#title: derivadas em maxima
#author: jj
#let:

s m  =     { ref2str(rand_sqr_matrix_nat(2,10)) }; 

s m1 = perl{maximamat(3,10) };

f m2 = perl{maximamat(3,10) };

f deter = determinant(#m2);

f m3 = perl{ maximamat(5,0,1) };

##s com           =     { if(#deter % 2 == 1){"impar"} else {"par"  } };

s com1 = perl{ if(#deter % 2 == 1){"impar"} else {"par"  } }; 
s com2 = perl{ #deter / 2 }; 

#format
"_OFD_"=\fbox{Out of domain}

#question:

\begin{enumerate}
\item m1: $ #m $
\item m2: $ #m1 $
\item m2 mais bonita: $ #m2 $
\item matriz booleana : $ #m3 $
\item determinante(m2): $ #deter $
\item comentário: o determinante é #com1; metade dele é #com2.
\end{enumerate}

#sugestion:
#resolution:
#result:
#Verify:

#usepackage
 % \usepackage{...}  latex preambula

#perl
sub maximamat{maxima_matrix(rand_sqr_matrix_nat(@_));} ## (dim, max)  or (dim, min, max)

sub rand_sqr_matrix_nat{ my($dim,$m1,$m2)=@_;  ## (dim, max)  or (dim, min, max)
  my ($m,$min,$max);
  if(defined $m2){ $min = $m1; $max = $m2 }
  else           { $min = 1  ; $max = $m1 }
  for my $i(0..$dim-1){
     for my $j(0..$dim-1){ $m->[$i][$j]= $min + int rand(1+$max-$min) }
  }
  return $m
}

sub ref2str{ my($v,$l) = @_;
  if(ref($v) eq "ARRAY"){
     return  "[" . join(",", (map{ ref2str($_) } @$v)). "]" }
  else { return $v }
}

sub maxima_matrix{ my($v,$l) = @_;
  return  "matrix(" . join(",", (map{ ref2str($_) } @$v)). ")" 
}