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After sage -pip install-ing, you can enable extensions in a cell in a notebook. For example to enable collapsible headin

After sage -pip install-ing, you can enable extensions in a cell in a notebook. For example to enable collapsible headin

I am trying to use the SageManifolds tensor modules package to work with the tensor power $T = E^{\otimes 2}$ where $E$ is itself the exterior power $E = \bigwedge^2 \mathbb{Z}$.

Here is what I have so far:

sage: M = FiniteRankFreeModule(ZZ, 3, name='M')
sage: E = M.exterior_power(2)
sage: T = E.tensor_module(2,0)

I then want to work with an element of $T$ by giving it coordinates. I can give an element of $E$ a coordinate by doing

sage: a = E([], name='a')
sage: a.set_comp()[0,1] = 3
sage: a.set_comp()[0,2] = 1
sage: a.display()
a = 3 e_0∧e_1 + e_0∧e_2

So I would have expected to be able to do the same for $T$:

sage: t = T([], name='t')
sage: t.set_comp()[0,0] = 1

but I get a ValueError:

ValueError: the None has not been defined on the 2nd exterior power of the Rank-3 free module M over the Integer Ring

The code in the source which prints None is raise ValueError("the {} has not been ".format(basis) +... and so the problem is that there is no basis for E.

sage: E.default_basis()
No default basis has been defined on the 2nd exterior power of the Rank-3 free module M over the Integer Ring

When I try to define a basis I get a type error:

sage: E.basis('e')
TypeError: __init__() missing 1 required positional argument: 'degree'

coming from the line

sage/tensor/modules/free_module_basis.py in __init__(self, fmodule, symbol, latex_symbol, indices, latex_indices, symbol_dual, latex_symbol_dual)
     637         ring_one = fmodule._ring.one()
     638         for i in fmodule.irange():
--> 639             v = fmodule.element_class(fmodule)
     640             v.set_comp(self)[i] = ring_one
     641             vl.append(v)

because E.element_class() has the init signature E.element_class(fmodule, degree, name=None, latex_name=None). There is no default degree passed, and there is no option for fmodule.element_class(fmodule) to take an argument degree. Are there any workarounds to this problem?

Many thanks!!

You could try creating creating a finite-dimensional algebra with basis specified by the relation iterator in the poset.

Tensor product of exterior power I am trying to use the SageManifolds tensor modules package to work with the tensor pow

Tensor product of exterior power I am trying to use the SageManifolds tensor modules package to work with the tensor pow

Tensor product of exterior power I am trying to use the SageManifolds tensor modules package to work with the tensor pow

`Save` slower than raw computation I have a computation which takes several minutes to run. Using cell magic %%time I ge

If you are using Sage in the terminal, you can simply type pdb and it will turn on the debugger when an error is raised.

If you are using Sage in the terminal, you can simply type pdb and it will turn on the debugger when an error is raised.

If you are using Sage in the terminal, you can simply type pdb and it will turn on the debugger when an error is raised.

For launching as an app not a browser: http://christopherroach.com/articles/jupyterlab-desktop-app/

from SAGE_ROOT, can you call ./sage -i jupyterlab

from SAGE_ROOT, can you call ./sage -i jupyter_lab

A better way to do it might be: E = algebras.Exterior(QQ, 'x', len(G)). Sorry for the clunky previous answer.

A better way to do it might be: E = algebras.Exterior(QQ, 'x', 7). Sorry for the clunky previous answer.

This link might also help

(This link might also help)[https://ask.sagemath.org/question/43599/what-is-a-coxetergroup/]

The first level of the list is each individual relation, and then the second level of the list is each term, so you shou

The relations can be found here. It gives the output as a list of the subscripts you want. What are you looking for fro

One way to do it is algebras.Exterior(QQ,[f'x{i}' for i in range(1, len(G)+1)])

Here is one way to get the generators of the Orlik-Solomon ideal: sage: M = matroids.CompleteGraphic(3) sage: OS = M.or

I'm coming at this with a minimal knowledge of GAP or quiver path algebras, but here is one way to get the Orlik-Solomon

I'm coming at this with a minimal knowledge of GAP or quiver path algebras, but here is how to get the relations M = ma

Ok it looks like this is the current (Sage 9.3beta8) behavior. In the source code for Ideal_nc, which is the type of I,

Ok it looks like this is the current (March 2021) behavior. In the source code for Ideal_nc, which is the type of I, th

Quotients of exterior algebras I am trying to take a quotient of an exterior algebra by a two-sided ideal, and having so