Options (concatenate any number of them into <Option-string>):

h print this information

f use as filter

g general output ; for P reflexive: numbers of (dual) points/vertices, Hodge numbers and if P is not reflexive: numbers of points, vertices, equations

p points of P

v vertices of P

e equations of P/vertices of P-dual

m pairing matrix between vertices and equations

d points of P-dual (only if P reflexive)

a all of the above except h,f

l LG-`Hodge numbers' from single weight input

r ignore non-reflexive input

D dual polytope as input (ref only)

n do not complete polytope or calculate Hodge numbers

i incidence information

s check for span property (only if P from CWS)

I check for IP property

S number of symmetries

T upper triangular form

N normal form

t traced normal form computation

V IP simplices among vertices of P*

P IP simplices among points of P* (with 1<=codim<=# when # is set)

Z lattice quotients for IP simplices

# #=1,2,3 fibers spanned by IP simplices with codim<=#

## ##=11,22,33,(12,23): all (fibered) fibers with specified codim(s) when combined: ### = (##)#

A affine normal form

B Barycenter and lattice volume [# ... points at deg #]

F print all facets

G Gorenstein: divisible by I>1

L like 'l' with Hodge data for twisted sectors

U simplicial facets in N-lattice

U1 Fano (simplicial and unimodular facets in N-lattice)

U5 5d fano from reflexive 4d projections (M lattice)

C1 conifold CY (unimodular or square 2-faces)

C2 conifold FANO (divisible by 2 & basic 2 faces)

E symmetries related to Einstein-Kaehler Metrics

Input

degrees and weights `d1 w11 w12 ... d2 w21 w22 ...' or `d np' or `np d' (d=Dimension, np=#[points]) and (after newline) np*d coordinates

Output

as specified by options