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Functions and commands 339
Division
Quotient Returns the integer quotient of the Euclidean division of two
integers.
iquo(Intgr1, Intgr2)
Example:
iquo(63, 23) returns 2
Remainder Returns the integer remainder from the Euclidean division of
two integers.
irem(Intgr1, Intgr2)
Example:
irem(63, 23) returns 17
a
n
MOD p For the three integers a, n, and p, returns a
n
modulo p in
[0, p−1].
powmod(a, n, p,[Expr],[Var])
Example:
powmod(5,2,13) returns 12
Chinese
Remainder
Integer Chinese Remainder Theorem for two equations. Takes
two vectors, [a p] and [b q], and returns a vector of two
integers, [r n] such that x ≡ r mod n. In this case, x is such that
x ≡ a mod p and x ≡ b mod q; also n=p*q.
ichinrem(LstIntg(a,p),LstIntg(b,q))
Example:
ichinrem([2, 7], [3, 5]) returns [-12, 35]
Polynomial
Find Roots Given a polynomial in x (or a vector containing the
coefficients of a polynomial), returns a vector containing its
roots.
proot(Poly)
or proot(Vector)
Example:
proot([1,0,-2]) returns
[-1.41421356237,1.41421356237]