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#199 integrate(exp(-x^2)+exp(x)/x,x) ←	↑	→ #200 display of TwoDimensionalArray of type Union(...) is not properly formatted

#20 D(1, z) fails

Edit detail for #20 D(1, z) fails revision 3 of 3

	1 2 3
Editor: Bill Page Time: 2008/05/21 20:56:48 GMT-7
Note:

changed:
-have a path to coerce PostiveInteger -> Expression(Integer).
have a path to coerce PositiveInteger -> Expression(Integer).

From: Vladimir Bondarenko Subject -- [Axiom-developer]? AXIOM BUG: D(1, z) Date -- Mon, 17 Jan 2005 07:35:49 +0200

Hi *,

A terrible bug in differentiation.

axiom

D(sin(z)^2+cos(z)^2, z)

$\label{eq1}0$

(1)

Type: Expression(Integer)

axiom

D(simplify(sin(z)^2+cos(z)^2), z)

$\label{eq2}0$

(2)

Type: Expression(Integer)

BUT

axiom

D(1, z)

   There are 5 exposed and 0 unexposed library operations named D
      having 2 argument(s) but none was determined to be applicable.
      Use HyperDoc Browse, or issue
                                )display op D
      to learn more about the available operations. Perhaps
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named D
      with argument type(s)
                               PositiveInteger
                                 Variable(z)

      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
D(cosh(z)^2-sinh(z)^2, z)

$\label{eq3}0$

(3)

Type: Expression(Integer)

axiom

D(simplify(cosh(z)^2-sinh(z)^2), z)

$\label{eq4}0$

(4)

Type: Expression(Integer)

wrong arument types: Mon, 17 Jan 2005 22:28:18 -0600 reply

D(1,z) is not a valid type signature. Try

axiom

D(1::Expression(Integer),z)

$\label{eq5}0$

(5)

Type: Expression(Integer)

In Axiom it is important to know the type of the arguments to a function. In this case you gave the D function a PositveInteger? and is does not have a path to coerce PositiveInteger? -> Expression(Integer).

Whenever you see the message about exposed and unexposed library functions the meaning is that you didn't match the type of the arguments and the interpreter couldn't get there from here.

The coercion/conversion tower in the interpreter is not well defined and sometimes it needs help.