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Thank you. I know this method.

I want to work in two variables symmetric functions. For example, expand $h_\lambda(X+Y)$ or $h_\lambda(X) e_\mu(Y)$ to $s_\lambda(X) s_\mu(Y)$.

I have try Arch linux and Ubuntu 18.04. All have the problem "NameError: name '_interact_' is not defined. " .

When I starting the sagenb notebook,there are some errors as follows: Failed to connect to the bus: Could not parse server address: Unknown address type (examples of valid types are "tcp" and on UNIX "unix") ERROR:ssl_client_socket_impl.cc(960)] handshake failed; returned -1, SSL error code 1, net_error -202

In the notebook, the error just as my question. That is "NameError: name '_interact_' is not defined. "

Unfortunately, I did this and still the same error。 have you tried？

Hi, I still want to run sagenb for sagemath 9.1. I follow wiki.sagemath.org/Python3-Switch use the following codes to compile sage 9.1.

make configure;   ./configure --with-python=2; make build

Then I run ‘ ./sage -i sagenb’. But I get errors in the notebook:

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

  File "_sage_input_6.py", line 8, in <module>

    _interact_.SAGE_CELL_ID=1

NameError: name '_interact_' is not defined

This problem may be caused by the codes in sage/local/lib/python2.7/site-packages/sagenb-1.1.3-py2.7.egg/sagenb/notebook/worksheet.py.

   def initialize_sage(self):
            S = self.__sage
            try:
                from . import misc
                cmd = '''import base64
import sagenb.misc.support as _support_
import sagenb.notebook.interact as _interact_ # for setting current cell id
....  '''

          S.execute(cmd)

I think 'cmd' is not be executed. If I put some error code in 'cmd', there were nothing happened.

This answer is wonderful. Thank you!

Yeah, you are right.

Given a matrix $m=(a_{i,j})$, where each $a_{i,j}$ is a Schur function, by default, m.det() will give the determinant using the original multiplication.

But I want it to use the Kronecker product for Schur functions.

I did not find any options to set the Kronecker product as default multiplication operator in the ring of Schur functions or in the matrix class.

To give an example, let us define such a matrix:

sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.schur()
sage: f = s[2]

sage: m = matrix([[f, 0], [0, f]])
sage: m
[s[2]    0]
[   0 s[2]]

Then compare:

sage: m.det()
s[2, 2] + s[3, 1] + s[4]

sage: f * f
s[2, 2] + s[3, 1] + s[4]

sage: f.kronecker_product(f)
s[2]

Thanks! I only use s for computation and do not know s can be used as a ring.

I try the following codes, but it does not work.

SF= SymmetricFunctions(QQ) 
s = SF.s() 
I = P.incidence_algebra(SF)
s([2,1])*I[1,1]  
TypeError: unsupported operand parent(s) for *: 'Symmetric Functions over Rational Field in the Schur basis' and 'Incidence algebra of Finite lattice containing 4 elements over Symmetric Functions over Rational Field'