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## how to find solution minimize the cost f...

Maple

3*rho1 - 2*rho2 + rho3 - rho4 = -1

4*rho1 +   rho2 - rho3        = 5

original without cost function:

with(Groebner):
K := {y1-(x1^3)*(x2^4),y2-(x2^(1+2))*(w^2),y3-(x1^(1+1))*(w^1),y4-(x2^1)*w,(y1^1000)*(y2^1)*(y3^1)*(y4^100)- x1*x2*w + 1};
G := Basis(K, plex(x1, x2, w, y1, y2, y3, y4));
Reduce((x2^(5+1))*(w^1), G, plex(x1, x2, w, y1, y2, y3, y4));

after have cost function 1000*rho1 + rho2...

## how to find use all possible reduce resu...

with(Groebner):
K := {y1-(x1^3)*(x2^4),y2-(x2^(1+2))*(w^2),y3-(x1^(1+1))*(w^1),y4-(x2^1)*w,x1*x2*w - 1};
G := Basis(K, plex(x1, x2, w, y1, y2, y3, y4));
Reduce((x2^(5+1))*(w^1), G, plex(x1, x2, w, y1, y2, y3, y4));
(1,1,0,2)

subs({rho1=1,rho2=1,rho3=0,rho4=2},3*rho1 - 2*rho2 + rho3 - rho4);
subs({rho1=1,rho2=1,rho3=0,rho4=2},4*rho1 +   rho2 - rho3       );

can also reduce with G8,G7

R1 := Reduce((x2^(5+1))*(w^1), {G[7...

## How to summation and simplify q calculus...

Maple

i am doing a Q Laplace and finally summation it

however, i find an AccurateQSummation which is not like Summation

Should i use it, if not, use SumTools' summation how to simplify it?

`restart;with(QDifferenceEquations):qexp := QPochhammer(-(-p*t), q, infinity);f:= qexp*t;b := subs(t=q^n,f);QSimplify((1-q)*AccurateQSummation(b*q^n,n=-infinity..infinity));with(SumTools):QSimplify((1-q)*Summation(b*q^n,n=-infinity..infinity));`

## when implement a new kind of differentia...

Maple

i am implementing q-Laplace

http://perso.uclouvain.be/alphonse.magnus/gbang/qbook712.pdf

when there are quite many differentiation rules

how to do a function for a new kind differentiation like a maple do?

## how to evaluate a density or distributio...

Maple

1.

qRacah := qhyperterm([q^(-x), alpha*q^(-x)/(gamma*delta)], [alpha*q], q, gamma*delta*q^(x+1)*t, k)*qhyperterm([beta*delta*q^(x+1), gamma*q^(x+1)], [beta*q], q, q^(-x)*t, k);

i use inverse laplace to transform ordinary generating function into exponential generating function

can not further evaluated

2.

i do not know whether x is main variable or q is main variable or both are.

ff := eval(subs(x=0, exponential_genfun));

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