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--- tutorial:polynomials_tutorial [2017/07/06 15:42] – rewrote first part. oroehrig
+++ user_guide:tutorials:polynomials_tutorial [2019/01/25 09:38] – ↷ Page moved from user_guide:polynomials_tutorial to user_guide:tutorials:polynomials_tutorial oroehrig
@@ Line 4: / Line 4: @@
 </code>
-===== Basic Usage of Polynomials in Perl =====
+===== Usage of Polynomials in Perl =====
 ===Constructors===
 The easiest way to create a simple [[https://polymake.org/release_docs/master/common.html#common__Polynomial__339 | Polynomial]] object is through a string:
@@ Line 46: / Line 46: @@
 </code>
-===Newton Polynomials===
+===Example: Newton Polynomials===
 Here is one way to produce polytopes from polynomials (as the convex hull of the exponent vectors of all terms).
 <code>
@@ Line 60: / Line 60: @@
 The final "1" means "true": The Newton polytope of the product of two polynomials always equals the Minkowski sum of the Newton polytopes of the factors.
-===== Example: Toric Degeneration =====
+=== Example: Toric Degeneration ===
 The following describes how to construct the polynomial which describes the toric deformation with respect to a point configuration and a height function.  This is the input data:
@@ Line 73: / Line 73: @@
 <code>
-polytope > @vars = ( "s", map { "x$_" } (1..$points->rows()) );
+polytope > $p = new Polynomial($coefficients,$height|$points);
-polytope > $R = new Ring(@vars);
-polytope > $p = new Polynomial($height|$points,$coefficients,$R);
 </code>