SAGE verification
I am doing my research in the area of finite field arithmetic for elliptic curve. i have implemented algorithm for elliptic curve and verified using sagemath. but my question is that i have to implement the same in C programming also for the justification? as most of the researcher said that sagemath is used only for verification. cannot used for justification of final work . please guide.
What is the question?
Sage is performing exact computer algebra, thus giving a proof for the computed stuff. There is no need to have a complementary system as a "main computational tool" or so. Feel free to use C, see if the libraries in there make life shorter while waiting for the answer, or longer, while implementing something particular case using them.
A verification is usually not a proof, just a "check" - possibly at a sensible point. (For instance - after we symbolically compute an integral, we may also ask for the numerical values of the integral, and of the result. If they are "almost equal", this is a "verification" - maybe.)
And if the story is determined by a supervisor, then one possibly has to do all, sage, C, maths, proofs, latex, type, publish, ... since she/he needs no "justification".
Sage is definitely not giving a proof of anything. If you type
cos(pi)you get the result-1but not a proof that this is the right answer. There is a huge difference between a theorem that is right and a theorem that is proven.