Hello,
does somebody see my error? I don't understand why the function "nicer"
does not work, but the individual commands on the input do.
What I also find strange is that the error message for "nicer" changes
in the end.
The commands of the following session are attached.
Thanks in advance.
Ralf
%%% (1) -> ZZ ==> Integer
Type: Void
%%% (2) -> EX ==> Expression
Type: Void
%%% (3) -> combineRadicals := rule sqrt(x)*sqrt(y) == sqrt(x*y)
+-+ +-+ +---+
(3) %B\|x \|y == %B\|x y
Type:
RewriteRule(Integer,Integer,Expression(Integer))
%%% (4) -> nicer(x: EX ZZ): AlgebraicNumber == ( AM ==>
AlgebraicManipulations(ZZ, EX ZZ); xx :=
combineRadicals(rootSplit(x)$AM); rs := rsimp((numer
xx)::EX(ZZ))$RootSimplification; zz := rootSplit(rs)$AM / denom xx;
combineRadicals(zz) :: AlgebraicNumber)
Function declaration nicer : Expression(Integer) -> AlgebraicNumber
has been added to workspace.
Type: Void
%%% (5) -> nicer x0
>> System error:
The variable $$$ is unbound.
%%% (5) -> x0 :=
sqrt((184726398605281*sqrt(-163)+14962838287027761)/20010)/17502080
+--------------------------------------------+
| +-----+
|184726398605281 \|- 163 + 14962838287027761
|--------------------------------------------
\| 20010
(5) -----------------------------------------------
17502080
Type:
AlgebraicNumber
%%% (6) -> AM ==> AlgebraicManipulations(ZZ, EX ZZ)
Type: Void
%%% (7) -> xx := combineRadicals(rootSplit(x0)$AM)
+--------------------------------------------+
| +-----+
\|184726398605281 \|- 163 + 14962838287027761
(7) -----------------------------------------------
+-----+
17502080 \|20010
Type:
Expression(Integer)
%%% (8) -> rs := rsimp((numer xx)::EX(ZZ))$RootSimplification;
Type:
Union(Expression(Integer),...)
%%% (9) -> zz := rootSplit(rs)$AM / denom xx;
Type:
Expression(Integer)
%%% (10) -> combineRadicals(zz) :: AlgebraicNumber
+-----+ +-------+
(13591409 \|- 163 + 2215399667)\|1630815
(10) ------------------------------------------
57085309190400
Type:
AlgebraicNumber
%%% (11) -> nicer x0
>> System error:
The function BOOT::|*1;nicer;1;initial| is undefined.
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ZZ ==> Integer
EX ==> Expression
combineRadicals := rule sqrt(x)*sqrt(y) == sqrt(x*y)
-- `nicer` transforms an expression of the form
-- $\frac{\sqrt{a+b\sqrt{c/d}}}{e}$ into something of the form
-- $\frac{u+v\sqrt{w}}{y}\sqrt{x}$ if possible.
nicer(x: EX ZZ): AlgebraicNumber == (_
AM ==> AlgebraicManipulations(ZZ, EX ZZ);_
xx := combineRadicals(rootSplit(x)$AM);_
rs := rsimp((numer xx)::EX(ZZ))$RootSimplification;_
zz := rootSplit(rs)$AM / denom xx;_
combineRadicals(zz) :: AlgebraicNumber)
nicer x0
x0 := sqrt((184726398605281*sqrt(-163)+14962838287027761)/20010)/17502080
AM ==> AlgebraicManipulations(ZZ, EX ZZ)
xx := combineRadicals(rootSplit(x0)$AM)
rs := rsimp((numer xx)::EX(ZZ))$RootSimplification;
zz := rootSplit(rs)$AM / denom xx;
combineRadicals(zz) :: AlgebraicNumber
nicer x0
