Logging to /Users/s/tmp/pari-16.04
GPRC Done.

        GP/PARI CALCULATOR Version 2.12.1 (development 25142-46eb34041)
          i386 running darwin (x86-64/GMP-6.2.0 kernel) 64-bit version
     compiled: Mar 22 2020, Apple clang version 11.0.0 (clang-1100.0.33.17)
                            threading engine: single
                 (readline v8.0 enabled, extended help enabled)

                     Copyright (C) 2000-2020 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes 
WITHOUT ANY WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?17 for how to get moral (and possibly technical) support.

parisizemax = 900001792, primelimit = 1000000
(17:31) gp > z=5+7*I
%1 = 5 + 7*I
(17:32) gp > z^2
%2 = -24 + 70*I
(17:32) gp > abs(z)
%3 = 8.6023252670426267717294735350497136320
(17:32) gp > abs(z^2)
%4 = 74
(17:32) gp > factor(%)
%5 = 
[ 2 1]

[37 1]

(17:32) gp > ?norm
norm(x): norm of x.

(17:32) gp > ??norm
norm(x):

   Algebraic  norm  of x,  i.e. the product of x with its conjugate  (no square
roots are taken), or conjugates for polmods. For vectors and matrices, the norm
is taken componentwise and hence is not the L^2-norm  (see norml2).   Note that
the  norm  of  an  element of R is its square,  so as to be compatible with the
complex norm.

   The library syntax is GEN gnorm(GEN x).

(17:32) gp > norm(z)
%6 = 74
(17:32) gp > w=2+3*I
%7 = 2 + 3*I
(17:33) gp > norm(w)
%8 = 13
(17:33) gp > gcd(z,w)
%9 = 1
(17:33) gp > lcm(z,w)
%10 = -11 + 29*I
(17:33) gp > norm(%)
%11 = 962
(17:33) gp > factor(%)
%12 = 
[ 2 1]

[13 1]

[37 1]

(17:33) gp > Mod(z,w)
  ***   at top-level: Mod(z,w)
  ***                 ^--------
  *** Mod: forbidden division t_COMPLEX % t_COMPLEX.
  ***   Break loop: type 'break' to go back to GP prompt
break> break

(17:34) gp > norm(z)
%13 = 74
(17:34) gp > norm(z-w)
%14 = 25
(17:34) gp > norm(z-w-w)
%15 = 2
(17:34) gp > z-2*w
%16 = 1 + I
(17:34) gp > z
%17 = 5 + 7*I
(17:35) gp > Z=Mod(5+7*j,j^2+1)
%18 = Mod(7*j + 5, j^2 + 1)
(17:35) gp > w
%19 = 2 + 3*I
(17:35) gp > W=Mod(2+3*j,j^2+1)
%20 = Mod(3*j + 2, j^2 + 1)
(17:35) gp > gcd(Z,W)
%21 = Mod(1, j^2 + 1)
(17:35) gp > lcm(Z,W)
%22 = Mod(29*j - 11, j^2 + 1)
(17:35) gp > lift(%)
%23 = 29*j - 11
(17:35) gp > norm(%)
%24 = 841*j^2 - 638*j + 121
(17:35) gp > subst(%23,j,I)
%25 = -11 + 29*I
(17:36) gp > norm(%)
%26 = 962
(17:36) gp > factor(%)
%27 = 
[ 2 1]

[13 1]

[37 1]

(17:36) gp > Mod(Z,W)
  ***   at top-level: Mod(Z,W)
  ***                 ^--------
  *** Mod: forbidden division t_POLMOD % t_POLMOD.
  ***   Break loop: type 'break' to go back to GP prompt
break> break

(17:36) gp > Z
%28 = Mod(7*j + 5, j^2 + 1)
(17:36) gp > W
%29 = Mod(3*j + 2, j^2 + 1)
(17:36) gp > Mod(Z,3*j+5)
%30 = Mod(0, 1)
(17:36) gp > Mod(Z,7*j+5)
%31 = Mod(0, 1)
(17:36) gp > Mod(Z,3*j+w)
%32 = Mod(0, 1)
(17:37) gp > Mod(Z,3*j+2)
%33 = Mod(0, 1)
(17:37) gp > 7%5
%34 = 2
(17:47) gp > z
%35 = 5 + 7*I
(17:47) gp > w
%36 = 2 + 3*I
(17:47) gp > z%w
  ***   at top-level: z%w
  ***                  ^--
  *** _%_: forbidden division t_COMPLEX % t_COMPLEX.
  ***   Break loop: type 'break' to go back to GP prompt
break> break

(17:47) gp > "Exercício - escrever uma função de divisão euclideano dos inteiros de Gauss"
%37 = "Exercício - escrever uma função de divisão euclideano dos inteiros de Gauss"
(17:48) gp > z/w
%38 = 31/13 - 1/13*I
(17:48) gp > floor(%)
  ***   at top-level: floor(%)
  ***                 ^--------
  *** floor: incorrect type in gfloor (t_COMPLEX).
  ***   Break loop: type 'break' to go back to GP prompt
break> break

(17:48) gp > frac(%38)
  ***   at top-level: frac(%38)
  ***                 ^---------
  *** frac: incorrect type in gfloor (t_COMPLEX).
  ***   Break loop: type 'break' to go back to GP prompt
break> break

(17:48) gp > gfrac(z)=frac(re(z))+I(frac(im(z))
  ***   syntax error, unexpected $end, expecting )-> or ',' or ')': 
  ***   ...=frac(re(z))+I(frac(im(z))
  ***                               ^-
(17:49) gp > ?real
real(x): real part of x.

(17:49) gp > ?imag
imag(x): imaginary part of x.

(17:49) gp > gfrac(z)=frac(real(z))+I*(frac(imag(z))
  ***   syntax error, unexpected $end, expecting )-> or ',' or ')': 
  ***   ...(real(z))+I*(frac(imag(z))
  ***                               ^-
(17:49) gp > gfrac(u)=frac(real(u))+I*(frac(imag(u))
  ***   syntax error, unexpected $end, expecting )-> or ',' or ')': 
  ***   ...(real(u))+I*(frac(imag(u))
  ***                               ^-
(17:49) gp > ?gfrac
gfrac: unknown identifier

(17:49) gp > ?u
u: unknown identifier

(17:50) gp > gfrac(u)=frac(real(u))+frac(imag(u))*I
%39 = (u)->frac(real(u))+frac(imag(u))*I
(17:50) gp > gfrac(z/w)
%40 = 5/13 + 12/13*I
(17:50) gp > z/w-gfrac(z/w)
%41 = 2 - I
(17:50) gp > %*w
%42 = 7 + 4*I
(17:50) gp > z-%
%43 = -2 + 3*I
(17:50) gp > norm(%)
%44 = 13
(17:50) gp > norm(w)
%45 = 13