Tue Feb 10 12:29:44 2004 run on Linux
% TeX-REDUCE-Interface 0.70
% set greek asserted
% set lowercase asserted
% set Greek asserted
% set Uppercase asserted
% \tolerance 10
% \hsize=150mm
% load tri;
global '(textest!*);
symbolic procedure texexa(code);
begin
prin2 "\TRIexa{"; prin2 textest!*;
if !*TeXindent then prin2 "}{TeXindent}{" else
if !*TeXbreak then prin2 "}{TeXBreak}{" else
if !*TeX then prin2 "TeX" else prin2 "}{---}{";
if !*TeXbreak then prin2 tolerance!* else prin2 "---";
prin2 "}{"; prin2 code; prin2 "}"; terpri()
end;
texexa
algebraic procedure exa(expression,code);
begin symbolic texexa code; return expression end;
exa
% ----------------------------------------------------------------------
% Examples from the Integrator Test File
% ----------------------------------------------------------------------
symbolic(textest!*:="Integration");
"Integration"
texsetbreak(120,1000);
% \tolerance 1000
% \hsize=120mm
on texindent;
off echo;
\TRIexa{Integration}{TeXindent}{1000}{int(1+x+x**2,x);}
$$\displaylines{\qdd
\frac{x\cdot
\(2\cdot x^{2}
+3\cdot x
+6
\)
}{
6}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**2*(2*x**2+x)**2,x);}
$$\displaylines{\qdd
\frac{x^{5}\cdot
\(60\cdot x^{2}
+70\cdot x
+21
\)
}{
105}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x*(x**2+2*x+1),x);}
$$\displaylines{\qdd
\frac{x^{2}\cdot
\(3\cdot x^{2}
+8\cdot x
+6
\)
}{
12}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/x,x);}
$$\displaylines{\qdd
\ln
\(x
\)
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int((x+1)**3/(x-1)**4,x);}
$$\displaylines{\qdd
\frac{3\cdot \ln
\(x
-1
\)
\cdot x^{3}
-9\cdot \ln
\(x
-1
\)
\cdot x^{2}
+9\cdot \ln
\(x
-1
\)
\cdot x
-3\cdot \ln
\(x
-1
\)
-6\cdot x^{3}
-2}{
3\cdot
\(x^{3}
-3\cdot x^{2}
+3\cdot x
-1
\)
}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/(x*(x-1)*(x+1)**2),x);}
$$\displaylines{\qdd
\(\ln
\(x
-1
\)
\cdot x
+\ln
\(x
-1
\)
+3\cdot \ln
\(x
+1
\)
\cdot x\nl
\off{327680}
+3\cdot \ln
\(x
+1
\)
-4\cdot \ln
\(x
\)
\cdot x
-4\cdot \ln
\(x
\)
+2\cdot x
\)
/\nl
\(4\cdot
\(x
+1
\)
\)
\Nl}$$
\TRIexa{Integration}{TeXindent}{1000}{int((a*x+b)/((x-p)*(x-q)),x);}
$$\displaylines{\qdd
\frac{\ln
\(p
-x
\)
\cdot a\cdot p
+\ln
\(p
-x
\)
\cdot b
-\ln
\(q
-x
\)
\cdot a\cdot q
-\ln
\(q
-x
\)
\cdot b}{
p
-q}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/(a*x**2+b*x+c),x);}
$$\displaylines{\qdd
\frac{2\cdot
\sqrt{4\cdot a\cdot c
-b^{2}}\cdot \atan
\(\frac{2\cdot a\cdot x
+b}{
\sqrt{4\cdot a\cdot c
-b^{2}}}
\)
}{
4\cdot a\cdot c
-b^{2}}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int((a*x+b)/(1+x**2),x);}
$$\displaylines{\qdd
\frac{2\cdot \atan
\(x
\)
\cdot b
+\ln
\(x^{2}
+1
\)
\cdot a}{
2}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/(x**2-2*x+3),x);}
$$\displaylines{\qdd
\frac{\sqrt{2}
\cdot \atan
\(\frac{x
-1}{
\sqrt{2}}
\)
}{
2}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/((x-1)*(x**2+1))**2,x);}
$$\displaylines{\qdd
\(\atan
\(x
\)
\cdot x^{3}
-\atan
\(x
\)
\cdot x^{2}
+\atan
\(x
\)
\cdot x
-\atan
\(x
\)
\nl
\off{327680}
+\ln
\(x^{2}
+1
\)
\cdot x^{3}
-\ln
\(x^{2}
+1
\)
\cdot x^{2}
+\ln
\(x^{2}
+1
\)
\cdot x
-\ln
\(x^{2}
+1
\)
-2\cdot \ln
\(x
-1
\)
\cdot x^{3}\nl
\off{327680}
+2\cdot \ln
\(x
-1
\)
\cdot x^{2}
-2\cdot \ln
\(x
-1
\)
\cdot x
+2\cdot \ln
\(x
-1
\)
-x^{3}
-2\cdot x
+1
\)
/\nl
\(4\cdot
\(x^{3}
-x^{2}
+x
-1
\)
\)
\Nl}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x/((x-a)*(x-b)*(x-c)),x);}
$$\displaylines{\qdd
\(\ln
\(a
-x
\)
\cdot a\cdot b
-\ln
\(a
-x
\)
\cdot a\cdot c
-\ln
\(b
-x
\)
\cdot a\cdot b\nl
\off{327680}
+\ln
\(b
-x
\)
\cdot b\cdot c
+\ln
\(c
-x
\)
\cdot a\cdot c
-\ln
\(c
-x
\)
\cdot b\cdot c
\)
/\nl
\(a^{2}\cdot b
-a^{2}\cdot c
-a\cdot b^{2}
+a\cdot c^{2}
+b^{2}\cdot c
-b\cdot c^{2}
\)
\Nl}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x/((x**2+a**2)*(x**2+b**2)),x);}
$$\displaylines{\qdd
\frac{-\ln
\(a^{2}
+x^{2}
\)
+\ln
\(b^{2}
+x^{2}
\)
}{
2\cdot
\(a^{2}
-b^{2}
\)
}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**2/((x**2+a**2)*(x**2+b**2)),x);}
$$\displaylines{\qdd
\frac{\atan
\(\frac{x}{
a}
\)
\cdot a
-\atan
\(\frac{x}{
b}
\)
\cdot b}{
a^{2}
-b^{2}}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x/((x-1)*(x**2+1)),x);}
$$\displaylines{\qdd
\frac{2\cdot \atan
\(x
\)
-\ln
\(x^{2}
+1
\)
+2\cdot \ln
\(x
-1
\)
}{
4}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x/(1+x**3),x);}
$$\displaylines{\qdd
\frac{2\cdot
\sqrt{3}\cdot \atan
\(\frac{2\cdot x
-1}{
\sqrt{3}}
\)
+\ln
\(x^{2}
-x
+1
\)
-2\cdot \ln
\(x
+1
\)
}{
6}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**3/((x-1)**2*(x**3+1)),x);}
$$\displaylines{\qdd
\(-4\cdot \ln
\(x^{2}
-x
+1
\)
\cdot x
+4\cdot \ln
\(x^{2}
-x
+1
\)
+9\cdot \ln
\(x
-1
\)
\cdot x\nl
\off{327680}
-9\cdot \ln
\(x
-1
\)
-\ln
\(x
+1
\)
\cdot x
+\ln
\(x
+1
\)
-6\cdot x
\)
/\nl
\(12\cdot
\(x
-1
\)
\)
\Nl}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/(1+x**4),x);}
$$\displaylines{\qdd
\(\sqrt{2}\cdot
\(-2\cdot \atan
\(\frac{\sqrt{2}
-2\cdot x}{
\sqrt{2}}
\)
+2\cdot \atan
\(\frac{\sqrt{2}
+2\cdot x}{
\sqrt{2}}
\)
-\ln
\(-
\sqrt{2}\cdot x
+x^{2}
+1
\)
+\ln
\(\sqrt{2}\cdot x
+x^{2}
+1
\)
\)
\)
/8
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**2/(1+x**4),x);}
$$\displaylines{\qdd
\(\sqrt{2}\cdot
\(-2\cdot \atan
\(\frac{\sqrt{2}
-2\cdot x}{
\sqrt{2}}
\)
+2\cdot \atan
\(\frac{\sqrt{2}
+2\cdot x}{
\sqrt{2}}
\)
+\ln
\(-
\sqrt{2}\cdot x
+x^{2}
+1
\)
-\ln
\(\sqrt{2}\cdot x
+x^{2}
+1
\)
\)
\)
/8
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/(1+x**2+x**4),x);}
$$\displaylines{\qdd
\frac{2\cdot
\sqrt{3}\cdot \atan
\(\frac{2\cdot x
-1}{
\sqrt{3}}
\)
+2\cdot
\sqrt{3}\cdot \atan
\(\frac{2\cdot x
+1}{
\sqrt{3}}
\)
-3\cdot \ln
\(x^{2}
-x
+1
\)
+3\cdot \ln
\(x^{2}
+x
+1
\)
}{
12}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(sin x**2/x,x);}
$$\displaylines{\qdd
\frac{-ci
\(2\cdot x
\)
+\ln
\(x
\)
}{
2}
\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x*cos(xi/sin(x))*cos(x)/sin(x)**2,x);}
$$\displaylines{\qdd
\int {\frac{\cos
\(\frac{\xi }{
\sin
\(x
\)
}
\)
\cdot \cos
\(x
\)
\cdot x}{
\sin
\(x
\)
^{2}}\,dx}
\cr}$$
Time for test: 60 ms, plus GC time: 10 ms