true, signature = `+ + +`, spacetimeindices = lowercaselatin]

(11)

#Define two rank 1 tensors

Now, further define these tensors as quantum operators and gives the usual commutation rule between position and momentum operators (Quantum Mechanics)

Physics:-Setup(hermitianoperators = {p, x}, algebrarules = {%Commutator(p[k], p[n]) = 0, %Commutator(x[k], p[l]) = Physics:-`*`(Physics:-`*`(I, `ℏ`), Physics:-KroneckerDelta[k, l]), %Commutator(x[k], x[l]) = 0}, realobjects = {`ℏ`})

[algebrarules = {%Commutator(p[k], p[n]) = 0, %Commutator(x[k], p[l]) = I*`ℏ`*Physics:-KroneckerDelta[k, l], %Commutator(x[k], x[l]) = 0}, hermitianoperators = {p, x}, realobjects = {`ℏ`}]

(12)

As expected:

(%Commutator = Physics:-Commutator)(p[a], x[b])

%Commutator(p[a], x[b]) = -I*`ℏ`*Physics:-KroneckerDelta[a, b]

(13)

Now, reset all the Hermitian operators, so that all quantum operators are destroyed.

Physics:-Setup(redo, hermitianoperators = {})

[hermitianoperators = none]

(14)

As expected, there are no quantum operators anymore...

Physics:-Setup(quantumoperators)

[quantumoperators = {}]

(15)

...so that the following expressions should commute (result should be true)

Physics:-Library:-Commute(p[a], x[b])

true

(16)

Result should be 0``

Physics:-Commutator(p[a], x[b])

0

(17)

p[a], x[b]

p[a], x[b]

(18)

NULL

``

NULL``

NULL


Download Quantum_operator_as_Tensors_August_23_2016.mw

A more honest and specific version of lemma 3.

CONGRUENT_FUNCTIONS_OF_THE_FRACTIONAL_PART_OVER_Q_LEMMA_4.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/CONGRUENT_FUNCTIONS_OF_THE_FRACTIONAL_PART_OVER_Q_LEMMA_4.mw .

Download CONGRUENT_FUNCTIONS_OF_THE_FRACTIONAL_PART_OVER_Q_LEMMA_4.mw

Using a mouse's back/forward buttons or alt+ left arrow/ alt+right arrow did not work in Maple 2015 and they still don't work in Maple 2016. 

Also, if you select anywhere in the search bar, it automatically selects all the words.  I sometimes (most the time) want to change only one word.  

Im using x64 Windows 10 and it also did it when running Windows 8/8.1 .   Does anybody else have this problem?

Can it be fixed please if not?

If you try and scroll a page up or down, it just selects the content.  How hard would it be to fix this?

It would be nice if the StringTools package had a function giving the number of primitive words of length n on an alphabet of size a.  The formula for this is well-known but tedious to code.

      General description of the method of solving underdetermined systems of equations. As a particular application of the idea proposed a universal method  kinematic analysis for all kinds of linkage (lever) mechanisms. With the description and examples.
      The method can be used for powerful CAD linkages.

Description: Calculation_method_of_linkages.pdf

Attachment:
figure_1.mw
figure_2.mw

Or all in one
Calculation_method_of_linkages_(with_attach.).pdf


        Some examples of a much larger number calculated by the proposed method. Examples gathered here not to look for them on the forum and opportunity to demonstrate the method.  Among the examples, I think, there are very complicated.

https://vk.com/doc242471809_408704758
https://vk.com/doc242471809_408704572
https://vk.com/doc242471809_376439263
https://vk.com/doc242471809_402619761
https://vk.com/doc242471809_402610228
https://vk.com/doc242471809_401188803
https://vk.com/doc242471809_400465891
https://vk.com/doc242471809_400711315
https://vk.com/doc242471809_387358164
https://vk.com/doc242471809_380837279
https://vk.com/doc242471809_379935473
https://vk.com/doc242471809_380217387
https://vk.com/doc242471809_363266817
https://vk.com/doc242471809_353980472
https://vk.com/doc242471809_375452868
https://vk.com/doc242471809_353988163 
https://vk.com/doc242471809_353986884 
https://vk.com/doc242471809_353987119
https://vk.com/doc242471809_324249241
https://vk.com/doc242471809_324102889
https://vk.com/doc242471809_322219275
https://vk.com/doc242471809_437298137
https://vk.com/doc242471809_437308238
https://vk.com/doc242471809_437308241
https://vk.com/doc242471809_437308243
https://vk.com/doc242471809_437308245
https://vk.com/doc242471809_437308246
https://vk.com/doc242471809_437401651
https://vk.com/doc242471809_437664558

 

 

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

 

eulermac(1/(n*ln(n)^2),n=2..N,1);  #Error
Error, (in SumTools:-DefiniteSum:-ClosedForm) summand is singular in the interval of summation


eulermac(1/(n*ln(n)^2+1),n=2..N,1);  #nonsense

 

 

The method of solving underdetermined systems of equations, and universal method for calculating link mechanisms. It is based on the Draghilev’s method for solving systems of nonlinear equations. 
When calculating link mechanisms we can use geometrical relationships to produce their mathematical models without specifying the “input link”. The new method allows us to specify the “input link”, any link of mechanism.

Example.
Three-bar mechanism.  The system of equations linkages in this mechanism is as follows:

f1 := x1^2+(x2+1)^2+(x3-.5)^2-R^2;
f2 := x1-.5*x2+.5*x3;
f3 := (x1-x4)^2+(x2-x5)^2+(x3-x6)^2-19;
f4 := sin(x4)-x5;
f5 := sin(2*x4)-x6;

Coordinates green point x'i', i = 1..3, the coordinates of red point x'i', i = 4..6.
Set of x0'i', i = 1..6 searched arbitrarily, is the solution of the system of equations and is the initial point for the solution of the ODE system. The solution of ODE system is the solution of system of equations linkages for concrete assembly linkage.
Two texts of the program for one mechanism. In one case, the “input link” is the red-green, other case the “input link” is the green-blue.
After the calculation trajectories of points, we can always find the values of other variables, for example, the angles.
Animation displays the kinematics of the mechanism.
MECAN_3_GR_P_bar.mw 
MECAN_3_Red_P_bar.mw

(if to use another color instead of color = "Niagara Dark Orchid", the version of Maple <17)

Method_Mechan_PDF.pdf






The method of solving underdetermined systems of equations, and universal method for calculating link mechanisms. It is based on the Draghilev’s method for solving systems of nonlinear equations. 
When calculating link mechanisms we can use geometrical relationships to produce their mathematical models without specifying the “input link”. The new method allows us to specify the “input link”, any link of mechanism.

Example.
Three-bar mechanism.  The system of equations linkages in this mechanism is as follows:

f1 := x1^2+(x2+1)^2+(x3-.5)^2-R^2;
f2 := x1-.5*x2+.5*x3;
f3 := (x1-x4)^2+(x2-x5)^2+(x3-x6)^2-19;
f4 := sin(x4)-x5;
f5 := sin(2*x4)-x6;

Coordinates green point x'i', i = 1..3, the coordinates of red point x'i', i = 4..6.
Set of x0'i', i = 1..6 searched arbitrarily, is the solution of the system of equations and is the initial point for the solution of the ODE system. The solution of ODE system is the solution of system of equations linkages for concrete assembly linkage.
Two texts of the program for one mechanism. In one case, the “input link” is the red-green, other case the “input link” is the green-blue.
After the calculation trajectories of points, we can always find the values of other variables, for example, the angles.
Animation displays the kinematics of the mechanism.
MECAN_3_GR_P_bar.mw 
MECAN_3_Red_P_bar.mw

(if to use another color instead of color = "Niagara Dark Orchid", the version of Maple <17)

Method_Mechan_PDF.pdf






1 2 3 4 5 6 7 Last Page 1 of 19