From 3a69907feeb99c772f2bb65235e453619643e931 Mon Sep 17 00:00:00 2001
From: trizen <trizen@protonmail.com>
Date: Mon, 11 Apr 2022 09:29:39 +0300
Subject: [PATCH] - Fixed the conversion of Polynomial objects to Number
 objects (when possible).

Example:

	var a = Poly([3])
	var b = Poly([3,4])

	say a.sqrt	#=> sqrt(3)
	say b.sqrt	#=> NaN

Only polynomials of degree 0 can be converted to a Number. When a Polynomial cannot be converted to a Number, Polynomial.to_n() now returns NaN.
---
 lib/Sidef/Types/Number/Polynomial.pm |  7 ++---
 scripts/Tests/polynomial.sf          | 42 ++++++++++++++++++++++++++++
 2 files changed, 45 insertions(+), 4 deletions(-)

diff --git a/lib/Sidef/Types/Number/Polynomial.pm b/lib/Sidef/Types/Number/Polynomial.pm
index cb572d11..0c1b8b6f 100644
--- a/lib/Sidef/Types/Number/Polynomial.pm
+++ b/lib/Sidef/Types/Number/Polynomial.pm
@@ -15,8 +15,8 @@ package Sidef::Types::Number::Polynomial {
     use overload
       q{bool} => sub { (@_) = ($_[0]); goto &__boolify__ },
       q{""}   => sub { (@_) = ($_[0]); goto &__stringify__ },
-      q{${}}  => sub { \$_[0] },
-      q{0+}   => sub { $_[0] };
+      q{${}}  => \&to_n,
+      q{0+}   => \&to_n;
 
     sub new {
         my (undef, @args) = @_;
@@ -73,8 +73,7 @@ package Sidef::Types::Number::Polynomial {
             return $x->{0};
         }
 
-        ## return Sidef::Types::Number::Number::ZERO;
-        return $x;    # maybe we should return zero?
+        return Sidef::Types::Number::Number::nan();
     }
 
     sub real {
diff --git a/scripts/Tests/polynomial.sf b/scripts/Tests/polynomial.sf
index 181d5ef4..77a4ead4 100644
--- a/scripts/Tests/polynomial.sf
+++ b/scripts/Tests/polynomial.sf
@@ -303,4 +303,46 @@ assert_eq(Mod(chebyshevT(42), 97)(100), chebyshevTmod(42, 100, 97))
 assert_eq(Mod(chebyshevT(42), 97)(15/13), chebyshevT(42, 15/13) % 97)
 assert_eq(Mod(chebyshevT(42), 97)(15/13), chebyshevTmod(42, 15/13, 97))
 
+do {
+
+    func derivative(f) {
+        Poly(f.coeffs.map_2d{|e,k| [e-1, k*e] }.flat...)
+    }
+
+    var coeffs = [
+        [5],
+        [4,-3],
+        [-1,6,5],
+        [-4,3,-2,1],
+        [-1, 6, 5],
+        [1,1,0,-1,-1],
+    ]
+
+    var got = []
+
+    for c in (coeffs) {
+        var poly = Poly(c.flip)
+        var derv = derivative(poly)
+
+        var d = { derv.coeff(_) }.map(0..derv.degree)
+
+        got << d
+
+        say "Polynomial : #{'%20s' % c} = #{poly}"
+        say "Derivative : #{'%20s' % d} = #{derv || 0}\n"
+    }
+
+    assert_eq(
+        got,
+        [
+            [0]
+            [-3]
+            [6, 10]
+            [3, -4, 3]
+            [6, 10]
+            [1, 0, -3, -4]
+        ]
+    )
+}
+
 say "** Test passed!"