Last time i see this question, then no one further answer this.

I just can say that i really want to know whether my concept wrong or book wrong or the script i write is wrong

It's glad to know any one of them wrong without knowing how to do actually, so that i can rethink and reread again

actually i worry that intersect is not only one command to do this. is other redundant except correct output?

i mean this is to calculate the Groebner basis of kernel of this map

Q[r,u,v,w] -> Q[x,y]

= G intersect k[r,u,v,w]

Leading power of product should be the term with a variable has the highest degree

i mean this map

r  ->  x^4
u  -> (x^3)*y
v  ->  x*y^3
w  -> y^4

this question is only allowed to use basis to solve this problem

correct output should be := {v*u-w*r,v^3-u*w^2,-u^2*w+v^2*r,u^3-v*r^2};

actually i am not sure whether k[r,u,v,w] is K[1],K[2],K[3],K[4] of above list

do we or can we need to further eliminate G2 to correct output stated above

i mean the term which contain the a variable which power is the highest among all the terms

in above case should be y^2

however after i search manual no function result in this

product means a product term only has product, for example a*b, a*b*c, a*b*c*d ,etc

i mean the term which contain the a variable which power is the highest among all the terms

in above case should be y^2

however after i search manual no function result in this

product means a product term only has product, for example a*b, a*b*c, a*b*c*d ,etc

if there is a framework to let me plug in integration rules in it, then it is very convenient

if there is a framework to let me plug in integration rules in it, then it is very convenient

After read

http://www.maplesoft.com/support/help/Maple/view.aspx?path=LREtools/HypergeometricTerm&term=LREtools[HypergeometricTerm]

it do not have q-Laplace, i need inverse q-Laplace, it has q for q-hypergoemetric

why look LREtools?

actually i need q integration, how to implement a new kind of integration like maple do such as

http://en.wikipedia.org/wiki/Integration_by_substitution

After read

http://www.maplesoft.com/support/help/Maple/view.aspx?path=LREtools/HypergeometricTerm&term=LREtools[HypergeometricTerm]

it do not have q-Laplace, i need inverse q-Laplace, it has q for q-hypergoemetric

why look LREtools?

actually i need q integration, how to implement a new kind of integration like maple do such as

http://en.wikipedia.org/wiki/Integration_by_substitution

i use continuous fourier transform continous to discrete, failed

i := 2;

disnetwork := int(exp(-I*s*u)*contnetwork, s=-infinity..infinity);

ztrans(disnetwork, s, z);

then i use dynamic system's function, can not convert because not a system object

restart;
with(inttrans):
with(SumTools):
with(DynamicSystems):
network := sqrt(2*p)*((s-p)^(i-1))/((s+p)^i):
sys := subs(i=2, network):
disnetwork := ToDiscrete(sys, 1, method = forward);
disnetwork := ToDiscrete(sys, 1, method = backward);
disnetwork := ToDiscrete(sys, 1, method = bilinear);

then i try matlab, it can convert but not the expected

syms s p;
contnetwork = sqrt(2*p)*((s-p)^(i-1))/((s+p)^i);
c2d(contnetwork,0.1,'foh')
c2d(contnetwork,0.1,'imp')

i use continuous fourier transform continous to discrete, failed

i := 2;

disnetwork := int(exp(-I*s*u)*contnetwork, s=-infinity..infinity);

ztrans(disnetwork, s, z);

then i use dynamic system's function, can not convert because not a system object

restart;
with(inttrans):
with(SumTools):
with(DynamicSystems):
network := sqrt(2*p)*((s-p)^(i-1))/((s+p)^i):
sys := subs(i=2, network):
disnetwork := ToDiscrete(sys, 1, method = forward);
disnetwork := ToDiscrete(sys, 1, method = backward);
disnetwork := ToDiscrete(sys, 1, method = bilinear);

then i try matlab, it can convert but not the expected

syms s p;
contnetwork = sqrt(2*p)*((s-p)^(i-1))/((s+p)^i);
c2d(contnetwork,0.1,'foh')
c2d(contnetwork,0.1,'imp')

when try to reverse find back alpha and x from existing equations

x and alpha are very complex

solve({sqrt(2*p)*exp(-p*t) = exp(x)*(x^(-alpha))/0!*exp(-x)*(x^(0+alpha)), sqrt(2*p)*(-2*p*t+1)*exp(-p*t) = exp(x)*(x^(-alpha))/1!*diff(exp(-x)*(x^(1+alpha)), x$1)},{alpha,x});

i still suspect this rodrigue formula is the source

when try to reverse find back alpha and x from existing equations

x and alpha are very complex

solve({sqrt(2*p)*exp(-p*t) = exp(x)*(x^(-alpha))/0!*exp(-x)*(x^(0+alpha)), sqrt(2*p)*(-2*p*t+1)*exp(-p*t) = exp(x)*(x^(-alpha))/1!*diff(exp(-x)*(x^(1+alpha)), x$1)},{alpha,x});

i still suspect this rodrigue formula is the source

https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!293
https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!292

here it is,

once you got it, tell me, i will delete it after you got it.