D.2.4.19 substitute
...................
Procedure from library poly.lib (see poly_lib).

Usage:
- case 1: typeof(#[1])==poly:

substitute (I,v,f[,v1,f1,v2,f2,...]); I object of basering which
can be mapped, v,v1,v2,.. ring variables, f,f1,f2,... poly

 - case 2: typeof(#[1])==ideal:
substitute1 (I,v,f); I object of basering which can be mapped,
v ideal of ring variables, f ideal

Return:
object of same type as I,

 - case 1: ring variable v,v1,v2,... substituted by polynomials
f,f1,f2,..., in this order

 - case 2: ring variables in v substituted by polynomials in f:
v[i] is substituted by f[i], i=1,...,i=min(size(v),ncols(f))

Note:
this procedure extends the built-in command subst which substitutes
ring variables only by monomials

Example:
LIB "poly.lib";
ring r = 0,(b,c,t),dp;
ideal I = -bc+4b2c2t,bc2t-5b2c;
substitute(I,c,b+c,t,0,b,b-1);
==> _[1]=-b2-bc+2b+c-1
==> _[2]=-5b3-5b2c+15b2+10bc-15b-5c+5
ideal v = c,t,b;
ideal f = b+c,0,b-1;
substitute(I,v,f);
==> _[1]=-b2-bc+2b+c-1
==> _[2]=-5b3-5b2c+15b2+10bc-15b-5c+5

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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