I found a condition for p, q that N=pq can be factored in plynominal time using Maple 2020.
Is fllowing Hypothesis and Proof is right?

Hypothesis

       N=pq  p and q are large prime respectively.
         R=q/p  q > p  R is very close to an small integer or a simple rational number.
       
        N=pq can be factorized in time polynomial

Proof
        point[p, q] is on y=N/x
        y=N/x  and y=Rx cross at point[p, q]
        N is n digit
        upper  2 digits N2  round off the 3rd digit
        upper  3 digits N3  round off the 4th digit
        upper  4 digits N4  round off the 5th digit
        
        y=N2/x and y=Rx cross at point[p2,q2]
        y=N3/x and y=Rx cross at point[p3,q3]
        y=N4/x and y=Rx cross at point[p4, p4]

        But we only know N.

        Let line up candidates point[p2,q2] , point[p3,q3] and point[p4, p4]

       N2 < 99  i=1..10 j=1..10
       R2=i/j
       f2=N2/R2 - j^2
       dn2=abs(N2-R2*j^2)   

      N4 < 9999  i=1..99 j=1.. sqrt(N4)
      R4=i/j
      f4=N4/R4 - j^2
      dn4=abs(N4-R4*j^2)

     Point[j, i] that have  small f2 and dn2 can be nominated as candidate for point[p2, q2]
     Point[j, i] that have  small f3 and dn3 can be nominated as candidate for point[p3, q3]
     Point[j, i] that have  small f4 and dn4 can be nominated as candidate for point[p4, q4]

    Find cross point[px, qx] of y=R2x and y=N/x , y=R3x, y=N/x and y=R4x, y=N/x
    Find the nearest prime pn for px and the nearest prime qn for qx
   
   pn*qn=N  bingo!

   Number of candidates are finit.
   You can factorized N=pq in time polynomial.
                                   
                                                                       Q.E.D. ?

In addition, using "https://www.mapleprimes.com/questions/228532-Strange-Factorization"

Rang from p - half digits of p to p + half degits of p and /or range q - half digits of q to q + half degits of q  N=pq can be factored in plynominal time.

Hi, everyone!

I'm trying to do some computations with (truncated) multivariable power series, which I'd like to put into Hironaka standard basis form.  This is almost the same as a Groebner basis, except that the "leading" terms have smallest degree instead of largest.  This requires slight changes to the algorithms in order to make sure they terminate.  Does anyone know if this has been implemented in Maple or have a good way to fake it?  Here's what I've thought of:

• Using the Groebner package with grlex_min instead of grlex.  The documentation warns that this may not terminate, and sure enough, it doesn't.  (At least not before my computer runs out of memory.)
• Replacing the truncated power series with their palindromes, using the Groebner package, and then switching back, making sure all the degrees are correctly accounted for.  This should work, but it's going to be a major pain.
• Reimplementing the Groebner routines.  I'd really rather not, but I'd love to know if anyone else has.

Anybody have any other ideas or suggestions?

Thanks!

----Josh

Hi,

I tried to find the set of real parameters a1, a2, a3, a4 and u1, u2, u3 which make a subalgebra L an ideal of a finite real Lie algebra LieAlg. Unfortunately, the "Query" command with the "Ideal" argument returns an error message that I can't get around. What should I change in this command?

restart: 
with(DifferentialGeometry):
with(LieAlgebras):
#
DGsetup([x1,x2,x3],R3):
#
Lie_Generators := [D_x1*x1+D_x2*x2+D_x3*x3, D_x3*k^2*x1+D_x1*x3, -D_x1*x2+D_x2*x1, D_x3*k^2*x2+D_x2*x3, D_x1, D_x2, D_x3]:
#
LieAlg:=LieAlgebraData(Lie_Generators):
#
DGsetup(LieAlg):
#
L:= evalDG([e3+u2*e5-u1*e6,e2-u3*e5-k^2*u1*e7,e4-u3*e6-k^2*u2*e7,e1-u1*e5-u2*e6-u3*e7]);
Sub_Alg_L:=LieAlgebraData(L);
#
TrueFalse,Equations,Solutions,IdealList:=Query(L,{u1,u2,u3},"Ideal");
#
TrueFalse,Equations,Solutions,IdealList:=Query([DGzip([a1,a2,a3,a4], L, "plus")],{a1,a2,a3,a4,u1,u2,u3},"Ideal");

Thanks for your help.

Jaqr

converts a Maple polynomial into a list of its coefficients.

Hey

Can anyone help me with this file?

I don't know how it happend, but the file somehow got corrupted. Is there anything i can do?

Thanks 

Videregående_beton_Gang_9.mw

I have a parametric polynomial which is defined based on the multiplication of different variables and I want to rearrange the polynomial based on specific variables. For example, suppose the polynomial is defined as follows:

a:= (1+x+y)(2x-yx+z)(y^2-zy)

and I want to have a based on first, and second orders of x, or even other variables. Thanks

Hi, my problem is the next differential equation:

In maple. I used this code to solved it, but throws this error:

dsolve({diff(y(x), x, x) = -P*x/(I*E), eval(y(x), x = L) = 0, eval((D(y))(x), x = L) = 0});
Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(L), y(x)}

What is the problem with my code? How can solve my ODE with tis boundary conditions? 

How to write down the differential equation for this practical question? 

I can use dsolve to solve the system equation. 

Thank you! 

EDIT TIME: 14:30 CET

where P(1) and P(2) are NxN matrix functions.

My trial code for STEP 0

 alpha times integral w.r.t. x

 Int_x__alpha:=proc(term,alpha): 
 return
select(has,term,x).P(alpha)^T.remove(has,term,x)
end proc: 

 alpha times integral w.r.t. t

Int_t__alpha:=proc(term,alpha):   #alpha times integral w.r.t. t
 return
remove(has,term,t).P(alpha).select(has,term,t)
end proc:

when I run the last procedure for the testing

 Int_t__alpha(Psi(x)^T.C. Psi(t),2);

I get

But it must be 

Because the multiplication is not commutative in Matrices. So, the last procedure must be corrected. 

DETAILS for the procedures:

-------------------------------------------------------------------------------------------------------------------------------------

MAIN QUESTION:

Suppose that we have a PDE as follows 

                                             ...(3)

subject to appropriate Initial and Boundary conditions.

-------------------------------------------------------------------------------------------------------------------------------------

STEP 1

• Find the highest derivative w.r.t. x and w.r.t. t. Then, Let the trial function be the summation derivative of these highest derivatives. I mean

Trial Function:                                           ...(4)

where Psi(x), Psi(t) are Nx1 vectors and C is a NxN matrix.

I can't write a maple code for selecting the trial function.  May be you can.

trial_function:=diff(u(x,t),x,t)=Psi(x)^T.C. Psi(t); 

# I deliberately used ^T instead of ^+ for Transpose.
# If I use ^+, the transpose sign doesn't appear in 2d output. May be you have an other idea.

-------------------------------------------------------------------------------------------------------------------------------------

STEP 2

• Integrate the Eq.4  w.r.t. t from 0 to t, we have

STEP2:=int(  lhs(trial_function) ,t=0..t)=Int_t__alpha(rhs(trial_function),1);


The code must be improved. Firstly, substitute t=s in lhs(trial_function) and then integrate s=0..t 

-------------------------------------------------------------------------------------------------------------------------------------

STEP 3

int(lhs(STEP2),x=0..x)= Int_x__alpha(rhs(STEP2),1);

The code must be improved.

-------------------------------------------------------------------------------------------------------------------------------------
STEP 4

• Integrate Eq.4 w.r.t x

-------------------------------------------------------------------------------------------------------------------------------------
STEP 5

• Substitute Eq. (5), Eq. (6), Eq. (7) to Eq. (3),
• I mean substituting  u_x(x,t), u_t(x,t), u(x,t) to PDE.

-------------------------------------------------------------------------------------------------------------------------------------

STEP 6

DOWNLOAD ALL MAPLE CODE: all_code.mw

How can I get Maple to simplify expressions into more meaningful forms?

For example, 

xc1 := -(2*Q*R1 + sqrt(4*Q^2*R1*RL - R1^2 + 2*R1*RL - RL^2))*R1/(4*Q^2*R1 + R1 - RL)

The numerator, under the radical, is more meaningful as sqrt(4 Q^2 R1 RL-(R1-RL)^2).

Similarly, the denominator can be simplified to Rs(4 Q^2+1)-RL.  

How do I get Maple to get me there?

I am wondering if there are examples of agent-based models in economics domain that have been implemented in Maple.

Any infomration/source is more than welcome!

Thanks in advance

I actually want to numerically solve Karhunen-Loeve Decomposition, which is reduced to homogenous Fredholm integral equation second kind when the kernel is the function of correlation of variables, by using any procedures (Galerkin is better if it is availabe). FYI, with "intsolve" I just got f(x)=0. 

I am a newbie in Maple! I tried both ThermophysicalData and its CoolProp package to find saturation pressure of vapor for given air-water mixture temperature.

I want to calculate water vapor density in air or simply Absolute humidity (kg/m3)

But i can not see any meaningful function or combination of functions/properties in CoolProp to give such output.

P_w in CoolProp, HApropSI takes this as input only that is not usefule either way inpoutput

The rationale is to work from RH and then calculate P_w as output: P_w=RH x P_g where P_g is vapor saturation pressure at the given ambient condition.

From there all world is yours!

You can use ideal gas rules to do everything. But i cant use CoolProp to calculate the ABsolute humidty for given RH and ambient condition.

Note that clearly i can calculate all these from hand calculation as well as approximation formuale of Clausius-Clapeyron equation. But i wanted to do in Maple with its packages.

Any help is appreciated!?

Regards

Sina

Hi

I have the following fractional  system of differential equation. How to plot it for alpha=0.5, beta=0.5?

eq1:=diff(y1(t),t$alpha)=0.04-(0.09*y1(t)*y2(t))-(0.00250*y1(t)*y2(t))/((0.03500+y2(t)))-0.04*y1(t);                                                                                                                                                                    

eq2:=diff(y2(t),t$beta)=(0.09*y1(t)*y2(t))+(0.00250*y1(t)*y2(t))/((0.035+y2(t)))-(0.02+0.04)*y2(t);

Hi, 

Whenever I open Maple 2020 and type one single letter or number (doesn't matter) Maple 2020 will "freeze" and load forever (i have had it open for a long time, just watching that f**king blue circle spin...

I have tried reinstalling, repairing, running as admin, and changing the compatibility mode, still, nothing works:(

I run Maple 2020 as a Student with WithGym

Pc specs:

Intel i5-10300h 2.6 ghz

Geforce 1660 ti 6gb

Windows 10 x64