oldk1331 wrote:
> 
> For the first part of your question, it seems that there is
> a very basic mistake of definition between
> 
>     int(cos(t^2),t)  and  int(cos(%pi*t^2/2),t)
> 

Yes, please commit.

> 
> diff --git a/src/algebra/limitps.spad b/src/algebra/limitps.spad
> index 02a85a8e..1ee8682a 100644
> --- a/src/algebra/limitps.spad
> +++ b/src/algebra/limitps.spad
> @@ -298,8 +298,8 @@
>              is?(ker, 'acsc) => 0
>              is?(ker, 'acsch) => 0
>              is?(ker, 'acoth) => 0
> -            is?(ker, 'fresnelS) => sqrt(pi()/(8 :: FE))
> -            is?(ker, 'fresnelC) => sqrt(pi()/(8 :: FE))
> +            is?(ker, 'fresnelS) => 1/(2 :: FE)
> +            is?(ker, 'fresnelC) => 1/(2 :: FE)
>              is?(ker, 'Si) => pi()/(2 :: FE)
>              is?(ker, 'Ci) => 0
>              is?(ker, 'airyAi) => 0
> @@ -323,8 +323,8 @@
>            is?(ker, 'acsc) => -pi()
>            is?(ker, 'acsch) => 0
>            is?(ker, 'acoth) => 0
> -          is?(ker, 'fresnelS) => -sqrt(pi()/(8 :: FE))
> -          is?(ker, 'fresnelC) => -sqrt(pi()/(8 :: FE))
> +          is?(ker, 'fresnelS) => -1/(2 :: FE)
> +          is?(ker, 'fresnelC) => -1/(2 :: FE)
>            is?(ker, 'Si) => -pi()/(2 :: FE)
>            is?(ker, 'airyAi) => 0
>            is?(ker, 'airyBi) => 0
> 
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-- 
                              Waldek Hebisch

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