mentioned the imaginary unit 'I'

[ginac.git] / doc / tutorial / ginac.texi

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index dcee9335e90270ccbc2ff045e7f792f9d258faa4..241de6761f8ce1bc0528f6d86fddd4b288033a7e 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -931,10 +931,22 @@ int main()
     numeric trott("1.0841015122311136151E-2");
     
     std::cout << two*p << std::endl;  // floating point 6.283...
+    ...
+@end example
+
+@cindex @code{I}
+@cindex complex numbers
+The imaginary unit in GiNaC is a predefined @code{numeric} object with the
+name @code{I}:
+
+@example
+    ...
+    numeric z1 = 2-3*I;                    // exact complex number 2-3i
+    numeric z2 = 5.9+1.6*I;                // complex floating point number
 @}
 @end example
 
-It may be tempting to construct numbers writing @code{numeric r(3/2)}.
+It may be tempting to construct fractions by writing @code{numeric r(3/2)}.
 This would, however, call C's built-in operator @code{/} for integers
 first and result in a numeric holding a plain integer 1.  @strong{Never
 use the operator @code{/} on integers} unless you know exactly what you
@@ -3191,11 +3203,11 @@ Some examples:
 b^3+a^3+(x+y)^3
 > subs(a^4+b^4+(x+y)^4,$1^2==$1^3);
 b^4+a^4+(x+y)^4
-> subs((a+b+c)^2,a+b=x);
+> subs((a+b+c)^2,a+b==x);
 (a+b+c)^2
 > subs((a+b+c)^2,a+b+$1==x+$1);
 (x+c)^2
-> subs(a+2*b,a+b=x);
+> subs(a+2*b,a+b==x);
 a+2*b
 > subs(4*x^3-2*x^2+5*x-1,x==a);
 -1+5*a-2*a^2+4*a^3
@@ -3443,9 +3455,34 @@ int ex::degree(const ex & s);
 int ex::ldegree(const ex & s);
 @end example
 
-which also work reliably on non-expanded input polynomials (they even work
-on rational functions, returning the asymptotic degree). To extract
-a coefficient with a certain power from an expanded polynomial you use
+These functions only work reliably if the input polynomial is collected in
+terms of the object @samp{s}. Otherwise, they are only guaranteed to return
+the upper/lower bounds of the exponents. If you need accurate results, you
+have to call @code{expand()} and/or @code{collect()} on the input polynomial.
+For example
+
+@example
+> a=(x+1)^2-x^2;
+(1+x)^2-x^2;
+> degree(a,x);
+2
+> degree(expand(a),x);
+1
+@end example
+
+@code{degree()} also works on rational functions, returning the asymptotic
+degree:
+
+@example
+> degree((x+1)/(x^3+1),x);
+-2
+@end example
+
+If the input is not a polynomial or rational function in the variable @samp{s},
+the behavior of @code{degree()} and @code{ldegree()} is undefined.
+
+To extract a coefficient with a certain power from an expanded
+polynomial you use
 
 @example
 ex ex::coeff(const ex & s, int n);