spielwiese
Last change
on this file since a7efa79 was
a7efa79,
checked in by Hans Schönemann <hannes@…>, 16 years ago

*hannes: new book version
gitsvnid: file:///usr/local/Singular/svn/trunk@10182 2c84dea37e6841379b89c4e89433aadc


Property mode set to
100644

File size:
1.5 KB

Line  

1  LIB "tst.lib"; 

2  tst_init(); 

3  

4  ================================= example B.5.10 ========================== 

5  ring R=2,(z,x,y),lp; 

6  poly f=x2+x+1; //minimal polynomial of the field 

7  //extension 

8  poly g=z2+z+1; //polynomial to factorize 

9  resultant(f,g,x); 

10  resultant(f,subst(g,z,z+x),x); 

11  

12  poly h=y5+y3+y2+y+1; //the minimal polynomial for the new 

13  //field extension 

14  poly G=subst(g,z,z+xy); //the transformed polynomial 

15  poly r=resultant(f,G,x); 

16  r; //the norm r of the transformed 

17  //polynomial 

18  

19  

20  poly s=resultant(h,r,y); 

21  s; //the norm of r 

22  

23  factorize(s); 

24  

25  ring S=(2,y),(z,x),lp; 

26  minpoly=y5+y3+y2+y+1; 

27  poly r=imap(R,r); 

28  poly f1=gcd(r,z10+z9+z7+z6+z3+z2+1); //the gcd with the first 

29  //factor 

30  f1; 

31  f1=simplify(f1,1); //we normalize f1 

32  f1; 

33  poly f2=gcd(r,z10+z9+z7+z5+z2+z+1); //the gcd with the second 

34  //factor 

35  f2=simplify(f2,1); 

36  f2; 

37  

38  rf1*f2; //test the result 

39  

40  f1=subst(f1,z,z+x*y); //the inverse transformation 

41  f1=simplify(f1,1); 

42  f1; 

43  f2=subst(f2,z,z+x*y); //the inverse transformation 

44  f2=simplify(f2,1); 

45  f2; 

46  

47  setring R; 

48  ideal I=std(ideal(f,h)); 

49  qring T=I; 

50  option(redSB); 

51  poly f1=imap(S,f1); 

52  poly f2=imap(S,f2); 

53  poly g=imap(R,g); 

54  std(ideal(f1,g)); //gcd of g with the first factor 

55  

56  std(ideal(f2,g)); //gcd of g with the second factor 

57  

58  std((x+z+1)*(x+z)); //test the result 

59  

60  tst_status(1);$ 

61  

Note: See
TracBrowser
for help on using the repository browser.