I have one more question is

using your method, v^3 belong to Q[r,u,v,w]

conclusion is Kernel belong to image, means injective

however when i solve(K,[x,y]) result in null

it can not represent x and y in terms of r,u,v,w

can i conclude that it is injective, but it is not surjective, so that it is not isomorphism ?

some book said image(ker) == ker(image) however, i do not know what exactly image is

if so, why need to check kernel belong to image, why not use solve(K,[x,y]) to check whether it has answer to check isomorphism?

if solve has answer, does subs(x=inverse(f), f) = 1 and subs(x=f, inverse(f)) = 1 hold ?

For (A+I) / I

A or I, which is polynomial map?

if one of them is polynomial map, What is the second one?

Eliminate return this,

if not this, how can you calcuate the kernel from basis of kernel in order to check isomorpism or exact sequence?

does it mean that need user to write a reduce function for rational cases?

Eliminate return this,

if not this, how can you calcuate the kernel from basis of kernel in order to check isomorpism or exact sequence?

does it mean that need user to write a reduce function for rational cases?

by the way, you tell me how to use typetools to add, i see that is a kind of learning

by the way, you tell me how to use typetools to add, i see that is a kind of learning

Wonderful skill

I haven't met my destination, i am not tired

it seems reduce can also do it

f reduce with basis to remainder

Wonderful skill

I haven't met my destination, i am not tired

it seems reduce can also do it

f reduce with basis to remainder

it is jesus work.

if i have your attitude, i may take many years to write this

it is jesus work.

if i have your attitude, i may take many years to write this

Great skill

Great skill

i understand now

remove polynomial which contains x and y

this match is really great thing, the word is like manupulate string, however it can use to calculate this

this match is really great thing, the word is like manupulate string, however it can use to calculate this