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/* First load the necessary file: */
/* LOAD('DECLIN); */
/* for DOE-MACSYMA */
load("declin.mc");
/* 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):=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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