fricas
(1) -> f:=operator 'f
fricas
differentiate(f(x),x) = differentiate(f(y),y)
\label{eq2}{{f^{\prime}}\left({x}\right)}={{f^{\prime}}\left({y}\right)}
(2) Type: Equation(Expression(Integer))
fricas
test %
\label{eq3} \mbox{\rm false}
(3) Type: Boolean
fricas
integrate(f(x),x) = integrate(f(y),y)
\label{eq4}{\int^{ \displaystyle x}{{f \left({\%C}\right)}\ {d \%C}}}={\int^{ \displaystyle y}{{f \left({\%C}\right)}\ {d \%C}}}
(4) Type: Equation(Expression(Integer))
fricas
test %
\label{eq5} \mbox{\rm false}
(5) Type: Boolean
fricas
-- y is replaced with x?
product(f(x),x) = product(f(y),y)
\label{eq6}{\prod_{ \displaystyle x}{f \left({x}\right)}}={\prod_{ \displaystyle x}{f \left({x}\right)}}
(6) Type: Equation(Expression(Integer))
fricas
test %
\label{eq7} \mbox{\rm true}
(7) Type: Boolean
fricas
smaller?(product(f(x),x),product(f(y),y))
\label{eq8} \mbox{\rm false}
(8) Type: Boolean
fricas
smaller?(product(f(y),y),product(f(x),x))
\label{eq9} \mbox{\rm false}
(9) Type: Boolean
fricas
sum(f(x),x) = sum(f(y),y)
\label{eq10}{\sum_{ \displaystyle x}{f \left({x}\right)}}={\sum_{ \displaystyle x}{f \left({x}\right)}}
(10) Type: Equation(Expression(Integer))
fricas
test %
\label{eq11} \mbox{\rm true}
(11) Type: Boolean
fricas
smaller?(sum(f(x),x),sum(f(y),y))
\label{eq12} \mbox{\rm false}
(12) Type: Boolean
fricas
smaller?(sum(f(y),y),sum(f(x),x))
\label{eq13} \mbox{\rm false}
(13) Type: Boolean