Error integrate with Fricas as algorithm fresnel_sin called

[gh-nasser1]

This ticket tracks the problem reported at

• ​Ask Sage question 44369: Error integrate with Fricas as algorithm fresnel_sin called

observed in SageMath 8.5.beta2:

sage: from sympy import fresnelc, fresnels
sage: var('b x')
sage: integrate(x^7*fresnels(b*x), x, algorithm="fricas")
Traceback (most recent call last)
...
TypeError: An error occurred when FriCAS evaluated '((x)^(7))*(fresnel_sin((b)*(x)))':
   There are no library operations named fresnel_sin
      Use HyperDoc Browse or issue
                              )what op fresnel_sin
      to learn if there is any operation containing " fresnel_sin " in its
      name.

   Cannot find a definition or applicable library operation named
      fresnel_sin with argument type(s)
                              Polynomial(Integer)

      Perhaps you should use "@" to indicate the required return type, or 
      "$" to specify which version of the function you need.

FriCAS does not have fresnel_sin but has fresnelS and fresnelC:

• ​http://fricas.github.io/api/FloatLiouvilianFunctions.html

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)

[mantepse]

I think that this was just fixed in #26746:

sage: from sympy import fresnelc, fresnels
sage: var('a b c d e m n x ')
sage: integrate(x^7*fresnels(b*x),x,algorithm="fricas")
1/8*((pi^3*b^7*x^7 - 35*pi*b^3*x^3)*cos(1/2*pi*b^2*x^2) + (pi^4*b^8*x^8 - 105)*fresnel_sin(b*x) - 7*(pi^2*b^5*x^5 - 15*b*x)*sin(1/2*pi*b^2*x^2))/(pi^4*b^8)

[gh-nasser1]

Thanks. This is confirmed fixed in

SageMath version 8.5.beta5, Release Date: 2018-11-25   

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

1/8*((pi^3*b^7*x^7 - 35*pi*b^3*x^3)*cos(1/2*pi*b^2*x^2) + (pi^4*b^8*x^8 - 105)*fresnel_sin(b*x) - 7*(pi^2*b^5*x^5 - 15*b*x)*sin(1/2*pi*b^2*x^2))/(pi^4*b^8)
sage: 

[embray]

Presuming these are all correctly reviewed as either duplicate, invalid, or wontfix.