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[Axiom-developer] 20080417.01.tpd.patch (fixed 14:150)
From: |
daly |
Subject: |
[Axiom-developer] 20080417.01.tpd.patch (fixed 14:150) |
Date: |
Thu, 17 Apr 2008 10:12:22 -0500 |
Doug,
I fired up Maxima this morning and got the same answer.
I finally saw that the mistake is a typo in the answer I transcribed
from the Schaum's book. Specifically, the answer from the book is the
variable 'bb' which needed the following change:
-bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
+bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))
So it is just a typo and thus the best of all possible worlds.
Schaums and Axiom now agree on 14:150.
Tim
=======================================================================
diff --git a/changelog b/changelog
index eda7bfd..456e2f9 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080417 tpd src/input/schaum7.input fix typo in --S 30
+20080417 tpd src/input/schaum5.input fix typo 14:88 -> 14:123
20080416 tpd src/input/schaum7.input show Schaums-Axiom equivalence
20080416 tpd src/input/schaum6.input show Schaums-Axiom equivalence
20080416 tpd src/input/schaum5.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum5.input.pamphlet b/src/input/schaum5.input.pamphlet
index 50ea618..a5d3fc3 100644
--- a/src/input/schaum5.input.pamphlet
+++ b/src/input/schaum5.input.pamphlet
@@ -1571,7 +1571,7 @@ cc3:=aa2-bb1
--R Type: Expression
Integer
--E
---S 42 14:88 Axiom cannot simplify these results
+--S 42 14:123 Axiom cannot simplify these results
cc4:=aa2-bb2
--R
--R (14)
diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet
index 3062d2e..ce37f19 100644
--- a/src/input/schaum7.input.pamphlet
+++ b/src/input/schaum7.input.pamphlet
@@ -356,71 +356,64 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x)
--E
--S 30
-bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
+bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))
--R
---R 2
---R x 2
---R - 2x log(-------) + a
---R 2 2
---R x - a
---R (2) ----------------------
---R 4
---R 4a x
+--R 2
+--R 2 x 2
+--R - x log(-------) + a
+--R 2 2
+--R x - a
+--R (2) ---------------------
+--R 4 2
+--R 2a x
--R Type: Expression
Integer
--E
--S 31
-cc:=aa-bb
---R
---R 2
---R 2 2 2 2 2 x 2 2
---R 2x log(x - a ) - 4x log(x) + 2x log(-------) - a x + 2a
---R 2 2
---R x - a
---R (3) ---------------------------------------------------------
---R 4 2
---R 4a x
---R Type: Expression
Integer
---E
-
---S 32
divlog:=rule(log(a/b) == log(a) - log(b))
--R
--R a
---R (4) log(-) == - log(b) + log(a)
+--R (3) log(-) == - log(b) + log(a)
--R b
--R Type: RewriteRule(Integer,Integer,Expression
Integer)
--E
---S 33
-dd:=divlog cc
+--S 32
+t1:=divlog bb
--R
---R 2 2 2 2 2
---R 2x log(x ) - 4x log(x) - a x + 2a
---R (5) ----------------------------------
---R 4 2
---R 4a x
+--R 2 2 2 2 2 2
+--R - x log(x ) + x log(x - a ) + a
+--R (4) ---------------------------------
+--R 4 2
+--R 2a x
--R Type: Expression
Integer
--E
---S 34
+--S 33
logpow:=rule(log(a^n) == n*log(a))
--R
--R n
---R (6) log(a ) == n log(a)
+--R (5) log(a ) == n log(a)
--R Type: RewriteRule(Integer,Integer,Expression
Integer)
--E
---S 35 14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
-ee:=logpow dd
+--S 34
+t2:=logpow t1
--R
---R - x + 2
---R (7) -------
---R 2 2
---R 4a x
+--R 2 2 2 2 2
+--R x log(x - a ) - 2x log(x) + a
+--R (6) -------------------------------
+--R 4 2
+--R 2a x
--R Type: Expression
Integer
--E
+--S 35 14:150 Schaums and Axiom agree
+cc:=aa-t2
+
+ (7) 0
+ Type: Expression Integer
+--E
@
\section{\cite{1}:14.151~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^2}}$}
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