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Macaulay2Doc :: lift

lift -- lift to another ring

Synopsis

Description

(Disambiguation: for division of matrices, which is thought of as lifting one homomorphism over another, see instead Matrix // Matrix. For lifting a map between modules to a map between their free resolutions, see extend.)

The ring R should be one of the base rings associated with the ring of f. An error is raised if f cannot be lifted to R.

The first example is lifting from the fraction field of R to R.

lift(4/2,ZZ)
R = ZZ[x];
f = ((x+1)^3*(x+4))/((x+4)*(x+1))
lift(f,R)

Another use of lift is to take polynomials in a quotient ring and lift them to the polynomial ring.

A = QQ[a..d];
B = A/(a^2-b,c^2-d-a-3);
f = c^5
lift(f,A)
jf = jacobian ideal f
lift(jf,A)

Elements may be lifted to any base ring, if such a lift exists.

use B;
g = (a^2+2*a-3)-(a+1)^2
lift(g,A)
lift(g,QQ)
lift(lift(g,QQ),ZZ)

The functions lift and substitute are useful to move numbers from one kind of coefficient ring to another.

lift(3.0,ZZ)
lift(3.0,QQ)

A continued fraction method is used to lift a real number to a rational number, whereas promote uses the internal binary representation.

lift(123/2341.,QQ)
promote(123/2341.,QQ)
factor oo

For numbers and ring elements, an alternate syntax with ^ is available, analogous to the use of _ for promote.

.0001^QQ
.0001_QQ

See also

Ways to use lift :