4.5.1 User language
Find the matrix of a quadratic form, return 0 if expression is not a quadratic form. Maple syntax :
quad:=proc(q,x)
local fonc,fonc2,fonc3,mat,_i,j,k;
n:=nops(x);
mat:=matrix(n,n,0);
fonc:=q;
for _i from 1 to n do
fonc:=subs((x[_i])=0,fonc)
od;;
if fonc<>0 then RETURN(0) fi;;
for _i from 1 to n do
fonc:=q;
fonc:=diff(fonc,x[_i]);
for j from 1 to n do
fonc:=subs((x[j])=0,fonc)
od;;
if fonc<>0 then RETURN(0) fi;
od;;
for _i from 1 to n do
fonc:=diff(q,x[_i]);
for j from 1 to n do
fonc1:=diff(fonc,x[j]);
for k from 1 to n do
fonc2:=diff(fonc1,x[k]);
if fonc2<>0 then RETURN(0) fi;
od;
od;
od;;
for _i from 1 to n do
for j from 1 to _i do
fonc:=diff(q,x[_i]);
fonc:=diff(fonc,x[j]);
mat[_i,j]:=fonc/2;
mat[j,_i]:=fonc/2
od;
od;;
RETURN(mat);
end;
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q=x^2+2*y^2+2*x*y and q+1 and q*x. Show the translation in mupad, TI89, xcas
syntax.
4.5.2 Standalone program using the library
// -*- compile-command: "g++ -g essai.cc -lgiac -lgmp" -*-
#include<giac/giac.h>
using namespace std;
using namespace giac;
int main(){
gen g;
cout << "Enter an expression: ";
cin >> g;
g=eval(g);
cout << "Factorization of " << g << " is " << factor(g) << endl;
}
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./a.out.
Debugging is easy with gdb and the following macro to print giac objects (in .gdbinit) :
echo Defining v as print command for giac types\n define v print ($arg0).dbgprint() end ; $ suppress this line (emacs latex colorization bug) |
gen class for generic object storage. It consists mainly of
a short int, the type of the object, another short int the "subtype" (e.g. lists, sets or
sequences have the same type but different subtypes), and an anonymous union that is
either the object itself if fixed-size (16 bits integers or double) or a pointer to a
referenced-counted object. More info on types are in the headers dispatch.h and gen.h.
Typically a code slice could be :
if (g.type==_VECT){
vecteur & v = *g._VECTptr;
int s=v.size();
for (int i=0;i<s;++i)
cout << i << ":" << factor(v[i]) << endl;
}
|
gen are derived from the STL (Standard Template Library), e.g.
vecteur is a typedef for std::vector<gen>, they should therefore be straightforward to
use. User functions C++-equivalent have most of the time the same name preceded by _ (for
non-unary functions, arguments are grouped in a vecteur before the function call, it
appears always as a unary gen'
gen function).
4.5.3 Dynamic modules
Writing a dynamic module requires in addition the declaration of user functions, so that
they can be called inside an xcas session after an insmod call. For example, a module to
have French names for the user language control words, is in the directory src, file
progfr.cc.
