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7.7.8.0. lpSubstitute
Procedure from library fpaprops.lib (see fpaprops_lib).
- Usage:
- lpSubstitute(f,s1,s2[,G]); f letterplace polynomial, s1 list (ideal) of variables
to replace, s2 list (ideal) of polynomials to replace with, G optional ideal to
reduce with.
- Return:
- poly, the substituted polynomial
- Assume:
- - basering is a Letterplace ring
- G is a groebner basis,
- the current ring has a sufficient degbound (can be calculated with
lpCalcSubstDegBound())
Example:
| | LIB "fpaprops.lib";
//////// EXAMPLE A ////////
ring r = 0,(x,y,z),dp;
def R = makeLetterplaceRing(4);
setring R;
ideal G = x(1)*y(2); // optional
poly f = 3*x(1)*x(2)+y(1)*x(2);
ideal s1 = x(1), y(1);
ideal s2 = y(1)*z(2)*z(3), x(1);
// the substitution probably needs a higher degbound
int minDegBound = lpCalcSubstDegBounds(f,s1,s2);
==> // ** int division with `/`: use `div` instead in line >> maxDegBound = \
maxDegBound + maxDegBound/2;<<
setring r;
def R1 = makeLetterplaceRing(minDegBound);
setring R1;
// the last parameter is optional
lpSubstitute(imap(R,f), imap(R,s1), imap(R,s2), imap(R,G));
==> y(1)*z(2)*z(3)*y(4)*z(5)*z(6)
//////// EXAMPLE B ////////
ring r = 0,(x,y,z),dp;
==> // ** redefining r (ring r = 0,(x,y,z),dp;)
def R = makeLetterplaceRing(4);
==> // ** redefining R (def R = makeLetterplaceRing(4);)
setring R;
poly f = 3*x(1)*x(2)+y(1)*x(2);
poly g = z(1)*x(2)+y(1);
poly h = 7*x(1)*z(2)+x(1);
ideal I = f,g,h;
ideal s1 = x(1), y(1);
ideal s2 = y(1)*z(2)*z(3), x(1);
int minDegBound = lpCalcSubstDegBounds(I,s1,s2);
==> // ** redefining minDegBound (int minDegBound = lpCalcSubstDegBounds(I,s1\
,s2);)
==> // ** int division with `/`: use `div` instead in line >> maxDegBound = \
maxDegBound + maxDegBound/2;<<
==> // ** int division with `/`: use `div` instead in line >> maxDegBound = \
maxDegBound + maxDegBound/2;<<
==> // ** int division with `/`: use `div` instead in line >> maxDegBound = \
maxDegBound + maxDegBound/2;<<
setring r;
def R1 = makeLetterplaceRing(minDegBound);
==> // ** redefining R1 (def R1 = makeLetterplaceRing(minDegBound);)
setring R1;
ideal I = imap(R,I);
ideal s1 = imap(R,s1);
ideal s2 = imap(R,s2);
for (int i = 1; i <= size(I); i++) {
lpSubstitute(I[i], s1, s2);
}
==> 3*y(1)*z(2)*z(3)*y(4)*z(5)*z(6)+x(1)*y(2)*z(3)*z(4)
==> z(1)*y(2)*z(3)*z(4)+x(1)
==> 7*y(1)*z(2)*z(3)*z(4)+y(1)*z(2)*z(3)
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