abs(pi+I) = pi+I

[benreynwar]

abs(pi+I) returns pi+I

one would have expected:

sqrt(pi^2+1)

Apply attachment:trac_11155-doctest.patch​

[kcrisman]

In the future, be sure to pick a component (for instance, calculus or symbolics); that will help people find it more easily. Thanks for the bug report; mathematically incorrect is definitely bad!

I can confirm this. Moving to major.

Note the following.

sage: abs(pi+i)
pi + I
sage: abs(1+i)
sqrt(2)
sage: abs(n(pi)+i)
3.29690830947562

Pynac is somehow missing this. Note that it gets e right.

sage: abs(e+i)
abs(e + I)

[was]

I can confirm this further. It's mathematically seriously incorrect... so now moving from major to critical, and cc'ing burcin.

Note:

sage: z = pi + i
sage: abs(z)
pi + I
sage: sqrt((z*z.conjugate()).expand())
sqrt(pi^2 + 1)

[burcin]

Reported to the ginac-devel list:

​http://thread.gmane.org/gmane.comp.mathematics.ginac.devel/1363

More detailed about the problem are in my message linked above.

[kcrisman]

Apparently ​already fixed!

[kcrisman]

​Here is the diff.

check/exam_numeric.cpp

@@ -68 +68 @@
                     << " erroneously not recognized as complex rational" << endl;
                ++result;
        }
+       if (test_crat.info(info_flags::nonnegative)) {
+               clog << test_crat
+                    << " erroneously recognized as non-negative number" << endl;
+               ++result;
+       }
        
        int i = numeric(1984).to_int();
        if (i-1984) {

ginac/numeric.cpp

@@ -700 +700 @@
                case info_flags::negative:
                        return is_negative();
                case info_flags::nonnegative:
-                       return !is_negative();
+                       return is_zero() || is_positive();
                case info_flags::posint:
                        return is_pos_integer();
                case info_flags::negint:

[kcrisman]

Making this change in Pynac does fix it:

sage: abs(pi+i)
abs(pi + I)
sage: abs(pi+i).n()
3.29690830947562

So now we just need to package this up. See #12501 for the most recently merged Pynac.

[titusn]

Pull request of the patch to the main repository ​https://bitbucket.org/burcin/pynac/pull-request/1/bugfix-numeric-info-nonnegative-correctly

[burcin]

Pynac 0.2.4 available in #12950 contains the upstream fix. This ticket can be closed once that is merged.