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SandBoxFormalProduct

Edit detail for SandBoxFormalProduct revision 3 of 3

	1 2 3
Editor: Bill Page Time: 2015/04/02 22:04:41 GMT+0
Note:

added:
differentiate(f(x),x) = differentiate(f(y),y)
test %
integrate(f(x),x) = integrate(f(y),y)
test %

added:
sum(f(x),x) = sum(f(y),y)
test %
smaller?(sum(f(x),x),sum(f(y),y))
smaller?(sum(f(y),y),sum(f(x),x))

fricas

f:=operator 'f

$\label{eq1}f$

(1)

Type: BasicOperator?

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