visualizeHypersurface -- visualize the tropical hypersurface of the given polynomial

Synopsis

Usage:

visualizeHypersurface(polyn)

visualizeHypersurface(Valuation=>p,polyn)

visualizeHypersurface(Valuation=>t,polyn)
Inputs:
- polyn, a ring element, polynomial
Optional inputs:
- Valuation (missing documentation) => a number, default value null, use p-adic coefficients with given p
- Valuation (missing documentation) => a ring element, default value null, use coefficients in R[t] with given t

Description

This function wraps the Polymake visualization for a tropical hypersurface given an input polynomial. The input should be entered as a homogeneous polynomial. Running this method opens an image in a new browser window. The coefficients can be interpreted as p-adic coefficients or as polynomials via the option Valuation. Examples are commented out because they open a new browser window.

i1 : R=ZZ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : f=2*x*y+x*z+y*z+z^2

                         2
o2 = 2x*y + x*z + y*z + z

o2 : R

i3 : f=2*x^2+x*y+2*y^2+x*z+y*z+2*z^2

       2           2                 2
o3 = 2x  + x*y + 2y  + x*z + y*z + 2z

o3 : R

i4 : R=ZZ[w,x,y,z]

o4 = R

o4 : PolynomialRing

i5 : f=8*x^2+8*y^2+8*z^2+8*w^2+2*x*y+2*x*z+2*y*z+2*x*w+2*y*w+2*z*w

       2            2                   2                          2
o5 = 8w  + 2w*x + 8x  + 2w*y + 2x*y + 8y  + 2w*z + 2x*z + 2y*z + 8z

o5 : R

Ways to use visualizeHypersurface :

visualizeHypersurface(RingElement)

For the programmer

The object visualizeHypersurface is a method function with options.