subst, psubst

subst(rat[,varn,ratn]*)

psubst(rat[,var,rat]*)

:: Substitute ratn for varn in expression rat. (n=1,2,.... Substitution will be done successively from left to right if arguments are repeated.)

return

rational expression

rat,ratn

rational expression

varn

indeterminate

• Substitutes rational expressions for specified kernels in a rational expression.
• subst(rat,var1,rat1,var2,rat2,...) has the same effect as subst(subst(rat,var1,rat1),var2,rat2,...).
• Note that repeated substitution is done from left to right successively. You may get different result by changing the specification order.
• Ordinary subst() performs substitution at all levels of a scalar algebraic expression creeping into arguments of function forms recursively. Function psubst() regards such a function form as an independent indeterminate, and does not attempt to apply substitution to its arguments. (The name comes after Partial SUBSTitution.)
• Since Asir does not reduce common divisors of a rational expression automatically, substitution of a rational expression to an expression may cause unexpected increase of computation time. Thus, it is often necessary to write a special function to meet the individual problem so that the denominator and the numerator do not become too large.
• The same applies to substitution by rational numbers.

[0] subst(x^3-3*y*x^2+3*y^2*x-y^3,y,2);
x^3-6*x^2+12*x-8
[1] subst(@@,x,-1);
-27
[2] subst(x^3-3*y*x^2+3*y^2*x-y^3,y,2,x,-1);
-27
[3] subst(x*y^3,x,y,y,x);  
x^4
[4] subst(x*y^3,y,x,x,y);    
y^4
[5] subst(x*y^3,x,t,y,x,t,y);
y*x^3
[6] subst(x*sin(x),x,t);
sint(t)*t
[7] psubst(x*sin(x),x,t);
sin(x)*t

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