Calculating Induced vs. Ambient Volume Using Lrs Engine

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Hi All,

I aim to calculate the volumes of not-full dimensional polytopes. Using ambient measure, the volume is always 0. So, I want to use induced measure. At the same time, though, I also want the engine to be Lrs.

If I just do .volume(engine = 'lrs'), I always get 0. Is this an error? Or is this because the system is using ambient measure for the volume?

To try and fix the issue, I want to have both induced measure and lrs engine. However, when I input something like .volume(measure = 'induced', engine = 'lrs'), I get an error. Is there some way for me to get both?

EDIT To address a comment, I'm pasting the code I used. Unfortunately, I don't have enough points to add attachments, so I'll also copy the entire error message below.

CODE

def getVolume(self):

        return self.poly.volume(measure = "induced", engine="lrs")*factorial(self.poly.dim())

ERROR MESSAGE (long)

KeyError                                  Traceback (most recent call last)
/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCaller.__call__ (build/cythonized/sage/misc/cachefunc.c:10347)()
   1942             try:
-> 1943                 return cache[k]
   1944             except TypeError:  # k is not hashable

KeyError: (('induced', 'lrs'), ())

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
/tmp/ipykernel_162824/3888703736.py in <module>
    200 G = DiGraph({Integer(0):[Integer(4),Integer(5),Integer(6),Integer(7),Integer(8)], Integer(1):[Integer(5),Integer(6),Integer(7),Integer(8)], Integer(2):[Integer(6),Integer(7),Integer(8)], Integer(3):[Integer(7),Integer(8)], Integer(4):[Integer(8)], Integer(5):[Integer(8)], Integer(6):[Integer(8)], Integer(7):[Integer(8)]})
    201 H=DiGraph({Integer(0):[Integer(2),Integer(3),Integer(4)], Integer(1):[Integer(3),Integer(4)], Integer(2):[Integer(4)], Integer(3):[Integer(4)]})
--> 202 FlowPolytope(H, [Integer(1),Integer(1),Integer(1),Integer(1),-Integer(4)]).getVolume().radical_expression()
    203 I=DiGraph({Integer(0):[Integer(4),Integer(5),Integer(6),Integer(7),Integer(8)], Integer(1):[Integer(5),Integer(6),Integer(7),Integer(8)], Integer(2):[Integer(6),Integer(7),Integer(8)], Integer(3):[Integer(7),Integer(8)], Integer(4):[Integer(8)], Integer(5):[Integer(8)], Integer(6):[Integer(8)], Integer(7):[Integer(8)]})
    204 FlowPolytope(I, [Integer(1),Integer(1),Integer(1),Integer(1),Integer(1),Integer(1),Integer(1),Integer(1),-Integer(8)]).getVolume().radical_expression()

/tmp/ipykernel_162824/3888703736.py in getVolume(self, eng)
     63         needs Sage 5.9 for 'lrs' engine
     64         """
---> 65         return self.poly.volume(measure = "induced", engine="lrs")*factorial(self.poly.dim())
     66 
     67     def getVertices(self):

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCaller.__call__ (build/cythonized/sage/misc/cachefunc.c:10483)()
   1946                 return cache[k]
   1947         except KeyError:
-> 1948             w = self._instance_call(*args, **kwds)
   1949             cache[k] = w
   1950             return w

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCaller._instance_call (build/cythonized/sage/misc/cachefunc.c:9949)()
   1822             True
   1823         """
-> 1824         return self.f(self._instance, *args, **kwds)
   1825 
   1826     cdef fix_args_kwds(self, tuple args, dict kwds):

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/geometry/polyhedron/base.py in volume(self, measure, engine, **kwds)
   4738             else:
   4739                 sqrt_Adet = AA(Adet).sqrt()
-> 4740                 scaled_volume = AA(scaled_volume)
   4741             return scaled_volume / sqrt_Adet
   4742         elif measure == 'induced_rational':

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/parent.pyx in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9388)()
    896         if mor is not None:
    897             if no_extra_args:
--> 898                 return mor._call_(x)
    899             else:
    900                 return mor._call_with_args(x, args, kwds)

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/coerce_maps.pyx in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4665)()
    159                 print(type(C), C)
    160                 print(type(C._element_constructor), C._element_constructor)
--> 161             raise
    162 
    163     cpdef Element _call_with_args(self, x, args=(), kwds={}):

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/coerce_maps.pyx in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4557)()
    154         cdef Parent C = self._codomain
    155         try:
--> 156             return C._element_constructor(x)
    157         except Exception:
    158             if print_warnings:

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/qqbar.py in _element_constructor_(self, x)
   1109         elif hasattr(x, '_algebraic_'):
   1110             return x._algebraic_(AA)
-> 1111         return AlgebraicReal(x)
   1112 
   1113     def _repr_(self):

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/qqbar.py in __init__(self, x)
   5292             -1.414213562373095?
   5293         """
-> 5294         AlgebraicNumber_base.__init__(self, AA, x)
   5295         self._ensure_real()
   5296 

/home/sc_serv/sage/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/qqbar.py in __init__(self, parent, x)
   3610                 self._descr = ANExtensionElement(QQbar_I_generator, QQbar_I_nf([x[0], -x[1]]))
   3611         else:
-> 3612             raise TypeError("Illegal initializer for algebraic number")
   3613 
   3614         prec = 64

TypeError: Illegal initializer for algebraic number