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/*************** -*- Mode: MACSYMA; Package: MAXIMA -*- ******************/
/***************************************************************************
*** *****
*** Copyright (c) 1984 by William Schelter,University of Texas *****
*** All rights reserved *****
***************************************************************************/
kill(all);
done$
linechar:%t;
%t$
atvalue(f(x,y),[x = 0,y = 1],a^2);
a^2$
atvalue('diff(f(x,y),x),x = 0,y+1);
\@2+1$
printprops(all,atvalue);
done$
diff(4*f(x,y)^2-u(x,y)^2,x);
8*f(x,y)*'diff(f(x,y),x,1)-2*u(x,y)*'diff(u(x,y),x,1)$
at(%,[x = 0,y = 1]);
16*a^2-2*u(0,1)*(''(at('diff(u(x,y),x,1),[x = 0,y = 1])))$
atvalue(f(x,y),[x = 0,y = 1],a^2);
a^2$
atvalue('diff(f(x,y),x),x = 0,y+1);
\@2+1$
printprops(all,atvalue);
done$
diff(4*f(x,y)^2-u(x,y)^2,x);
8*f(x,y)*'diff(f(x,y),x,1)-2*u(x,y)*'diff(u(x,y),x,1)$
at(%,[x = 0,y = 1]);
16*a^2-2*u(0,1)*(''(at('diff(u(x,y),x,1),[x = 0,y = 1])))$
listofvars(f(x[1]+y)/g^(2+a));
[g,a,x[1],y]$
coeff(2*a*tan(x)+tan(x)+b = 5*tan(x)+3,tan(x));
2*a+1 = 5$
coeff(y+x*%e^x+1,x,0);
y+1$
a*x+b*x+5;
b*x+a*x+5$
ratcoef(%,a+b);
x$
islinear(exp,var):=block([c],c:bothcoef(rat(exp,var),var),
is(freeof(var,c) and c[1] # 0));
islinear(exp,var):=block([c],c:bothcoef(rat(exp,var),var),
is(freeof(var,c) and c[1] # 0))$
islinear((r^2-(x-r)^2)/x,x);
true$
(a+b)^4*(1+x*(2*x+(c+d)^2));
(b+a)^4*(x*(2*x+(d+c)^2)+1)$
(linenum:0,isolate(%,x));
%t2*(x*(2*x+%t1)+1)$
ratexpand(%);
2*%t2*x^2+%t1*%t2*x+%t2$
ev(%);
2*(b+a)^4*x^2+(b+a)^4*(d+c)^2*x+(b+a)^4$
(a+b)*(x+a+b)^2*%e^(x^2+a*x+b);
(b+a)*(x+b+a)^2*%e^(x^2+a*x+b)$
block([linenum:2],ev(isolate(%,x),exptisolate:true));
%t3*%t4*(x+%t3)^2*%e^(x^2+a*x)$
exp1:integrate(1/(x^3+2),x);
-log(x^2-2^(1/3)*x+2^(2/3))/(6*2^(2/3))+atan((2*x-2^(1/3))/(2^(1/3)*sqrt(3)))
/(2^(2/3)*sqrt(3))
+log(x+2^(1/3))/(3*2^(2/3))$
/* got this at one point but it differentiates ok
-2^(1/3)*log(2^(2/3)*x^2-2*x+2*2^(1/3))/12+2^(1/3)*atan((2*2^(2/3)*x-2)/(2*sqrt(3)))/(2*sqrt(3))+2^(1/3)*log(x+2^(1/3))/6; */
radcan(diff(%,x));
1/(x^3+2);
block([linenum:4],pickapart(exp1,1));
%t7+%t6+%t5$
gamma(7/2);
15*sqrt(%pi)/8$
numfactor(%);
15/8$
'diff(y,x,2)+'diff(y,z,3)*2+'diff(y,x,1)*x^2;
2*'diff(y,z,3)+'diff(y,x,2)+x^2*'diff(y,x,1)$
derivdegree(%,y,x);
2$
(%i*v+u)/(f+%i*e)+%e^(%i*alpha);
(%i*v+u)/(f+%i*e)+%e^(%i*alpha)$
realpart(%);
(e*v+f*u)/(f^2+e^2)+cos(alpha)$
rectform(sin(2*%i+x));
cosh(2)*sin(x)+%i*sinh(2)*cos(x)$
polarform(%);
sqrt(cosh(2)^2*sin(x)^2+sinh(2)^2*cos(x)^2)
*%e^(%i*atan2(sinh(2)*cos(x),cosh(2)*sin(x)))$
rectform(log(3+4*%i));
log(5)+%i*atan(4/3)$
polarform(%);
sqrt(log(5)^2+atan(4/3)^2)*%e^(%i*atan(atan(4/3)/log(5)))$
%emode:false;
false;
ev(rectform((2+3.5*%i)^0.25),numer);
0.3682587918166914*%i+1.368266274774369;
polarform(%);
1.416956998795383*%e^(0.2629125531370934*%i);
/* %emode:false is needed to keep above answer from being converted out of polar form
before being compared to result of polarform() */
%emode:true;
true;
delete(sin(x),x+sin(x)+y);
y+x$
/* SF bug 2014436 */
at(f(x),[]);
f(x)$
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