Hello there,
I tried to evaluate the integral of a Pari/GP function but failed so far. Here is an example code on (SageMath version 8.9, Release Date: 2019-09-29 and windows 10):
sage: lchi4 = DirichletGroup(4).list()[1].lfunction(); lchi4
PARI L-function associated to Dirichlet character modulo 4 of conductor 4 mapping 3 |--> -1
sage: numerical_integral(lambda t: lchi4(t).real(), 2,3)
---------------------------------------------------------------------------
SystemError Traceback (most recent call last)
/opt/sagemath-8.9/local/lib/python2.7/site-packages/sage/all_cmdline.pyc in <module>()
----> 1 numerical_integral(lambda t: lchi4(t).real(), Integer(2),Integer(3))
/opt/sagemath-8.9/local/lib/python2.7/site-packages/sage/calculus/integration.pyx in
sage.calculus.integration.numerical_integral (build/cythonized/sage/calculus/integration.c:4061)()
353 _b = b
354 W = <gsl_integration_workspace*> gsl_integration_workspace_alloc(n)
--> 355 sig_on()
356 gsl_integration_qag(&F,_a,_b,eps_abs,eps_rel,n,rule,W,&result,&abs_err)
357 sig_off()
SystemError: calling remove_from_pari_stack() inside sig_on()
However, for the Riemann zeta function, numerical_integral works fine as below:
sage: numerical_integral(lambda t: zeta(t), 2,3)
(1.3675256886839795, 1.518258506343328e-14)
It looks like it would work for lchi4 if lchi4(x) can be coerced into a symbolic expression like zeta(x) as shown below:
sage: type(lchi4(3))
<type 'sage.rings.complex_number.ComplexNumber'>
sage: type(zeta(3))
<type 'sage.symbolic.expression.Expression'>
Can you please let me know how to evaluate the integral numerically for a Pari/GP function as lchi4?
Thank you in advance.
