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The subgraph_cound should be subgraph_count. Similarly for cycle_subgraph_cound.

Suppose i have a polynomial matrix like:

var('x')
g=graph.CompleteGraph(4)
h=g.am()
t=h-x*identity_matrix(4)
t1=t.adjugate()
t1

Then, how do i get t1 in the factorized/simplified form. Specifically, I see that there are exactly two distinct entries in t1, and each of them can be factorized into two distinct monomial powers. But, how do I get this directly, without having to factorize each element separately. Any hints? Thanks beforehand.

Thanks to @MaxAlexseyev, to get what I wanted, which is the adjugate matrix having all its individual entries factored,

Got it! I used t1.apply_map(lambda z:factor(z))to get what I wanted.

Thanks! I actually wanted to factorize each of the individual matrix entries. On writing factor(t1.list()), I get error

Factorizing matrix entries that are polynomials Suppose i have a polynomial matrix like: var('x') g=graph.CompleteGraph

Suppose I have a matrix A which is m x n in order. How do I extract a submatrix of specified rows and colums from A. Like I want a p x q submatrix of A. Will the expanded_submatrix method help in this regard? Thanks beforehand.

The syntax was unexpectedly easy. It is similar to the one used in Matlab/Octave. We just use the syntax A[i-1:p,j-1:q],

Extracting specific rows of a matrix Suppose I have a matrix A which is m x n in order. How do I extract a submatrix of

@dan_fulea Modified the question. Added a reference. At least, if there was a workaround when q or n in this question is

Representing Code over integer rings Is there a method to deal with all codewords over the integer rings Z_n where n=p^

@dan_fulea By codewords I mean a submodule over the ring [math]\mathbb{Z}_n[/math]. And yes, it is best to get them as a

@dan_fulea By codewords I mean a submodule over the group [math]\mathbb{Z}_n[/math]. And yes, it is best to get them as

If an equation has several radicals, is it possible to remove the radicals to get a radical free equation in SageMath? The simplify_radical() method seems not to exist in SageMath. The canonicalize_radical() seems to do nothing. For example,

E=a^2 + b^2 + c^2 + sqrt(a^2 + b^2 + c^2)==0
E.canonicalize_radical()

gives the output same as E

Any alternative? Thanks beforehand.

@dan_fulea By codewords I mean the module over the group [math]\mathbb{Z}_n[/math]. And yes, it is best to get them as a

How to remove radicals from an equation If an equation has several radicals, is it possible to remove the radicals to ge

How to remove radicals from an equation If an equation has several radicals, is it possible to remove the radicals to ge

But that dosent seem to work

Representing Code over integer rings Is there a method to deal with all codewords over the integr rings Z_n wheren=p^k

How to remove radicals from an equation If an equation has several radicals, is it possible to remove the radicals to ge

The method simplify_radical() does not seem to exist

@EmmanuelCharpentier The accepted answer is exactly what I wanted to do.

Suppose I wish to plot the function

import numpy as np
var('a,y') 
A=np.linspace(-1,1,10)
for a in A:
    z=a+x-(e^(-y^2/2))/sqrt((2*pi))
    plot3d(z,(x,-1,1),(y,-1,1))

That is, I wish to plot the function z over a range of a. Actually the original function was z=a+x. But, in order to introduce randomization, I changed the variable x to x-y', where y' is the standard normal variable. I wish to obtain the plot of z as a kind of variable probability distribution over the grid of x and y with the variation of a (so kind of series of probability distributions overlapping each other). How do I do this? Any hints? Thanks beforehand.

Plotting a Probability distribution with varying parameter Suppose I wish to plot the function import numpy as np var('

Plotting a Probability distribution with varying parameter Suppose I wish to plot the function import numpy as np var('

Plotting a Probability distribution with varying parameter Suppose I wish to plot the function import numpy as np var('

Plotting a Probability distribution with varying parameter Suppose I wish to plot the function import numpy as np var('

How is edge coloring satisfied in this code? I saw the beautiful code written on this site of using Mixed Integer Linear

I wish to construct the graph polynomial (as given here) of any given graph. To do so, I wrote the following code. But, the output was null. What needs to be modified in the following code to get the appropriate graph polynomial (the product of binomials corresponding each edge):

 def grappoly(G):
 R=PolynomialRing(ZZ,['x_'+str(k) for k in G.vertices()])
 R.inject_variables()
 for i in G.vertices():
      for j in G.vertices():
           P=1
           if set((i,j)).intersection(set(G.edges()))==(i,j):
                         P=('x_'+str(i)-'x_'+str(j))*P
           return P           
 X=graphs.CompleteBipartiteGraph(5,5)
 grappoly(X)

Thanks beforehand.

The code required the following modifications after which it worked smoothly: def grappoly(G): R=PolynomialRing(ZZ,[

Graph polynomial construction I wish to construct the graph polynomial (as given here) of any given graph. To do so, I w

Graph polynomial construction I wish to construct the graph polynomial (as given here of any given graph. To do so, I wr

Graph polynomial construction I wish to construct the graph polynomial (as given here of any given graph. To do so, I wr

Graph polynomial construction I wish to construct the graph polynomial (as given here of any given graph. To do so, I wr