diff --git a/changelog b/changelog index c94aa65..6e74f31 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,20 @@ +20080428 tpd src/input/schaum19.input post-mortem fixes +20080428 tpd src/input/schaum23.input post-mortem fixes +20080428 tpd src/input/schaum24.input post-mortem fixes +20080428 tpd src/input/schaum27.input post-mortem fixes +20080428 tpd src/input/schaum28.input post-mortem fixes +20080428 tpd src/input/schaum29.input post-mortem fixes +20080428 tpd src/input/schaum33.input post-mortem fixes +20080428 tpd src/input/schaum6.input post-mortem fixes +20080428 tpd src/input/schaum7.input post-mortem fixes +20080428 tpd src/input/schaum9.input post-mortem fixes +20080427 tpd src/input/schaum34.input show Schaums-Axiom equivalence +20080427 tpd src/input/schaum33.input show Schaums-Axiom equivalence +20080427 tpd src/input/schaum32.input show Schaums-Axiom equivalence +20080427 tpd src/input/schaum31.input show Schaums-Axiom equivalence +20080427 tpd src/input/schaum30.input show Schaums-Axiom equivalence +20080427 tpd src/input/schaum29.input show Schaums-Axiom equivalence +20080427 tpd src/input/schaum28.input fix Schaums-Axiom equivalence 20080426 tpd src/input/schaum28.input show Schaums-Axiom equivalence 20080426 tpd src/input/schaum27.input show Schaums-Axiom equivalence 20080426 tpd src/input/schaum26.input show Schaums-Axiom equivalence diff --git a/src/input/schaum19.input.pamphlet b/src/input/schaum19.input.pamphlet index bf580f0..343ab8a 100644 --- a/src/input/schaum19.input.pamphlet +++ b/src/input/schaum19.input.pamphlet @@ -1569,7 +1569,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 125 14:416 Schaums and Axiom differ by a constant +--S 125 14:416 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 diff --git a/src/input/schaum23.input.pamphlet b/src/input/schaum23.input.pamphlet index c24ef73..d285a80 100644 --- a/src/input/schaum23.input.pamphlet +++ b/src/input/schaum23.input.pamphlet @@ -658,6 +658,34 @@ aa:=integrate(1/(q+p*csc(a*x)),x) --S 47 t1:=integrate(1/(p+q*sin(a*x)),x) +--R +--R (2) +--R [ +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (p q sin(a x) + (q - p )cos(a x) + q )\|q - p +--R + +--R 2 3 3 2 3 2 +--R (- p q + p )sin(a x) + (- q + p q)cos(a x) - q + p q +--R / +--R q sin(a x) + p +--R / +--R +-------+ +--R | 2 2 +--R a\|q - p +--R , +--R +---------+ +--R | 2 2 +--R (p sin(a x) + q cos(a x) + q)\|- q + p +--R 2atan(-----------------------------------------) +--R 2 2 2 2 +--R (q - p )cos(a x) + q - p +--R - ------------------------------------------------] +--R +---------+ +--R | 2 2 +--R a\|- q + p +--R Type: Union(List Expression Integer,...) --E --S 48 diff --git a/src/input/schaum24.input.pamphlet b/src/input/schaum24.input.pamphlet index 9c034da..24b4527 100644 --- a/src/input/schaum24.input.pamphlet +++ b/src/input/schaum24.input.pamphlet @@ -2318,10 +2318,10 @@ ff:=expandLog ee --R 2 --R Type: Expression Complex Integer --E +@ And we get the surprising result that they are not equal. In fact, they differ by a complex value depending on x. Likely there is a branch-cut issue lurking somewhere. -@ \section{\cite{1}:14.506~~~~~$\displaystyle \int{x^m\cot^{-1}\frac{x}{a}}~dx$} diff --git a/src/input/schaum27.input.pamphlet b/src/input/schaum27.input.pamphlet index cc233e4..68d33a3 100644 --- a/src/input/schaum27.input.pamphlet +++ b/src/input/schaum27.input.pamphlet @@ -355,7 +355,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 27 14:548 Axiom cannot simplify this expression +--S 27 14:548 Schaums and Axiom agree ff:=sinhcoshrule ee --R --R (9) 0 diff --git a/src/input/schaum28.input.pamphlet b/src/input/schaum28.input.pamphlet index 3ba0bfc..49efb0e 100644 --- a/src/input/schaum28.input.pamphlet +++ b/src/input/schaum28.input.pamphlet @@ -410,7 +410,9 @@ cc:=aa-bb --R 2 2 --R a sinh(a x) + 2a cosh(a x)sinh(a x) + a cosh(a x) + a --R Type: Expression Integer ---S 32 +--E + +--S 32 14:571 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 1 @@ -526,7 +528,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 41 14:572 Schaums and Axiom agree +--S 41 14:572 Axiom cannot simplify this expression ff:=sinhcoshrule ee --R --R (9) @@ -787,9 +789,9 @@ dd:=tanhrule cc --S 61 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R ---I %B sinh(y + x) - %B sinh(y - x) ---I (6) %B cosh(y)sinh(x) == ------------------------------- ---R 2 +--I %BC sinh(y + x) - %BC sinh(y - x) +--I (6) %BC cosh(y)sinh(x) == ------------------------------- +--R 2 --R Type: RewriteRule(Integer,Integer,Expression Integer) --E @@ -809,9 +811,9 @@ ee:=sinhcoshrule dd --S 63 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R ---I %B cosh(y + x) - %B cosh(y - x) ---I (8) %B sinh(x)sinh(y) == ------------------------------- ---R 2 +--I %BD sinh(y + x) - %BD sinh(y - x) +--I (8) %BD cosh(y)sinh(x) == ------------------------------- +--R 2 --R Type: RewriteRule(Integer,Integer,Expression Integer) --E @@ -1485,7 +1487,7 @@ bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3 --R Type: Expression Integer --E ---S 107 14:580 Axiom cannot compute this integral +--S 107 14:580 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -2681,7 +2683,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 134 14:584 Axiom cannot compute this integral +--S 134 14:584 Axiom cannot simplify this expression cc2:=aa-bb2 --R --R (5) diff --git a/src/input/schaum29.input.pamphlet b/src/input/schaum29.input.pamphlet index 1aff49f..9c79630 100644 --- a/src/input/schaum29.input.pamphlet +++ b/src/input/schaum29.input.pamphlet @@ -77,7 +77,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 7 14:590 Schaums and Axiom agree +--S 7 14:590 Schaums and Axiom differ by a constant ee:=coshsqrrule dd --R --R 1 @@ -209,6 +209,7 @@ bb:=cosh(a*x)^(n+1)/((n+1)*a) --E --S 16 14:593 Axiom cannot simplify this expression +cc:=aa-bb --R --R (3) --R - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x))) @@ -727,6 +728,7 @@ bb:=-(2*coth(2*a*x))/a --E --S 47 14:598 Axiom cannot simplify this expression +cc:=aa-bb --R --R (3) --R 4 3 diff --git a/src/input/schaum33.input.pamphlet b/src/input/schaum33.input.pamphlet index 74e0c8b..61506d7 100644 --- a/src/input/schaum33.input.pamphlet +++ b/src/input/schaum33.input.pamphlet @@ -666,7 +666,7 @@ gg:=sinhcoshrule ff --R Type: Expression Integer --E ---S 38 14:642 Axiom cannot simplify this expression +--S 38 14:642 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R - log(- 1) + log(- 2) diff --git a/src/input/schaum6.input.pamphlet b/src/input/schaum6.input.pamphlet index 854e780..ca2c6aa 100644 --- a/src/input/schaum6.input.pamphlet +++ b/src/input/schaum6.input.pamphlet @@ -467,7 +467,7 @@ bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a) --R Type: Expression Integer --E ---S 38 14:134 Schaums and Axiom differ by a constant +--S 38 14:134 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet index fcdd71c..52e0b97 100644 --- a/src/input/schaum7.input.pamphlet +++ b/src/input/schaum7.input.pamphlet @@ -410,9 +410,9 @@ t2:=logpow t1 --S 35 14:150 Schaums and Axiom agree cc:=aa-t2 - - (7) 0 - Type: Expression Integer +--R +--R (7) 0 +--R Type: Expression Integer --E @ diff --git a/src/input/schaum9.input.pamphlet b/src/input/schaum9.input.pamphlet index d632de7..fa7d4f2 100644 --- a/src/input/schaum9.input.pamphlet +++ b/src/input/schaum9.input.pamphlet @@ -392,12 +392,12 @@ dd:=expandLog cc --S 28 14:188 Schaums and Axiom differ by a constant ee:=complexNormalize dd - - log(- 1) - (5) -------- - 3 - 2a - Type: Expression Integer +--R +--R log(- 1) +--R (5) -------- +--R 3 +--R 2a +--R Type: Expression Integer --E @