From: Richard Kreckel Date: Sat, 24 Mar 2001 22:09:41 +0000 (+0000) Subject: * Documented sqrfree. X-Git-Tag: release_0-8-0^0 X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=9b8f6fbce674012291e6343ff429e6515a10086f;hp=197594750cb42582eb69c8690fea2221e3f72205 * Documented sqrfree. --- diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi index 520e75a7..bb8c5cbf 100644 --- a/doc/tutorial/ginac.texi +++ b/doc/tutorial/ginac.texi @@ -1250,6 +1250,9 @@ Indexed expressions in GiNaC are constructed of two special types of objects, @itemize @bullet +@cindex contravariant +@cindex covariant +@cindex variance @item Index objects are of class @code{idx} or a subclass. Every index has a @dfn{value} and a @dfn{dimension} (which is the dimension of the space the index lives in) which can both be arbitrary expressions but are usually @@ -1481,6 +1484,7 @@ simplifications: @end example @cindex @code{get_free_indices()} +@cindex Dummy index @subsection Dummy indices GiNaC treats certain symbolic index pairs as @dfn{dummy indices} meaning @@ -2254,6 +2258,39 @@ int main() @end example +@subsection Square-free decomposition +@cindex square-free decomposition +@cindex factorization +@cindex @code{sqrfree()} + +GiNaC still lacks proper factorization support. Some form of +factorization is, however, easily implemented by noting that factors +appearing in a polynomial with power two or more also appear in the +derivative and hence can easily be found by computing the GCD of the +original polynomial and its derivatives. Any system has an interface +for this so called square-free factorization. So we provide one, too: +@example +ex sqrfree(const ex & a, const lst & l = lst()); +@end example +Here is an example that by the way illustrates how the result may depend +on the order of differentiation: +@example + ... + symbol x("x"), y("y"); + ex BiVarPol = expand(pow(x-2*y*x,3) * pow(x+y,2) * (x-y)); + + cout << sqrfree(BiVarPol, lst(x,y)) << endl; + // -> (y+x)^2*(-1+6*y+8*y^3-12*y^2)*(y-x)*x^3 + + cout << sqrfree(BiVarPol, lst(y,x)) << endl; + // -> (1-2*y)^3*(y+x)^2*(-y+x)*x^3 + + cout << sqrfree(BiVarPol) << endl; + // -> depending on luck, any of the above + ... +@end example + + @node Rational Expressions, Symbolic Differentiation, Polynomial Arithmetic, Methods and Functions @c node-name, next, previous, up @section Rational expressions