More agreement between Schaums and Axiom
======================================================================
diff --git a/changelog b/changelog
index 0a7317c..366d13f 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20080505 tpd src/input/schaum23.input post-mortem fixes
+20080505 tpd src/input/schaum22.input post-mortem fixes
+20080505 tpd src/input/schaum21.input post-mortem fixes
20080504 tpd src/input/schaum19.input post-mortem fixes
20080504 tpd src/input/schaum18.input post-mortem fixes
20080502 tpd src/input/schaum17.input post-mortem fixes
diff --git a/src/input/schaum21.input.pamphlet
b/src/input/schaum21.input.pamphlet
index 4d6a8be..2c24de5 100644
--- a/src/input/schaum21.input.pamphlet
+++ b/src/input/schaum21.input.pamphlet
@@ -614,7 +614,7 @@
bb:=(p*x)/(p^2+q^2)-q/(a*(p^2+q^2))*log(p*sin(a*x)+q*cos(a*x))
--R Type: Expression
Integer
--E
---S 47 14:449 Axiom cannot simplify this expression
+--S 47
cc:=aa-bb
--R
--R (3)
@@ -631,6 +631,61 @@ cc:=aa-bb
--R Type: Expression
Integer
--E
+--S 48
+sindblrule:=rule(sin(2*a) == 2*sin(a)*cos(a))
+--R
+--R (4) sin(2a) == 2cos(a)sin(a)
+--R Type: RewriteRule(Integer,Integer,Expression
Integer)
+--E
+
+--S 49
+dd:=sindblrule cc
+--R
+--R (5)
+--R 2q log(p sin(a x) + q cos(a x))
+--R +
+--R 2p cos(a x)sin(a x) + q cos(2a x) + q 2
+--R - 2q log(-------------------------------------) + q
log(-------------)
+--R cos(2a x) + 1 cos(2a x) + 1
+--R /
+--R 2 2
+--R 2a q + 2a p
+--R Type: Expression
Integer
+--E
+
+--S 50
+cosdblrule:=rule(cos(2*a) == 2*cos(a)^2-1)
+--R
+--R 2
+--R (6) cos(2a) == 2cos(a) - 1
+--R Type: RewriteRule(Integer,Integer,Expression
Integer)
+--E
+
+--S 51
+ee:=cosdblrule dd
+--R
+--R (7)
+--R p sin(a x) + q cos(a x)
+--R 2q log(p sin(a x) + q cos(a x)) - 2q log(-----------------------)
+--R cos(a x)
+--R +
+--R 1
+--R q log(---------)
+--R 2
+--R cos(a x)
+--R /
+--R 2 2
+--R 2a q + 2a p
+--R Type: Expression
Integer
+--E
+
+--S 52 14:449 Schaums and Axiom agree
+ff:=expandLog %
+--R
+--R (8) 0
+--R Type: Expression
Integer
+--E
+
@
\section{\cite{1}:14.450~~~~~$\displaystyle
@@ -641,7 +696,7 @@ $$
<<*>>=
)clear all
---S 48 14:450 Axiom cannot compute this integral
+--S 53 14:450 Axiom cannot compute this integral
aa:=integrate(cot(a*x)^n,x)
--R
--R
diff --git a/src/input/schaum22.input.pamphlet
b/src/input/schaum22.input.pamphlet
index 173338a..42fad96 100644
--- a/src/input/schaum22.input.pamphlet
+++ b/src/input/schaum22.input.pamphlet
@@ -418,7 +418,7 @@ bb:=sec(a*x)^n/(n*a)
--R Type: Expression
Integer
--E
---S 31 14:454 Axiom cannot simplify this expression
+--S 31
cc:=aa-bb
--R
--R 1
@@ -432,6 +432,13 @@ cc:=aa-bb
--R a n
--R Type: Expression
Integer
--E
+
+--S 32 14:454 Schaums and Axiom agree
+normalize cc
+--R
+--R (4) 0
+--R Type: Expression
Integer
+--E
@
\section{\cite{1}:14.455~~~~~$\displaystyle
@@ -442,7 +449,7 @@ $$
<<*>>=
)clear all
---S 32
+--S 33
aa:=integrate(1/sec(a*x),x)
--R
--R
@@ -452,7 +459,7 @@ aa:=integrate(1/sec(a*x),x)
--R Type: Union(Expression
Integer,...)
--E
---S 33
+--S 34
bb:=sin(a*x)/a
--R
--R sin(a x)
@@ -461,7 +468,7 @@ bb:=sin(a*x)/a
--R Type: Expression
Integer
--E
---S 34 14:455 Schaums and Axiom agree
+--S 35 14:455 Schaums and Axiom agree
cc:=aa-bb
--R
--R (3) 0
@@ -478,7 +485,7 @@ $$
<<*>>=
)clear all
---S 35 14:456 Axiom cannot compute this integral
+--S 36 14:456 Axiom cannot compute this integral
aa:=integrate(x*sec(a*x),x)
--R
--R
@@ -499,7 +506,7 @@ $$
<<*>>=
)clear all
---S 36 14:457 Axiom cannot compute this integral
+--S 37 14:457 Axiom cannot compute this integral
aa:=integrate(sec(a*x)/x,x)
--R
--R
@@ -519,7 +526,7 @@ $$
<<*>>=
)clear all
---S 37
+--S 38
aa:=integrate(x*sec(a*x)^2,x)
--R
--R
@@ -533,7 +540,7 @@ aa:=integrate(x*sec(a*x)^2,x)
--R Type: Union(Expression
Integer,...)
--E
---S 38
+--S 39
bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x))
--R
--R log(cos(a x)) + a x tan(a x)
@@ -543,7 +550,7 @@ bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x))
--R Type: Expression
Integer
--E
---S 39
+--S 40
cc:=aa-bb
--R
--R (3)
@@ -560,7 +567,7 @@ cc:=aa-bb
--R Type: Expression
Integer
--E
---S 40
+--S 41
tanrule:=rule(tan(a) == sin(a)/cos(a))
--R
--R sin(a)
@@ -569,7 +576,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a))
--R Type: RewriteRule(Integer,Integer,Expression
Integer)
--E
---S 41
+--S 42
dd:=tanrule cc
--R
--R 2 2cos(a x)
@@ -581,7 +588,7 @@ dd:=tanrule cc
--R Type: Expression
Integer
--E
---S 42 14:458 Schaums and Axiom differ by a constant
+--S 43 14:458 Schaums and Axiom differ by a constant
ee:=expandLog dd
--R
--R - log(2) + log(- 2)
@@ -600,7 +607,7 @@ $$
<<*>>=
)clear all
---S 43
+--S 44
aa:=integrate(1/(q+p*sec(a*x)),x)
--R
--R
@@ -626,7 +633,7 @@ aa:=integrate(1/(q+p*sec(a*x)),x)
--R Type: Union(List Expression
Integer,...)
--E
---S 44
+--S 45
t1:=integrate(1/(p+q*cos(a*x)),x)
--R
--R (2)
@@ -651,7 +658,7 @@ t1:=integrate(1/(p+q*cos(a*x)),x)
--R Type: Union(List Expression
Integer,...)
--E
---S 45
+--S 46
bb1:=x/q-p/q*t1.1
--R
--R (3)
@@ -667,7 +674,7 @@ bb1:=x/q-p/q*t1.1
--R Type: Expression
Integer
--E
---S 46
+--S 47
bb2:=x/q-p/q*t1.2
--R
--R +---------+
@@ -682,7 +689,7 @@ bb2:=x/q-p/q*t1.2
--R Type: Expression
Integer
--E
---S 47
+--S 48
cc1:=aa.1-bb1
--R
--R (5)
@@ -704,7 +711,7 @@ cc1:=aa.1-bb1
--R Type: Expression
Integer
--E
---S 48
+--S 49
cc2:=aa.1-bb2
--R
--R (6)
@@ -726,7 +733,7 @@ cc2:=aa.1-bb2
--R Type: Expression
Integer
--E
---S 49
+--S 50
cc3:=aa.2-bb1
--R
--R (7)
@@ -748,7 +755,7 @@ cc3:=aa.2-bb1
--R Type: Expression
Integer
--E
---S 50 14:459 Schaums and Axiom agree
+--S 51 14:459 Schaums and Axiom agree
cc4:=aa.2-bb2
--R
--R (8) 0
@@ -765,7 +772,7 @@ $$
<<*>>=
)clear all
---S 51 14:460 Axiom cannot compute this integral
+--S 52 14:460 Axiom cannot compute this integral
aa:=integrate(sec(a*x)^n,x)
--R
--R
diff --git a/src/input/schaum23.input.pamphlet
b/src/input/schaum23.input.pamphlet
index d285a80..96485e2 100644
--- a/src/input/schaum23.input.pamphlet
+++ b/src/input/schaum23.input.pamphlet
@@ -436,7 +436,7 @@ bb:=-csc(a*x)^n/(n*a)
--R Type: Expression
Integer
--E
---S 34 14:464 Axiom cannot simplify this expression
+--S 34
cc:=aa-bb
--R
--R 1
@@ -450,6 +450,13 @@ cc:=aa-bb
--R a n
--R Type: Expression
Integer
--E
+
+--S 35 14:464 Schaums and Axiom agree
+normalize cc
+--R
+--R (4) 0
+--R Type: Expression
Integer
+--E
@
\section{\cite{1}:14.465~~~~~$\displaystyle
@@ -460,7 +467,7 @@ $$
<<*>>=
)clear all
---S 35
+--S 36
aa:=integrate(1/csc(a*x),x)
--R
--R
@@ -470,7 +477,7 @@ aa:=integrate(1/csc(a*x),x)
--R Type: Union(Expression
Integer,...)
--E
---S 36
+--S 37
bb:=-cos(a*x)/a
--R
--R cos(a x)
@@ -479,7 +486,7 @@ bb:=-cos(a*x)/a
--R Type: Expression
Integer
--E
---S 37 14:465 Schaums and Axiom agree
+--S 38 14:465 Schaums and Axiom agree
cc:=aa-bb
--R
--R (3) 0
@@ -496,7 +503,7 @@ $$
<<*>>=
)clear all
---S 38 14:466 Axiom cannot compute this integral
+--S 39 14:466 Axiom cannot compute this integral
aa:=integrate(x*csc(a*x),x)
--R
--R
@@ -517,7 +524,7 @@ $$
<<*>>=
)clear all
---S 39 14:467 Axiom cannot compute this integral
+--S 40 14:467 Axiom cannot compute this integral
aa:=integrate(csc(a*x)/x,x)
--R
--R
@@ -537,7 +544,7 @@ $$
<<*>>=
)clear all
---S 40
+--S 41
aa:=integrate(x*csc(a*x)^2,x)
--R
--R
@@ -550,7 +557,7 @@ aa:=integrate(x*csc(a*x)^2,x)
--R Type: Union(Expression
Integer,...)
--E
---S 41
+--S 42
bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))
--R
--R log(sin(a x)) - a x cot(a x)
@@ -560,7 +567,7 @@ bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))
--R Type: Expression
Integer
--E
---S 42
+--S 43
cc:=aa-bb
--R
--R (3)
@@ -577,7 +584,7 @@ cc:=aa-bb
--R Type: Expression
Integer
--E
---S 43
+--S 44
cotrule:=rule(cot(a) == cos(a)/sin(a))
--R
--R cos(a)
@@ -586,7 +593,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a))
--R Type: RewriteRule(Integer,Integer,Expression
Integer)
--E
---S 44
+--S 45
dd:=cotrule cc
--R
--R sin(a x) 2
@@ -598,7 +605,7 @@ dd:=cotrule cc
--R Type: Expression
Integer
--E
---S 45 14:468 Schaums and Axiom differ by a constant
+--S 46 14:468 Schaums and Axiom differ by a constant
ee:=expandLog dd
--R
--R log(2)
@@ -617,7 +624,7 @@ $$
<<*>>=
)clear all
---S 46
+--S 47
aa:=integrate(1/(q+p*csc(a*x)),x)
--R
--R
@@ -656,7 +663,7 @@ aa:=integrate(1/(q+p*csc(a*x)),x)
--R Type: Union(List Expression
Integer,...)
--E
---S 47
+--S 48
t1:=integrate(1/(p+q*sin(a*x)),x)
--R
--R (2)
@@ -688,7 +695,7 @@ t1:=integrate(1/(p+q*sin(a*x)),x)
--R Type: Union(List Expression
Integer,...)
--E
---S 48
+--S 49
bb1:=x/q-p/q*t1.1
--R
--R (3)
@@ -715,7 +722,7 @@ bb1:=x/q-p/q*t1.1
--R Type: Expression
Integer
--E
---S 49
+--S 50
bb2:=x/q-p/q*t1.2
--R
--R +---------+
@@ -731,7 +738,7 @@ bb2:=x/q-p/q*t1.2
--R Type: Expression
Integer
--E
---S 50
+--S 51
cc1:=aa.1-bb1
--R
--R (5)
@@ -765,7 +772,7 @@ cc1:=aa.1-bb1
--R Type: Expression
Integer
--E
---S 51
+--S 52
cc2:=aa.2-bb1
--R
--R (6)
@@ -796,7 +803,7 @@ cc2:=aa.2-bb1
--R Type: Expression
Integer
--E
---S 52
+--S 53
cc3:=aa.1-bb2
--R
--R (7)
@@ -827,7 +834,7 @@ cc3:=aa.1-bb2
--R Type: Expression
Integer
--E
---S 53 14:469 Schaums and Axiom agree
+--S 54 14:469 Schaums and Axiom agree
cc4:=aa.2-bb2
--R
--R (8) 0
@@ -844,7 +851,7 @@ $$
<<*>>=
)clear all
---S 54 14:470 Axiom cannot compute this integral
+--S 55 14:470 Axiom cannot compute this integral
aa:=integrate(csc(a*x)^n,x)
--R
--R
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