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Multivariate Pade approximation, recognizing rational function (Question edited) Suppose that I have a taylor polynomia

Let me show my work so far. S.<y> = QQ[] R.<x> = S[] T.<y,x> = PowerSeriesRing(QQ,default_prec=8) U.&

Multivariate Pade approximation, recognizing rational function Suppose that I have a taylor polynomial approximation of

Multivariate Pade approximation, recognizing rational function Suppose that I have a taylor polynomial approximation of

Multivariate Pade approximation, recognizing rational function Suppose that I have a taylor polynomial approximation of

Multivariate Pade approximation, recognizing rational function Suppose that I have a taylor polynomial approximation of

Multivariate Pade approximation, recognizing rational function Suppose that I have a taylor polynomial approximation of

Your matrix is not symmetric: A = matrix(QQbar, [[2,-1,0],[-1,2,1],[0,-1,2]]) A.is_symmetric()

Adding dot2tex to the Sage installation, as suggested by FrédéricC and John Palmieri, did work for me and produces Hass

latex for Hasse diagram of poset not properly laid out The plot method on a poset displays the Hasse diagram in a satisf

latex for Hasse diagram of poset not properly laid out The plot method on a poset displays the Hasse diagram in a satisf

You could expand around t=0 instead, for t = w + 0.1 var('t') bmac = b.substitute(w=t-0.1).taylor(t,0,3) cmac = c.subst

You could expand around t=0 instead, for t = w + 0. var('t') bmac = b.substitute(w=t-0.1).taylor(t,0,3) cmac = c.substi

Displaying and typesetting partitions A partition can be viewed as a list or pretty-printed using ascii art. This works

I am trying to simplify some binomial expressions using Sage.

var('a,n,c,m')
H = binomial(2*m-c,m-c)-binomial(2*m-c,m+1)
Cn = binomial(2*n,n)/(n+1)
Uan = (H.substitute(m=n,c=a+1) + a*H.substitute(m=n-1,c=a))/Cn 
assume(a>0)
assume(n>0)
assume(n,'integer')
assume(a,'integer')
UUan=Uan.full_simplify()
UUan

Now I want the limit of this expression as n -> +Infininty. Maple can do it, it correctly returns

                                                             2                  (-a)
                                                          (a  + 3 a + 4) 2
                                                          --------------------
                                                                   4

I can get Sage to calculate the limit for specific values of a:

limit(UUan.substitute(a=5),n=+Infinity)

However, when I try

limit(UUan,n=+Infinity)

I get an error from the underlying Maxima engine:

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
<ipython-input-70-59aa81a6cc92> in <module>
----> 1 limit(UUan,n=+Infinity)

~/sage/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/calculus/calculus.py in limit(ex, dir, taylor, algorithm, **argv)
   1415     if algorithm == 'maxima':
   1416         if dir is None:
-> 1417             l = maxima.sr_limit(ex, v, a)
   1418         elif dir in dir_plus:
   1419             l = maxima.sr_limit(ex, v, a, 'plus')

~/sage/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in sr_limit(self, expr, v, a, dir)
    985             elif dir == "minus":
    986                 L.append(max_minus)
--> 987             return max_to_sr(maxima_eval(([max_limit], L)))
    988         except RuntimeError as error:
    989             s = str(error)

~/sage/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.EclObject.__call__ (build/cythonized/sage/libs/ecl.c:8511)()
    836         """
    837         lispargs = EclObject(list(args))
--> 838         return ecl_wrap(ecl_safe_apply(self.obj,(<EclObject>lispargs).obj))
    839 
    840     def __richcmp__(left, right, int op):

~/sage/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.ecl_safe_apply (build/cythonized/sage/libs/ecl.c:6053)()
    357             raise KeyboardInterrupt("ECL says: {}".format(message))
    358         else:
--> 359             raise RuntimeError("ECL says: {}".format(message))
    360     else:
    361         return ret

RuntimeError: ECL says: BINDING-STACK overflow at size 10240. Stack can probably be resized.
Proceed with caution.

---------------------------------------------------------------------------------------------------------------------------------------------

Is SAGE able to compute this limit? Should i provide other provisos? Is there another approach I should try?

Edit: The following works:

Uan.limit(n=Infinity,dir='+',taylor=True)

so I guess all is well. I do not know if the fact that Maxima throws an exception when the taylor keyword is ommitted is a bug or not. The documentation for limit says

• "taylor" - (default: False); if True, use Taylor series, which allows more limits to be computed (but may also crash in some obscure cases due to bugs in Maxima).

Maybe this should be amended to indicate that in some cases, taylor=False causes crashes.

The function limit() has a keyword taylor, which might help or hinder. In this case, Uan.limit(n=Infinity,dir='+',taylo

The function limit() has a keyword taylor, which might help or hinder. In this case, Uan.limit(n=Infinity,dir='+'

++++++++++

Uan.limit(n=Infinity,dir='+',taylor=True) works in this case, in other cases it is better to use taylor=False.

Uan.limit(n=Infinity,dir='+',taylor=True) works in this case, in other cases it is better to use taylor=False.

Simplifying factorials, limits, Maxima crash I am trying to simplify some binomial expressions using Sage. var('a,n,c,m

Simplifying factorials, limits, Maxima crash I am trying to simplify some binomial expressions using Sage. var('a,n,c,m

Simplifying factorials, limits, Maxima crash I am trying to simplify some binomial expressions using Sage. var('a,n,c,m

Simplifying factorials, limits, Maxima crash I am trying to simplify some binomial expressions using Sage. var('a,n,c,m

Simplifying factorials, limits, Maxima crash I am trying to simplify some binomial expressions using Sage. var('a,n,c,m

Simplifying factorials, limits, Maxima crash I am trying to simplify some binomial expressions using Sage. var('a,n,c,m

Basis elements in the incidence algebra. i.e. a single interval, are added like this: R = posets.YoungDiagramPoset([2,

Incidence algebras, entering elements I have been trying to use incidence algebras, but immediately stumbled on a proble

Incidence algebras, entering elements I have been trying to use incidence algebras, but immediately stumbled on a proble

Incidence algebras, entering elements I have been trying to use incidence algebras, but immediately stumbled on a proble

Incidence algebras, entering elements I have been trying to use incidence algebras, but immediately stumbled on a proble

Group algebra of permutation group, error Why does not GroupAlgebra(PermutationGroup([(1,2,3),(2,3,4)]),QQ).center_basi

Group algebra of permutation group, error Why does not GroupAlgebra(PermutationGroup([(1,2,3),(2,3,4)]),QQ).center_basi

Thank you for your answer. I tried restricting the problem to simplifying max of two piecewise linear expressions (hopin

max_symbolic, polynomial expressions, assumptions The following works as expected: var('b') with assuming(b>1):