Another applyrule bug?

Question:Another applyrule bug?

Posted: Rouben Rostamian 7711 Product: Maple 2021

February 11 2022

This also looks like an applyrule bug.

restart;

>	kernelopts(version);

>	double_angle_rule := [ sin(x::name/2)cos(x::name/2) = 1/2sin(x), sin(x::name/2)^2 = 1/2(1-cos(x)), cos(x::name/2)^2 = 1/2(1+cos(x)) ];

[sin((1/2)*x::name)*cos((1/2)*x::name) = (1/2)*sin(x), sin((1/2)*x::name)^2 = 1/2-(1/2)*cos(x), cos((1/2)*x::name)^2 = 1/2+(1/2)*cos(x)]

>	C := < cos(1/2u)sin(1/2u), cos(1/2u)^2 >;

$Vector(2, {(1) = cos((1/2)*u)*sin((1/2)*u), (2) = cos((1/2)*u)^2})$

This application fails. Why?

>	applyrule~(double_angle_rule, C);

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