Existing CAS commands --> Prime discussion

[Anders]

(06-27-2017 05:04 AM)parisse Wrote:  Some comments:
as_function_of is more an internal function than something else, it is used by locus to build a function from a construction. For example in an Xcas session enter
a:=1;
b:=a*x+1;
as_function_of(b,a)

is_prime is the same as is_pseudoprime on the Prime, it links to PARI in Xcas.

c1oc2 and c1op2 are there in Xcas, it's a 1 not a l, read this as compose permutation as a cycle 1 with permutation as a cycle 2 or as a permutation 2.
Same for p1oc2 and p1op2

conique_reduite and quadrique_reduite have been translated to reduced_conic and reduced_quadric, the French keywords work only if you have selected French.

realroot is not the same functionnality as zeros or proot. zeros is an exact algorithm to find exact roots, proot is an approx algorithm to find approx roots, while realroot is an exact algorithm to find isolation interval for roots, it means you have a proof that there is 1 and exactly 1 root in the returned intervals.

makevector is not really useful, just put bracket on the sequence.

Z/pZ is available on the Prime, but you must enter %% instead of % in Xcas.

I don't want to make change to the parser that could have side effects, therefore I don't want to enable user_operator .

combine: it was added for maple compat.
SortA and SortD: added for TI compat.

count_eq, count_inf and count_sup were added at the request of teachers using Xcas, because they don't want to explain how to use count : count is indeed more elaborate since you must pass a function to a command

Sorry if I miss understand you above:

isprime on HP Prime return one value either true/false (if it is prime or not = 1/0 =)

is_pseudoprime in Xcas returns to values 2/1/0. 2 if it is true prime, 1 if it is a pseudo prime number otherwise it return 0.

So not sure what you mean....?

For very large numbers I still think is_pseudoprime is very valuable, or do you always calculate if every number is prime fully in isprime on HP Prime regardless on how large the number is?

I can see the value of realroot, complexroot and rationalroot for use with polynomial functions. I understand the distinction in how you arrive at the solution (algorithms). I can also see how this is useful in calculus (sign analysis of the function).

But then again, if I read you correctly and based on my own experience, zeros() always give you all roots exactly regardless. so... if you have all the roots exactly in Z if possible and also as expression of radicals if possible, if not then a decimal number within +/- epsilon error.

So what does realroot give us that zeros() does not. Same applies to complexroot() vs czeros().

Great that Z/pZ works 1:1 :-) also with vectors and matrices