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## Re: [Axiom-developer] Re: [Axiom-mail] Problem with real/imag/conjugate

 From: Bill Page Subject: Re: [Axiom-developer] Re: [Axiom-mail] Problem with real/imag/conjugate Date: Thu, 18 Jun 2009 01:08:24 -0400

```Tim,

I think the following patch fixes this problem but I have not yet done
very extensive testing. It might well have some impact on results in
the regression tests.

The patch is against open-axiom sources so you might have to apply it
manually but I do not think this code has changed much in other
versions.

https://sourceforge.net/tracker/?func=detail&atid=984524&aid=2806053&group_id=203172

----

address@hidden:~\$ svn diff ~/open-axiom-src/src/algebra > itrigmnp.patch

===================================================================
(revision
1216)
(working copy)
@@ -545,6 +545,7 @@
macro NTHR == 'nthRoot
ker2explogs: (KG, List KG, List SY) -> FG
smp2explogs: (PG, List KG, List SY) -> FG
+    nthroot:     (GF,GF) -> GF
supexp     : (UP, GF, GF, Z) -> GF
GR2GF      : GR -> GF
GR2F       : GR -> F
@@ -626,13 +627,23 @@
map(explogs2trigs(#1::FG),GR2GF, p)\$PolynomialCategoryLifting(
IndexedExponents KG, KG, GR, PG, GF)

-    explogs2trigs f ==
-      (m := mainKernel f) case "failed" =>
+    nthroot(a:GF,n:GF):GF ==
+      r := nthRoot(sqrt(norm(a)),retract(n)@Z)
+      e := exp(complex(0, 1)*argument(a)/n)
+      r*e
+
+    explogs2trigs(f:FG):GF ==
+      m := mainKernel f
+      m case "failed" =>
GR2GF(retract(numer f)@GR) / GR2GF(retract(denom f)@GR)
-      op  := operator(operator(k := m::KG))\$F
+      k := m::KG
+      op  := operator(operator(k))\$F
arg := [explogs2trigs x for x in argument k]
num := univariate(numer f, k)
den := univariate(denom f, k)
+      is?(op,'nthRoot) =>
+        h := nthroot(first arg, second arg)
+        supexp(num,h,0,0)/supexp(den,h,0,0)
is?(op,'exp) =>
e  := exp real first arg
y  := imag first arg

----

Regards,
Bill Page.

On Tue, Jun 16, 2009 at 5:45 PM, Tim Daly<address@hidden> wrote:
> This one is queued as bug number 7199.
>
> When you say the latest "Gold" sources can you tell me the
> result of the "Version" and "Timestamp" lines from the Axiom banner?
> Where did you get the sources?
>
> Tim
>
>
> Arnold Doray wrote:
>>
>> I get the wrong answer for real/imag for some forms of complex numbers.
>> For example:
>>
>> a := (-1*%i)^(1/2)
>> b := (%i)^(3/2)
>>
>> are both equivalent, but imag/real gives complex (and incorrect) answers
>> for "a" (ie, real(a) and imag(a) are both complex), but I get the right
>> answers for "b". Also "conjugate" fails on both with an error message.
>>
>> Am I missing something here?
>> I am using Axiom compiled from the latest "Gold" source.
>> Thanks,
>> Arnold
>>
```

itrigmnp.patch
Description: Binary data