Error integrate with Fricas as algorithm fresnel_sin called

asked 2018-11-21 14:01:59 -0500

Nasser gravatar image

reference question https://ask.sagemath.org/question/43237/does-sagemath-support-fresnels-function/

I am using

sage: version()
    'SageMath version 8.5.beta2, Release Date: 2018-11-01'

Here is the problem. When I type

from sympy import fresnelc, fresnels
var('a b c d e m n x ')
r=integrate(x^7*fresnels(b*x),x,algorithm="fricas")

sage gives the error

TypeError: An error occurred when FriCAS evaluated '((x)^(7))*(fresnel_sin((b)*(x)))':
   There are no library operations named fresnel_sin

But FriCAS does not have fresnel_sin. It has fresnelS and fresnelC , link here

When running the same command inside Fricas 1.3.4 itself, it works OK

integrate(x^7*fresnelS(b*x),x)   

   (3)
                                    2     2
             5   2 5               b %pi x       8   4 8
       (- 7 b %pi x  + 105 b x)sin(--------) + (b %pi x  - 105)fresnelS(b x)
                                       2
     + 
                                    2     2
         7   3 7       3     3     b %pi x
       (b %pi x  - 35 b %pi x )cos(--------)
                                       2
  /
        8   4
     8 b %pi

Why the error says when FriCAS evaluated '((x)^(7))*(fresnel_sin((b)*(x))) when Fricas itself does not have this function?

Notice that there is no problem using default integrate algorithm in sage

sage: integrate(x^7*fresnels(b*x),x)
1/8*x^8*fresnel_sin(b*x) - 1/16*sqrt(1/2)*((105*I + 105)*(1/4)^(1/4)*pi*erf(sqrt(1/2*I*pi)*b*x) - (105*I - 105)*(1/4)^(1/4)*pi*erf(sqrt(-1/2*I*pi)*b*x) - 4*(sqrt(1/2)*pi^4*b^7*x^7 - 35*sqrt(1/2)*pi^2*b^3*x^3)*cos(1/2*pi*b^2*x^2) + 28*(sqrt(1/2)*pi^3*b^5*x^5 - 15*sqrt(1/2)*pi*b*x)*sin(1/2*pi*b^2*x^2))/(pi^5*b^8)

I was not sure if I am doing something wrong myself, or if I should enter a ticket on this.

Thanks, --Nasser

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