/* A demonstration of the qualitative analysis functions
described in file SHARE;QUAL USAGE.

Consider the following expression: */
TEMP: TANH(COS(X/3)**2-COS(X/3-%PI/2)**2) + SIN(X/5)*ERF(TAN(X)) + ATAN(Y);
/* To do a qualitative analysis of this expression, we write: */
QUAL(TEMP);
/* We may use the ASSUME function to establish non-default bounds
on indeterminates.  For example: */
ASSUME(P>0, Q>=-1/4, Q<=1/4, B<=BMAX)$
/* We may also individually invoke the various property analysis
functions invoked by QUAL.  For example: */
TEMP: -ASIN(Q+1/2) - Q**2 + P*Q - 4*Q
      + LOG(P) - P**2 + 3*P + SQRT(P) - B**2 + B - 18;
CURVATURE(TEMP);
TEMP: EXPAND((X-1)**4 + (X-1)**2 + (Y-2)**2 + 5);
STATIONARYPOINTS(TEMP);
TEMP: EXPAND((LOG(X-3)-5)*(X-Y+8)/TAN(X-Y+2));
ZEROSANDSINGULARITIES(TEMP);
/* QUAL also automatically reveals successive levels of the
struecture of lengthier expressions.  For example, the second
derivative of TEMP with respect to X is about 2 pages long, but: */
QUAL(DIFF(TEMP,X,2))$