Maple 12 Questions and Posts

These are Posts and Questions associated with the product, Maple 12

If A then B After clustering B , how to find a set of A in machine learning topic and fuzzy topic?

Is there lifting function for polynomials or algebra use?

expect input a list univariate polynomial , then output a list of polynomials of two variables.

it should be the reverse operation of projection.

Which library has this function in maple 12 or maple 2015?

   1 1 1 2 2 3 3  

(  1 3 3 2 2 1 2 )

how to input this permutation into permgroup ?

 

If maple can auto discover derived equations, 

then most variable are unknown name which may or may not be physics variable.

so, how to guess which physics data suitable for these look like meaningless variable?

or these tools only visualize the relationship of existing known equations?

can anyone help me to calculate the exact  value of the eigenvalues of this matrix:
 

Download mat.mw

 
with(RegularChains);
R := PolynomialRing([x, y, z]);
p1 := x^2+5-2*x*z;
p2 := z^3*y+x*y^2;
p3 := -8*z^3+3*y^2;
F := [p1, p2, p3];
MainVariable(p1, PolynomialRing([x, y, z]));
MainVariable(p1, PolynomialRing([z, y, x]));
prem(p1, p2, x);
prem(p2, p1, z);
prem(p3, p2, y);
premcustom := proc(Fparam,Gparam, xparam)
local R, G, F, lcg, lcr, dr, dg:
R := Fparam:
G := Gparam:
F := Fparam:
if degree(G,xparam) = 0 then
 print("return 0"):
 return 0:
elif degree(F, xparam) < degree(G, xparam) then
 print("return R"):
 return R:
else
 lcg := coeff(G, xparam, degree(G, xparam)):
 dg := degree(G, xparam):
 while degree(R, xparam) > degree(G, xparam) do
  lcr := coeff(R, xparam, degree(R, xparam)):
  dr := degree(R, xparam):
  R := lcg * R - lcr * G * (x^(dr - dg)):
 od:
end if:
return R:
end proc:
coeff(p1, x, degree(p1, x));
coeff(p2, x, degree(p2, x));
prem(p1,p2,x);
prem(p2,p1,z);

premcustom(p1,p2,x);
premcustom(p2,p1,z);
 
why premcustom looping?
 
is this coeff(p1, x, degree(p1, x)); wrong ?
 
should this to get real coefficient in number instead of variable and how?
 
is there equivalent function as dprem?
 
with(diffalg):with(diffalg):
FlessThanG := proc(Fparam, Gparam, PRing)
F := Fparam:
G := Gparam:
if leader(F,PRing) < leader(G,PRing) or (leader(F,PRing) = leader(G,PRing) and degree(F, leader(F,PRing)) < degree(G, leader(G,PRing))) then
 return True:
else
 return False:
end if:
end proc:
dprem := proc(Fparam, Gparam, x, PRing)
local R, theta, thetax, thetaG, F, G;
F := Fparam:
G := Gparam:
R := F:
thetax := leader(G, PRing);
while FlessThanG(R, G, PRing) or FlessThanG(G, R, PRing) do
theta := leader(R, PRing);
R := prem(R, thetaG, theta)
od:
return R:
end proc:
R := differential_ring(ranking = [[x,y,r]], derivations = [t], field_of_constants=[m,l], notation = diff):
p1 := m*x[2] + r*x;
p2 := m*y[2] + r*y - g;
p3 := x^2 + y^2 - l^2;
dprem(p1, p3, x, R);
 
 
is x[2] = diff(x,t$2) in diffalg ?
 
if not how to write in this way?
 
i had defined constant
but got error
 
Error, (in DifferentialAlgebra:-Tools:-LeadingDerivative) unknown symbol (approx. error location: [m*x[2 --> ] <-- +r*x])
 
 

https://math.stackexchange.com/questions/301068/how-do-you-find-a-corresponding-recurrence-relation-for-some-random-algorithm/301709

according to this link, how to parse or walk through the algorithm in maple to generate recurrence relation formula?

how to convert a function to transition matrix?

how to convert a differential system to transition matrix?

 

I search saveplot and sleep function here

i had kept close filename function and move plot setup default to first line

but thread no sleep in maple 12

then I remove sleep and can save image file

but after I call it in a function and run a for loop for this function

the file is not updated after sleep 3 seconds 

how to run a for loop call it and it can refresh 

 Dear all

Is there a nice idea to determine the Lyapunov function of the following system

Lyapunov_function.mw

Some parameters used in the code:

b fixed parameter

a any parameter in R

Many thanks for your help

 

 

If I know the direction of up and down

how to control normal distribution to fill in missing data to the direction I want in maple?

just like fill in missing pixel in bitmap file.

Hi all;

I need to compute the stabilizing feedback for the system of nonlinear ODEs

stabilizing_Feedback.mw

 

Many thanks for your help

Second terms coefficient = 2/3*x when (....)^2

9/16*x^2 when (...)^3

64/125*x^3 when (...)^4

625/1296*x^4

Which Bernstein has these result?

Which limit function of x^n = (n^(n-1))/((n+1)^(n-1))*x^(n-1)?

how to find and calculate?

 

 

Variable disappear after read file and then pass parameter to create thread

 

How i convert the following mathematica code to Maple

f1[t^m_] := Gamma [m + 1] t^(m - a[t]) /Gamma[m + 1 + a[t]];
f1[t] := Gamma [2] t^(1 - a[t]) /Gamma[2 + a[t]];

f1[p_Plus] := Map[f1, p]
f1[c_*f_] := c*f1[f] /; FreeQ[c, t]
f1[c_] := 0 /; FreeQ[c, t]

f1[x^2*t^2 + t + x]

gives

t^(1 - a[t])/Gamma[2 + a[t]] + (2 t^(2 - a[t]) x^2)/Gamma[3 + a[t]]

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