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if there is a set of identities, such as a+b = b+a, a^2 = 2*a + 1

and one input or a few input,

how to make use of these identities to derive some output?

any algorithm can do this?

we use modern computer algebra books

i) computer the GSO of (22,11,5),(13,6,3),(-5,-2,-1) belong to R^3.

ii)trace algorithm 16.10 on computer a reduced basis of the lattice in Z^3 spanned by the vectors form(i).

trace also the values of the d_i and of D, and compare the number of exchange steps to the theoretical upper bound from section 16.3


we use Modern Computer Algebra book  

trace algorithm 15.2 on factoring f=30x^5+39x^4+35x^3+25x^2+9x+2 belong to Z[x].choose the prime p=5003 in step.

I have recently written a maple program to deconvolute gamma-ray spectra using the Richardson-Lucy algrithm. Although this method works well I would prefer to use a method based on the Maximum Entropy algorithm, and would like to know if anyone has tried to write a Maple program to deconvolute 1 dimensional data?

Greetings to all.

At the following Math.Stackexchange Discussion a certain constant was computed in relation to a Master Theorem Type recurrence being solved. This prompted me to try to identify it by the use of the eponymous command. What follows is the content of the Maple session. You may want to read the post in order to get an understanding of what the constant means and how its exact value is calculated.

> fsolve(2/2^a+1/4^a=1, a);

> identify(%);

> identify(%,all);
                                 1/2    1/2
                              2 2      3
                      arcsech(------ + ---- - 1/6 Zeta(5))
                                7       6

> evalf(log[2](1+sqrt(2)));

My questions/observations are:

  • Why does the algorithm fail to spot as simple a constant as the one above or am I just not invoking it correctly?
  • If that last formula were true the author of this code would certainly win a prize for calculating a closed form expression for an odd integer zeta function value! (To be fair here I did notice that the spurious identification disappears when the number of working digits is increased and I do understand that the identification depends critically on the number of digits.)

In concluding I would like to say, why the complicated formula and not the simple one? Let me congratulate you just the same on providing this very useful command. I have worked on pandigital approximations which are slightly related and I understand that adding an operation like the logarithm to an integer base up to some max base value can dramatically increase the search space and may not always be feasible.

Best regards,

Marko Riedel

Trace  on computing the distinct-degree decomposition of the squarefree polynomial
f=x^17+2x^15+4x^13+x^12+2x^11+2x^10+3x^9+4x^4+3x^3+2x^2+4x belong to F_5[x].tell from the output only how many irreducible factors of degree i the polynomial f has, for all i.


Dear Sirs,

I actually rigoruos to know what is the algorithm of BVP[midrich]? how it can obtain the solution of ODE with singularities?


Did anyone introduce a reference about the algorithm like this?

Thanks for your attention in advance


Greetings to all.

The multiplicative partition function is defined here at Wikipedia and was recently the subject of a discussion at Math Stackexchange.

I posted two solutions to the task of computing this function at the above page that use Maple code. One of them employs the Polya Enumeration Theorem and is of mostly theoretical interest as it cannot be used to effectively compute the function for n with many factors. I posted two additional implementations in order to remedy this defect, one of them in Maple and the other in Perl. I think the Maple implementation is easy enough to read not to require additional commentary. Note, however, that even though the Maple code and the Perl code implement the same algorithm (dynamic programming), the Maple version is dramatically slower than the Perl version and consumes a lot of memory. E.g. Maple takes 58 seconds for the value for 9! and Perl takes 1.5 seconds.

My question is, can someone explain this difference? Note that both are interpreted languages so there is no gain due to potential compilations.

Your commentary is appreciated.

This is with Maple 15 (X86 64 LINUX).

Best regards,

Marko Riedel

I want to write maple code of the following algorithm with

the following parameters and initial values please help me.

T0 = 5.5556 × 107 cells, I0 = 1.1111 × 107 cells, V0 = 6.3096 × 109 copies/ml,


c = 0.67, h = 1, d = 3.7877 × 10−3, δ = 3.259d,

λ = 2/3× 108d, R0 = 1.33,

p = (cV0δR0)/λ(R0−1)

and β = dδcR0/λp .


step 1 :
T(0) = T0, I(0) = I0, V (0) = V0 λi(100 ) = 0 (i=1, ..., 3), u1(0) = 0 =

step 2 :
for i=1, ..., n-1, do :
Ti+1=(Ti + hλ)/(1 + h[d + (1 − u1i)βVi]),

Ii+1 =(Ii + h(1 − u1i)βViTi+1)/(1 + hδ),

Vi+1 =(Vi + h(1 − u2i)pIi+1)/(1 + hc),

λ1n−i−1 =(λ1n−i + h[1 + (1 − u1i)βVi+1])/(1 + h[d + (1 − u1i)βVi+1]),

λ2n−i−1 =(λ2n−i+ hλ3n−i (1 − u2i)p)/(1 + hδ),

λ3n−i−1 =(λ3n−i + h(λ2n−i−1− λ1n−i−1 )(1 − u1i)βTi+1)/(1 + hc),

R1i+1 =(1/A1)(λ1n−i−1−λ2n−i−1 )βVi+1Ti+1,

R2i+1 =−(1/A2)λ3n−i−1 pIi+1,


u1i+1 = min(1, max(R1i+1 , 0)),

u2i+1 = min(1, max(R2i+1 , 0)),

end for


step 3 :
for i=1, ..., n-1, write
T(ti) = Ti, I(ti) = Ii, V(ti) = Vi,

u1(ti) = u1i, u2(ti) = u2i.

end for


I want to solve two odes with their boundary condition. I wrote the code below:




sys_ode:=  eq2=0,eq3=0;
bcs := phi(0)=0,phi(h)=1,T(0)=0,T(h)=1;
sol:=dsolve([sys_ode, ics]);

however, this code doesnt get my desired results (the results are complex!). but when I (with hand) integrate Eq3 twice and substitute boundary conditions and replace in Eq2 the answer is easy and straightforward.

How can I change the following algorithm to get my results?

Thanks for your attention in advance


Following previous question at

and also

I wrote the following code






eq2:=diff(T(eta),eta,eta)+1/(k(eta)/k1[w])*(2/(1-zet^2)*rho(eta)*c(eta)*u(eta)/(p2*10000)+( (a[k1]+2*b[k1]*phi(eta))/(1+a[k1]*phi1[w]+b[k1]*phi1[w]^2)*diff(phi(eta),eta)-k(eta)/k1[w]/(1-eta)*diff(T(eta),eta) )):
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):



p:=proc(pp2) global res,F0,F1,F2:
if not type([pp2],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve({eq1=0,subs(p2=pp2,eq2)=0,eq3=0,u(0)=0,u(1-zet)=0,phi(0)=phi0,T(0)=0,D(T)(0)=1}, numeric,output=listprocedure):
evalf(2/(1-zet^2)*Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*( F1(eta)*rhop*cp+(1-F1(eta))*rhobf*cbf )/(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))-pp2*10000:
end proc:




phb:=evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet))) :



as you can see at the second line of the code, the value of phi0:=0.00789. however, I want to modify the code in a way that phi0 is calculated with the following addition constraint

evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet)))-0.02=0

I would be most grateful if you could help me in this problem.

Thanks for your attention in advance



If I wirite in an algorithm in MapleTA 9.5 the number 0, and later use it (for export to latex), it becomes negative, but not if I pass through Maple:



results in:

null 0
zero 0
nullstring -0
zerostring 0


Why, and what can be done without passing through Maple?




I think Maple is missing some lines and significant points. Here I leave another contribution to the possible implementation of a new algorithm to draw the circle of Taylor.


L. Araujo C.

What does convert(max(a,b), piecewise) algorithm use?

convert(max(a,b), piecewise)

convert(min(a,b), piecewise)

assume i have a number 26 and assume a prime number not greater than a value, let it be 5

then it is like a division and factor into 5^2 + 1

if prime number set to 17, then it will output 17 + 3^2, 

the output will be in terms of prime number, such as  a^3+b^2 + c  where a and b are prime number

it should start from greatest prime number given as a parameter in function

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