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/* First load the necessary file: */
load("declin");
/* For example, define the linearity properties of F.
F is to be linear in its first, third and fifth arguments.
The predicate to be used for distinguishing the coefficients
of these arguments will be called FVARP. */
declare_linear_operator(f,[1,3,5],fvarp);
fvarp(exp):=member(exp,[a,b,c]);
/* An example of an expression with the necessary property is: */
ff(x,e,y,f,z,g,x):=(k1*x+k2*y+k3*z)/(e+f)^g;
/* In this expression, FF is linear in [X, Y, Z], taken
as the components of a vector. Note that this is distinguished
from being linear in X, Y, or Z taken one at a time.
Here is an expression that is equivalent to 0. */
exp1:(f(a,x,b,y,c,z)*2-f(2*a,x,2*b,y,2*c,z))*h(q)/(a+b)*(f+h);
/* The function LINSIMP looks at sums contained in its
first argument and combines the F expressions whenever possible. */
linsimp(exp1,f);
/* The function LINSIMP extracts coefficients from the arguments
of F whenever it can. */
exp2:f(6*a,x,2*b,y,4*c,z);
linsimp(exp2,f);
/* To remove the LINEAR_OPERATOR property from F, use REM. */
rem(f,linear_operator);
/* Now verify that it is gone: */
errcatch(linsimp(exp,f));
/* LINSIMP can simplify with respect to several operators.
To illustrate this, we first make the
necessary declarations. */
declare_linear_operator(f,[1,2,3],fvarp);
declare_linear_operator(h,[1,2],hvarp);
hvarp(exp):=member(exp,[d,e,f])$
exp3:(f(2*a,-a*x,b/3,w)-f(a,b*x,c,w)
+h(w*e,f*(a+b),3)+2*h(-w*e,f*a,3))/a;
linsimp(exp3,f,h);
/* Notice that in the above example, LINSIMP was NOT confused
by the presence of F as both a variable and an undefined
operator.
LINSIMP will not combine forms that differ in the
arguments that are not specified in the linearity
declaration: */
exp4:f(a,b,c,d,e)-f(a,b,c,d,h);
linsimp(exp4,f);
/* But it will make combinations whenever possible, even
when the operator appears with varying numbers of
arguments: */
exp5:f(a,b,c,d,e)-f(a,b,2*c,d,e)+2*f(b,a,c)-h*f(c,2*b,a);
linsimp(exp5,f);
/* LINSIMP also recognizes the zero case: */
exp6:f(0,0,0,a,b,c);
linsimp(exp6,f);
/* Here is an example with SUM: */
declare_linear_operator(nounify(sum),[1],'sumvarp);
sumvarp(exp):=not(freeof('n,exp));
a*'sum(f(n)*x^n,n,0,inf)+b*x*'sum(g(n)*x^(n-1),n,0,inf);
factor(linsimp(%,nounify('sum)));
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