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gcfactor

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gcfactor

z1:25-5*%i;

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gcfactor

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gcfactor

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gcfactor

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gcfactor

Run Example
(%i1)? gcfactor;

 -- Function: gcfactor (<n>)
     Factors the Gaussian integer <n> over the Gaussian integers, i.e.,
     numbers of the form `<a> + <b> `%i'' where <a> and <b> are
     rational integers (i.e.,  ordinary integers).  Factors are
     normalized by making <a> and <b> non-negative.


(%o1)                                true
(%i2) 
Run Example
gcfactor(x^2+y^2+xy-39);
                                2         2
(%o1)                          y  + xy + x  - 39
(%i2) 
Run Example
z1:25-5*%i;
(%o1)                              25 - 5 %i
(%i2)  z2:8+14*%i;
(%o2)                              14 %i + 8
(%i3) z3:1-%i;
(%o3)                               1 - %i
(%i4) d:7-4*%i;
(%o4)                              7 - 4 %i
(%i5) d:3+2*%i;
(%o5)                              2 %i + 3
(%i6) gcfactor(z1);
(%o6)              - (1 + %i) (1 + 2 %i) (2 + %i) (3 + 2 %i)
(%i7) gcfactor(z2);
                                   2
(%o7)                 - %i (1 + %i)  (2 + %i) (3 + 2 %i)
(%i8) expand(z1/d);
                                 25        5 %i
(%o8)                         -------- - --------
                              2 %i + 3   2 %i + 3
(%i9) z2/d;
                                   14 %i + 8
(%o9)                              ---------
                                   2 %i + 3
(%i10) 

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