Simplifying Expressions Involving Radicals
... the simplification of expressions. Since many algorithms in Computer Algebra systems like Mathematica, Maple, and Reduce work in quite general
settings they do not necessarily find a solution to a given problem described
in the easiest possible way. Simplification algorithms can be applied to expres ...
A (biased) survey on Arithmetic Circuits
... derivatives of C according to X1,…,Xk (any k)
is at most s (spanned by Li,k+1(Xk+1) ⋅ … ⋅ Li,d(Xd))
Algorithm: compute a basis for all derivatives
according to X1,…,Xk starting from k=1 to k=d.
C≡0 if at the end all basis elements are 0
Same idea also in the general case
In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called eliminant.The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation.The resultant of n homogeneous polynomials in n variables or multivariate resultant, sometimes called Macaulay's resultant, is a generalization of the usual resultant introduced by Macaulay. It is, with Gröbner bases, one of the main tools of effective elimination theory (elimination theory on computers).